From 64fe2ee22823828c69c8f2455e6e4f968af73b43 Mon Sep 17 00:00:00 2001 From: jgarnek Date: Thu, 30 Mar 2023 15:49:22 +0000 Subject: [PATCH] naprawione regular form; superelliptyczne maja C.x_series itd --- sage/.run.term-0.term | 39711 +++------------- sage/drafty/draft.sage | 12 +- sage/superelliptic/superelliptic_class.sage | 27 +- .../superelliptic_form_class.sage | 8 +- .../superelliptic_function_class.sage | 28 +- sage/superelliptic_drw/de_rham_witt_lift.sage | 2 +- sage/superelliptic_drw/regular_form.sage | 4 +- .../superelliptic_drw_auxilliaries.sage | 14 + .../superelliptic_drw_cech.sage | 27 +- sage/tests.sage | 6 +- 10 files changed, 6605 insertions(+), 33234 deletions(-) diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term index 2e31ef2..2cbf9a1 100644 --- a/sage/.run.term-0.term +++ b/sage/.run.term-0.term @@ -1,33194 +1,4 @@ -5h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lor i, x in eumerate(lista:[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l i, x in enumerate(lista):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: for om in C.basis_ - C.basis_de_rham_degrees  - C.basis_holomorphic_differentials_degree - - - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l -....: [?7h[?12l[?25h[?25l[?7lprint(i, x)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f))[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l() -....: [?7h[?12l[?25h[?25l[?7lsage: for om in C.holomorphic_differentials_basis(): -....:  print(om.cartier()) -....:  -[?7h[?12l[?25h[?2004l(1/y^3) dx -(x/y^2) dx -(1/y^2) dx -0 dx -0 dx -(1/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for om in C.holomorphic_differentials_basis(): -....:  print(om.cartier())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).carter() - [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx) -[?7h[?12l[?25h[?2004l[?7h(1/x) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx)[?7h[?12l[?25h[?25l[?7l().cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx).cartier() -[?7h[?12l[?25h[?2004l[?7h0 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.cartier()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.cartier()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()^*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l2*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^2*C.dx).cartier() -[?7h[?12l[?25h[?2004l[?7h0 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^2*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l.*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lx*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)*C.x*C.dx).cartier() -[?7h[?12l[?25h[?2004l[?7h0 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd -]0;~~$ cd Research/2021\ De\ Rham/DEReRhamComputation/ -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add draft/supsage/drafty/superelliptic_cohomology_class.sage  -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gid add -u -bash: gid: command not found -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gid add -u[1@t -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""C"o"h"o"m"o"l"o"g"y" "o"f" "s"t"r"u"c"t"u"r"e" "s"h"e"a"f" "o"f" "s"u"p"e"r"e"l"l"i"p"t"i"c" -[master be66e7b] Cohomology of structure sheaf of superelliptic - 11 files changed, 7056 insertions(+), 82 deletions(-) - delete mode 100644 sage/as_covers/as_cover/uniformizer.sage - rewrite sage/drafty/draft3.sage (90%) - create mode 100644 sage/drafty/superelliptic_cohomology_class.sage -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push -Username for 'https://git.wmi.amu.edu.pl': jgarnek -Password for 'https://jgarnek@git.wmi.amu.edu.pl': -Enumerating objects: 37, done. -Counting objects: 2% (1/37) Counting objects: 5% (2/37) Counting objects: 8% (3/37) Counting objects: 10% (4/37) Counting objects: 13% (5/37) Counting objects: 16% (6/37) Counting objects: 18% (7/37) Counting objects: 21% (8/37) Counting objects: 24% (9/37) Counting objects: 27% (10/37) Counting objects: 29% (11/37) Counting objects: 32% (12/37) Counting objects: 35% (13/37) Counting objects: 37% (14/37) Counting objects: 40% (15/37) Counting objects: 43% (16/37) Counting objects: 45% (17/37) Counting objects: 48% (18/37) Counting objects: 51% (19/37) Counting objects: 54% (20/37) Counting objects: 56% (21/37) Counting objects: 59% (22/37) Counting objects: 62% (23/37) Counting objects: 64% (24/37) Counting objects: 67% (25/37) Counting objects: 70% (26/37) Counting objects: 72% (27/37) Counting objects: 75% (28/37) Counting objects: 78% (29/37) Counting objects: 81% (30/37) Counting objects: 83% (31/37) Counting objects: 86% (32/37) Counting objects: 89% (33/37) Counting objects: 91% (34/37) Counting objects: 94% (35/37) Counting objects: 97% (36/37) Counting objects: 100% (37/37) Counting objects: 100% (37/37), done. -Delta compression using up to 4 threads -Compressing objects: 4% (1/23) Compressing objects: 8% (2/23) Compressing objects: 13% (3/23) Compressing objects: 17% (4/23) Compressing objects: 21% (5/23) Compressing objects: 26% (6/23) Compressing objects: 30% (7/23) Compressing objects: 34% (8/23) Compressing objects: 39% (9/23) Compressing objects: 43% (10/23) Compressing objects: 47% (11/23) Compressing objects: 52% (12/23) Compressing objects: 56% (13/23) Compressing objects: 60% (14/23) Compressing objects: 65% (15/23) Compressing objects: 69% (16/23) Compressing objects: 73% (17/23) Compressing objects: 78% (18/23) Compressing objects: 82% (19/23) Compressing objects: 86% (20/23) Compressing objects: 91% (21/23) Compressing objects: 95% (22/23) Compressing objects: 100% (23/23) Compressing objects: 100% (23/23), done. -Writing objects: 4% (1/23) Writing objects: 8% (2/23) Writing objects: 13% (3/23) Writing objects: 17% (4/23) Writing objects: 26% (6/23) Writing objects: 34% (8/23) Writing objects: 39% (9/23) Writing objects: 43% (10/23) Writing objects: 47% (11/23) Writing objects: 52% (12/23) Writing objects: 56% (13/23) Writing objects: 60% (14/23) Writing objects: 65% (15/23) Writing objects: 69% (16/23) Writing objects: 73% (17/23) Writing objects: 78% (18/23) Writing objects: 82% (19/23) Writing objects: 86% (20/23) Writing objects: 91% (21/23) Writing objects: 95% (22/23) Writing objects: 100% (23/23) Writing objects: 100% (23/23), 73.16 KiB | 337.00 KiB/s, done. -Total 23 (delta 15), reused 0 (delta 0) -remote: . Processing 1 references -remote: Processed 1 references in total -To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git - d77adde..be66e7b master -> master -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[5] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_matrix[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [3], in () -----> 1 C.frobenius_matrix() - -File :163, in frobenius_matrix(self, prec) - -TypeError: unsupported operand type(s) for ** or pow(): 'superelliptic_cohomology' and 'method' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_matrix()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [5], in () -----> 1 C.frobenius_matrix(prec=Integer(50)) - -File :163, in frobenius_matrix(self, prec) - -TypeError: unsupported operand type(s) for ** or pow(): 'superelliptic_cohomology' and 'method' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2441, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__() - 2440 try: --> 2441 right = Integer(right) - 2442 except TypeError: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__() - 716 ---> 717 raise TypeError("unable to coerce %s to an integer" % type(x)) - 718 - -TypeError: unable to coerce to an integer - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [7], in () -----> 1 C.frobenius_matrix(prec=Integer(50)) - -File :163, in frobenius_matrix(self, prec) - -File :71, in __pow__(self, exp) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2443, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__() - 2441 right = Integer(right) - 2442 except TypeError: --> 2443 raise TypeError("non-integral exponents not supported") - 2444 - 2445 d = self.degree() - -TypeError: non-integral exponents not supported -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)*C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.one/[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: (C.x)^p -[?7h[?12l[?25h[?2004l[?7hx^7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(len(lista))[?7h[?12l[?25h[?25l[?7lsage: p -[?7h[?12l[?25h[?2004l[?7h7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50) -[?7h[?12l[?25h[?2004l[?7h[0 0 0 0 0 1] -[0 0 1 0 0 0] -[0 1 0 0 0 0] -[1 0 0 0 0 0] -[0 0 0 0 0 0] -[0 0 0 0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.cartier()[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: C.basis_ - C.basis_de_rham_degrees  - C.basis_holomorphic_differentials_degree - C.basis_of_cohomology  - - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_degrees - C.basis_de_rham_degrees  - - - [?7h[?12l[?25h[?25l[?7lholomorphic_differentials_degree - C.basis_de_rham_degrees  - C.basis_holomorphic_differentials_degree[?7h[?12l[?25h[?25l[?7lof_cohomology - - C.basis_holomorphic_differentials_degree - C.basis_of_cohomology [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.basis_of_cohomology() -[?7h[?12l[?25h[?2004l[?7h[1/x*y, 1/x*y^2, 1/x^2*y^2, 1/x*y^3, 1/x^2*y^3, 1/x^3*y^3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lC.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.basis_of_cohomology()[0]^p)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.basis_of_cohomology()[0]^p).coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 1, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: p -[?7h[?12l[?25h[?2004l[?7h7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l = 5[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: p = 3 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp = 3[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l(C.basis_of_cohomology()[0]^p).coordinates()[?7h[?12l[?25h[?25l[?7lsage: (C.basis_of_cohomology()[0]^p).coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd .. -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd ..sagegit pushcommit -m "Cohomology of structure sheaf of superelliptic" add -u -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -ucd ..sagegit pushsagecd ..git add -ugit add -ucd ..sagegit pushcommit -m "Cohomology of structure sheaf of superelliptic" add -ucommit -m "Cohomology of structure sheaf of superelliptic"""""""""""""""""""""""""""""""""""""""""""""""c"o"h"o"m"o"l"o"g"y" "o"f" "s"t"r" "s"h"e"a"f" "d"o"d"a"n"y";" "z"m"i"""a"c"z"y"n"a"m"y" "z"m"i"e"n"i"a"c" "w"s"p"o"l"r"z"e"d"n"e" "w" "s"u"p"e"r"e"l"l"i"p"t"i"c" "h"o"l"o" -[master f683017] cohomology of str sheaf dodany; zaczynamy zmieniac wspolrzedne w superelliptic holo - 5 files changed, 194 insertions(+), 4 deletions(-) -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push -Username for 'https://git.wmi.amu.edu.pl': jgarnek -Password for 'https://jgarnek@git.wmi.amu.edu.pl': -Enumerating objects: 16, done. -Counting objects: 6% (1/16) Counting objects: 12% (2/16) Counting objects: 18% (3/16) Counting objects: 25% (4/16) Counting objects: 31% (5/16) Counting objects: 37% (6/16) Counting objects: 43% (7/16) Counting objects: 50% (8/16) Counting objects: 56% (9/16) Counting objects: 62% (10/16) Counting objects: 68% (11/16) Counting objects: 75% (12/16) Counting objects: 81% (13/16) Counting objects: 87% (14/16) Counting objects: 93% (15/16) Counting objects: 100% (16/16) Counting objects: 100% (16/16), done. -Delta compression using up to 8 threads -Compressing objects: 11% (1/9) Compressing objects: 22% (2/9) Compressing objects: 33% (3/9) Compressing objects: 44% (4/9) Compressing objects: 55% (5/9) Compressing objects: 66% (6/9) Compressing objects: 77% (7/9) Compressing objects: 88% (8/9) Compressing objects: 100% (9/9) Compressing objects: 100% (9/9), done. -Writing objects: 11% (1/9) Writing objects: 22% (2/9) Writing objects: 33% (3/9) Writing objects: 44% (4/9) Writing objects: 55% (5/9) Writing objects: 66% (6/9) Writing objects: 77% (7/9) Writing objects: 88% (8/9) Writing objects: 100% (9/9) Writing objects: 100% (9/9), 4.68 KiB | 4.68 MiB/s, done. -Total 9 (delta 7), reused 0 (delta 0) -remote: . Processing 1 references -remote: Processed 1 references in total -To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git - be66e7b..f683017 master -> master -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage -]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd drafty/sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l=C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3b[1][?7h[?12l[?25h[?25l[?7l*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l=3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l3*b[1][?7h[?12l[?25h[?25l[?7l3*b[1][?7h[?12l[?25h[?25l[?7l3*b[1][?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l=3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = 3*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*b[1] -[?7h[?12l[?25h[?25l[?7l2*b[1] -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa = 2*bbb[1] + 2*bbb[2] + bbb[5] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = 2*bbb[1] + 2*bbb[2] + bbb[5][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates() -[?7h[?12l[?25h[?2004l[?7h(0, 2, 2, 0, 0, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [6], in () -----> 1 aaa.coordinates2() - -File :101, in coordinates2(self, basis) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l = 2*bbb[1] + 2*bbb[2] + bbb[5][?7h[?12l[?25h[?25l[?7lbbbC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2() -[?7h[?12l[?25h[?2004lbasis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [8], in () -----> 1 aaa.coordinates2() - -File :102, in coordinates2(self, basis) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7laa.coordinates2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2() -[?7h[?12l[?25h[?2004lbasis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [10], in () -----> 1 aaa.coordinates2() - -File :102, in coordinates2(self, basis) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: bbb -[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2() -[?7h[?12l[?25h[?2004l[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] -basis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [13], in () -----> 1 aaa.coordinates2() - -File :103, in coordinates2(self, basis) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1) -[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3 -basis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [14], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :22, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :103, in coordinates2(self, basis) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: bbb -[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1) -[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3 -basis [y^2, y, x*y, 1, x, x^2] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [16], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :22, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :103, in coordinates2(self, basis) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1) -[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3 -basis [y^2, y, x*y, 1, x, x^2] -[0, 2, 2, 0, 0, 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1) -[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3 -basis [y^2, y, x*y, 1, x, x^2] -[0, 2, 2, 0, 0, 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test: -[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3 -basis [y^2, y, x*y, 1, x, x^2] -False -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test: -[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3 -basis [y^2, y, x*y, 1, x, x^2] -False -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test: -[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3 -basis [y^2, y, x*y, 1, x, x^2] -True -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('tests.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7ln.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[0, 2, 2, 0, 0, 1] ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [22], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :22, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -AttributeError: 'superelliptic_form' object has no attribute 'coordinates2' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test: -True -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ldx.cartier()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxC.dx[?7h[?12l[?25h[?25l[?7l^C.dx[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)C.dx[?7h[?12l[?25h[?25l[?7l-)C.dx[?7h[?12l[?25h[?25l[?7l1)C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l=C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ffff = C.x^(p-1)*C.dx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffff = C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ffff -[?7h[?12l[?25h[?2004l[?7h(x^6) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffff.cartier() -[?7h[?12l[?25h[?2004l[?7h0 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffff.cartier()[?7h[?12l[?25h[?25l[?7lor om in C.holomorphic_differentials_basis():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li,x in enumerate(lista):[?7h[?12l[?25h[?25l[?7l inrange(0, p):[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linr[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l range(0, p):[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for i in range(0, p^2): -....: [?7h[?12l[?25h[?25l[?7lfor B in range(-10, 30):[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l....:  ffff = (C.x)^i*C.dx -....: [?7h[?12l[?25h[?25l[?7lprint(om.cartier())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(ffff.cartier()) -....: [?7h[?12l[?25h[?25l[?7lsage: for i in range(0, p^2): -....:  ffff = (C.x)^i*C.dx -....:  print(ffff.cartier()) -....:  -[?7h[?12l[?25h[?2004l0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -0 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7ln.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [29] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :22 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :9 - a = C.x**(p-_sage_const_1 )C.dx - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 0 -0 0 -0 0 -0 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lx^2 1 -0 0 -0 0 -0 0 -1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7l.prod(C.holomorphic_differentials_basis()[3])[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.cartier() -[?7h[?12l[?25h[?2004lx^2 1 -0 0 -0 0 -0 0 -[?7h1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7lsage: a.cartier() -[?7h[?12l[?25h[?2004l[?7h1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7l = basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7l = basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: a = C.dx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.dx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: a/C.x -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [36], in () -----> 1 a/C.x - -TypeError: unsupported operand type(s) for /: 'superelliptic_form' and 'superelliptic_function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(0, p^2):[?7h[?12l[?25h[?25l[?7l =d/(e*g)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1.[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, 1/x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: f*C.dx -[?7h[?12l[?25h[?2004l[?7h(1/x) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(f*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (f*C.dx).cartier() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [39], in () -----> 1 (f*C.dx).cartier() - -File :52, in cartier(self) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() - 1329 normalize(x._numer, x._denom, self.p) - 1330 if nmod_poly_degree(x._denom) != 0: --> 1331 raise ValueError("not integral") - 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) - 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: - -ValueError: not integral -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(f*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lf*C.dx[?7h[?12l[?25h[?25l[?7l = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7la/C.x[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, 1/x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(f*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: (f*C.dx).cartier() -[?7h[?12l[?25h[?2004l[?7h0 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1/x) dx -1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llist_of_m = [m for m in list_of_m if m%p != 0][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1/x) dx -1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [3], in () -----> 1 C.frobenius_matrix(prec=Integer(50)) - -File :164, in frobenius_matrix(self, prec) - -File :90, in coordinates(self, basis, basis_holo, prec) - -NameError: name 'basis_of_cohomology' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lis_of_cohomology()[?7h[?12l[?25h[?25l[?7lsage: C.basis_of_cohomology() -[?7h[?12l[?25h[?2004l[?7h[1/x*y, 1/x*y^2, 1/x^2*y^2, 1/x*y^3, 1/x^2*y^3, 1/x^3*y^3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1/x) dx -1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50) -[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0] -[0 0 1 0 0 0] -[0 1 0 0 0 0] -[0 0 0 0 0 0] -[0 0 0 0 0 0] -[1 0 0 0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0] -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [7], in () -----> 1 frobenius_kernel(C, prec=Integer(50))[Integer(0)] - -File :3, in frobenius_kernel(C, prec) - -NameError: name 'frobenius_matrix' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1/x) dx -1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0] -[?7h[?12l[?25h[?2004l[?7h1/x*y^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50) -[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier() -[?7h[?12l[?25h[?2004l[?7h(1/y^3) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [13], in () -----> 1 C.cartier_matrix() - -File :155, in cartier_matrix(self) - -File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1507, in sage.matrix.matrix0.Matrix.__setitem__() - 1505 else: - 1506 if row_list_len != len(value_list): --> 1507 raise IndexError("value does not have the right number of rows") - 1508 for value_row in value_list: - 1509 if col_list_len != len(value_row): - -IndexError: value does not have the right number of rows -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1/x) dx -1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix() -[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0] -[0 0 1 0 0 0] -[0 1 0 0 0 0] -[0 0 0 0 0 0] -[0 0 0 0 0 0] -[1 0 0 0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].cartier()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[0].cartier()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l].cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(*)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier().coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 1, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1/x) dx -1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix() -[?7h[?12l[?25h[?2004l[?7h[0 0 0 0 0 1] -[0 0 1 0 0 0] -[0 1 0 0 0 0] -[1 0 0 0 0 0] -[0 0 0 0 0 0] -[0 0 0 0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differntials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier().coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 1, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differntials_basis()[?7h[?12l[?25h[?25l[?7l[0].cartier().coordinats()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].cartier().cordinates()[?7h[?12l[?25h[?25l[?7l1].cartier().cordinates()[?7h[?12l[?25h[?25l[?7lsage: bbb[1].cartier().coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 1, 0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[1].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l].cartier().cordinates()[?7h[?12l[?25h[?25l[?7l5].cartier().cordinates()[?7h[?12l[?25h[?25l[?7lsage: bbb[5].cartier().coordinates() -[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [24], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :10, in  - -File :137, in pth_root(self) - -AttributeError: 'superelliptic_form' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l2*x^2*y^3 + x^5*y^2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l2*x^2*y^3 + x^5*y^2 2*x^2*y^3 + x^5*y^2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^p[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x).pth_root() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [27], in () -----> 1 (C.x).pth_root() - -File :132, in pth_root(self) - -ValueError: Function is not a p-th power. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lFalse ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [28], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :134, in pth_root(self) - -ValueError: Function is not a p-th power. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTrue ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [29], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :139, in pth_root(self) - -ValueError: Function is not a p-th power. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7l(ests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004lp-th root test: -True ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [30], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :4, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :139, in pth_root(self) - -ValueError: Function is not a p-th power. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lnel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50) -[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0] -[?7h[?12l[?25h[?2004l[?7h1/x*y^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la/C.x[?7h[?12l[?25h[?25l[?7laacoordinates2()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = 2*bbb[1] + 2*bbb[2] + bbb[5][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lnius_kernel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa = frobenius_kernel(C)[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = frobenius_kernel(C)[0][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: aaa^p -[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[5].cartier().coordinates()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differntials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: bbb = aaa^p -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = aaa^p[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: bbb.function -[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcb.function[?7h[?12l[?25h[?25l[?7lcb.function[?7h[?12l[?25h[?25l[?7lcb.function[?7h[?12l[?25h[?25l[?7l b.function[?7h[?12l[?25h[?25l[?7l-b.function[?7h[?12l[?25h[?25l[?7l b.function[?7h[?12l[?25h[?25l[?7lsage: ccc - bbb.function -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [38], in () -----> 1 ccc - bbb.function - -NameError: name 'ccc' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc - bbb.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l b.function[?7h[?12l[?25h[?25l[?7l= b.function[?7h[?12l[?25h[?25l[?7lsage: ccc = bbb.function -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc = bbb.function[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnc[?7h[?12l[?25h[?25l[?7luc[?7h[?12l[?25h[?25l[?7lmc[?7h[?12l[?25h[?25l[?7lec[?7h[?12l[?25h[?25l[?7lrc[?7h[?12l[?25h[?25l[?7lac[?7h[?12l[?25h[?25l[?7ltc[?7h[?12l[?25h[?25l[?7loc[?7h[?12l[?25h[?25l[?7lrc[?7h[?12l[?25h[?25l[?7l(c[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: numerator(ccc) -[?7h[?12l[?25h[?2004l[?7h(x^8 + 2*x^4 + 1)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmm.f[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: monomials(ccc) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [41], in () -----> 1 monomials(ccc) - -TypeError: monomials() missing 1 required positional argument: 'n' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmonomials(ccc)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcmonomials()[?7h[?12l[?25h[?25l[?7lcmonomials()[?7h[?12l[?25h[?25l[?7lcmonomials()[?7h[?12l[?25h[?25l[?7l.monomials()[?7h[?12l[?25h[?25l[?7lsage: ccc.monomials() -[?7h[?12l[?25h[?2004l[?7h[y] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc.monomials()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpc[?7h[?12l[?25h[?25l[?7lac[?7h[?12l[?25h[?25l[?7lrc[?7h[?12l[?25h[?25l[?7lec[?7h[?12l[?25h[?25l[?7lnc[?7h[?12l[?25h[?25l[?7ltc[?7h[?12l[?25h[?25l[?7l(c[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(ccc) -[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFF = FractionField(F)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Fxy -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [44], in () -----> 1 Fxy - -NameError: name 'Fxy' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = self.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y = self.fct_field -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [45], in () -----> 1 Fxy, Rxy, x, y = self.fct_field - -NameError: name 'self' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = self.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsel.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7lC.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y = C.fct_field -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Fxy -[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [48], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :30, in  - -File :13, in decomposition_g0_g8(fct) - -AttributeError: 'list' object has no attribute 'curve' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y] ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [49], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :31, in  - -File :14, in decomposition_g0_g8(fct) - -AttributeError: 'list' object has no attribute 'curve' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: ker -[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa^p[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa -[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa -[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: ker[0]^p -[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^8 + 2*x^4 + 1)/x)*y ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [54], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :31, in  - -File :15, in decomposition_g0_g8(fct) - -NameError: name 'self' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^8 + 2*x^4 + 1)/x)*y ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'function' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [55], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :31, in  - -File :19, in decomposition_g0_g8(fct) - -File :14, in __init__(self, C, g) - -File :209, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert /1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'function' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [56], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :31, in  - -File :19, in decomposition_g0_g8(fct) - -File :14, in __init__(self, C, g) - -File :209, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert /1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa -[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: aaa[0].function -[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lna[0].function[?7h[?12l[?25h[?25l[?7lua[0].function[?7h[?12l[?25h[?25l[?7lma[0].function[?7h[?12l[?25h[?25l[?7lea[0].function[?7h[?12l[?25h[?25l[?7lra[0].function[?7h[?12l[?25h[?25l[?7la[0].function[?7h[?12l[?25h[?25l[?7lta[0].function[?7h[?12l[?25h[?25l[?7loa[0].function[?7h[?12l[?25h[?25l[?7lra[0].function[?7h[?12l[?25h[?25l[?7l(a[0].function[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: numerator(aaa[0].function) -[?7h[?12l[?25h[?2004l[?7h(x^8 + 2*x^4 + 1)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpa[0][?7h[?12l[?25h[?25l[?7la[0][?7h[?12l[?25h[?25l[?7lra[0][?7h[?12l[?25h[?25l[?7lea[0][?7h[?12l[?25h[?25l[?7lna[0][?7h[?12l[?25h[?25l[?7lta[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: parent(aaa[0]) -[?7h[?12l[?25h[?2004l[?7h -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(aaa[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lsage: parent(aaa[0].function) -[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0].function[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lna[0][?7h[?12l[?25h[?25l[?7lua[0][?7h[?12l[?25h[?25l[?7lma[0][?7h[?12l[?25h[?25l[?7lea[0][?7h[?12l[?25h[?25l[?7lra[0][?7h[?12l[?25h[?25l[?7la[0][?7h[?12l[?25h[?25l[?7lta[0][?7h[?12l[?25h[?25l[?7loa[0][?7h[?12l[?25h[?25l[?7lra[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF(a[0][?7h[?12l[?25h[?25l[?7lx(a[0][?7h[?12l[?25h[?25l[?7ly(a[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Fxy(aaa[0]) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'superelliptic_function' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [62], in () -----> 1 Fxy(aaa[Integer(0)]) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert ((x^8 + 2*x^4 + 1)/x)*y/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lsage: Fxy(aaa[0].function) -[?7h[?12l[?25h[?2004l[?7h(x^8*y - x^4*y + y)/x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0].function)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Fxy(aaa[0].function).denominator() -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0].function).denominator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'function' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [65], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :31, in  - -File :19, in decomposition_g0_g8(fct) - -File :14, in __init__(self, C, g) - -File :209, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert /1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x -x^8*y - x^4*y + y x ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'function' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [66], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :32, in  - -File :20, in decomposition_g0_g8(fct) - -File :14, in __init__(self, C, g) - -File :209, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert /1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x -x^8*y - x^4*y + y x ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1008 # now try calling the base ring's __call__ methods --> 1009 element = self.base_ring()(element) - 1010 _p = p_NSet(sa2si(element,_ring), _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) - 1184 try: --> 1185 return integer_mod.IntegerMod(self, x) - 1186 except (NotImplementedError, PariError): - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() - 200 t = modulus.element_class() ---> 201 return t(parent, value) - 202 - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 390 else: ---> 391 raise - 392 self.set_from_mpz(z.value) - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 379 try: ---> 380 z = integer_ring.Z(value) - 381 except (TypeError, ValueError): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__() - 716 ---> 717 raise TypeError("unable to coerce %s to an integer" % type(x)) - 718 - -TypeError: unable to coerce to an integer - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [67], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :32, in  - -File :20, in decomposition_g0_g8(fct) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1013, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1011 return new_MP(self,_p) - 1012 except (TypeError, ValueError): --> 1013 raise TypeError("Could not find a mapping of the passed element to this ring.") - 1014 - 1015 def _repr_(self): - -TypeError: Could not find a mapping of the passed element to this ring. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x -x^8*y - x^4*y + y x ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1008 # now try calling the base ring's __call__ methods --> 1009 element = self.base_ring()(element) - 1010 _p = p_NSet(sa2si(element,_ring), _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) - 1184 try: --> 1185 return integer_mod.IntegerMod(self, x) - 1186 except (NotImplementedError, PariError): - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() - 200 t = modulus.element_class() ---> 201 return t(parent, value) - 202 - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 390 else: ---> 391 raise - 392 self.set_from_mpz(z.value) - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 379 try: ---> 380 z = integer_ring.Z(value) - 381 except (TypeError, ValueError): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__() - 716 ---> 717 raise TypeError("unable to coerce %s to an integer" % type(x)) - 718 - -TypeError: unable to coerce to an integer - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [68], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :33, in  - -File :20, in decomposition_g0_g8(fct) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1013, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1011 return new_MP(self,_p) - 1012 except (TypeError, ValueError): --> 1013 raise TypeError("Could not find a mapping of the passed element to this ring.") - 1014 - 1015 def _repr_(self): - -TypeError: Could not find a mapping of the passed element to this ring. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x -x^8*y - x^4*y + y x Multivariate Polynomial Ring in x, y over Finite Field of size 3 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1008 # now try calling the base ring's __call__ methods --> 1009 element = self.base_ring()(element) - 1010 _p = p_NSet(sa2si(element,_ring), _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) - 1184 try: --> 1185 return integer_mod.IntegerMod(self, x) - 1186 except (NotImplementedError, PariError): - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() - 200 t = modulus.element_class() ---> 201 return t(parent, value) - 202 - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 390 else: ---> 391 raise - 392 self.set_from_mpz(z.value) - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 379 try: ---> 380 z = integer_ring.Z(value) - 381 except (TypeError, ValueError): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__() - 716 ---> 717 raise TypeError("unable to coerce %s to an integer" % type(x)) - 718 - -TypeError: unable to coerce to an integer - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [69], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :33, in  - -File :20, in decomposition_g0_g8(fct) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1013, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1011 return new_MP(self,_p) - 1012 except (TypeError, ValueError): --> 1013 raise TypeError("Could not find a mapping of the passed element to this ring.") - 1014 - 1015 def _repr_(self): - -TypeError: Could not find a mapping of the passed element to this ring. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^8 + 2*x^4 + 1)*y, 0) -((x^8 + 2*x^4)*y, y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(((x^8 + 2*x^4 + 1)/x)*y, 0) -((x^4 + 2)*y, 1/x^4*y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x).coordinates() -[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa -[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[0].function[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].function[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linates()[?7h[?12l[?25h[?25l[?7lsage: aaa[0].coordinates() -[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[0]^p[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: ker -[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[0]^p[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(aaa[0].function)[?7h[?12l[?25h[?25l[?7lsage: p -[?7h[?12l[?25h[?2004l[?7h3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[0]^p[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^p[?7h[?12l[?25h[?25l[?7lsage: ker[0]^p -[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[0]^p[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(ker[0]^p)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (ker[0]^p).coordinates() -[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50) -[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0] -[0 0 1 0 0 0] -[0 1 0 0 0 0] -[0 0 0 0 0 0] -[0 0 0 0 0 0] -[1 0 0 0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = frbenus_kernel(C)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCbasis_of[?7h[?12l[?25h[?25l[?7l.basis_of[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_cohomology[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa = C.basis_of_cohomology() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = C.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[0].coordinates()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa[0] -[?7h[?12l[?25h[?2004l[?7h1/x*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0][?7h[?12l[?25h[?25l[?7l[].coordinates()[?7h[?12l[?25h[?25l[?7lfuncton[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa[0].frobenius() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [84], in () -----> 1 aaa[Integer(0)].frobenius() - -AttributeError: 'superelliptic_function' object has no attribute 'frobenius' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa[0]^p.coordinates() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [85], in () -----> 1 aaa[Integer(0)]**p.coordinates() - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'coordinates' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0]^p.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a[0]^p.cordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().cordinates()[?7h[?12l[?25h[?25l[?7lsage: (aaa[0]^p).coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0]^p.coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa[4] -[?7h[?12l[?25h[?2004l[?7h1/x^2*y^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa[4]^p.coordinates() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [88], in () -----> 1 aaa[Integer(4)]**p.coordinates() - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'coordinates' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4]^p.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a[4]^p).cordinates()[?7h[?12l[?25h[?25l[?7lsage: (aaa[4]^p).coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(aaa[4]^p).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]^p).cordinates()[?7h[?12l[?25h[?25l[?7l5]^p).cordinates()[?7h[?12l[?25h[?25l[?7lsage: (aaa[5]^p).coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4]^p.coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa[4] -[?7h[?12l[?25h[?2004l[?7h1/x^2*y^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l5][?7h[?12l[?25h[?25l[?7lsage: aaa[5] -[?7h[?12l[?25h[?2004l[?7h1/x^3*y^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50) -[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 1, 0, 0), -(0, 0, 0, 0, 1, 0) -] -(((x^8 + 2*x^4 + 1)/x)*y, 0) -((x^4 + 2)*y, 1/x^4*y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).kernel().basis() -[?7h[?12l[?25h[?2004l[?7h[ -(0, 0, 0, 1, 0, 0), -(0, 0, 0, 0, 1, 0) -] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).kernel().basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.frobenius_matrix(prec=50).kernel().basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrkernel().basis()[?7h[?12l[?25h[?25l[?7lkernel().basis()[?7h[?12l[?25h[?25l[?7ltkernel().basis()[?7h[?12l[?25h[?25l[?7lrkernel().basis()[?7h[?12l[?25h[?25l[?7lakernel().basis()[?7h[?12l[?25h[?25l[?7lnkernel().basis()[?7h[?12l[?25h[?25l[?7lskernel().basis()[?7h[?12l[?25h[?25l[?7lpkernel().basis()[?7h[?12l[?25h[?25l[?7lokernel().basis()[?7h[?12l[?25h[?25l[?7lskernel().basis()[?7h[?12l[?25h[?25l[?7lekernel().basis()[?7h[?12l[?25h[?25l[?7l(kernel().basis()[?7h[?12l[?25h[?25l[?7l()kernel().basis()[?7h[?12l[?25h[?25l[?7l().kernel().basis()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis() -[?7h[?12l[?25h[?2004l[?7h[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldimension_of_RHS = p*gY + (len(list_of_m) - 1)*(p-1) + sum(sum(i*alpha(i, m, p) for i in range(1, p)) for m in list_of_m)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -((x^4 + 2)*y, 1/x^4*y) -(x*y, ((2*x^4 + 1)/x^7)*y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -((x^4 + 2)*y, 1/x^4*y) -(x*y, ((2*x^4 + 1)/x^7)*y) -((x/(x^4 + 1))*y^3, (1/(x^7 + x^3))*y^3) -(0, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -((x^4 + 2)*y, 1/x^4*y) -(x*y, ((2*x^4 + 1)/x^7)*y) -! ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [99], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :52, in  - -File :47, in decomposition_omega0_omega8(omega, prec) - -File :38, in __add__(self, other) - -AttributeError: 'superelliptic_form' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -((x^4 + 2)*y, 1/x^4*y) -(x*y, ((2*x^4 + 1)/x^7)*y) -! -((x^2/y) dx, (1/(x^2*y)) dx) -(0 dx, 0 dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[0]^p[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: ker -[?7h[?12l[?25h[?2004l[?7h[1/x^2*y^3, 1/x^3*y^3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -((x^4 + 2)*y, 1/x^4*y) -(x*y, ((2*x^4 + 1)/x^7)*y) -! -1 -1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -((x^4 + 2)*y, 1/x^4*y) -(x*y, ((2*x^4 + 1)/x^7)*y) -! -1 -1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basi()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [104], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :8, in  - -NameError: name 'basis_W2Omega' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[<__main__.superelliptic_drw_form object at 0x7f0b7df25930>, <__main__.superelliptic_drw_form object at 0x7f0b7df26050>, <__main__.superelliptic_drw_form object at 0x7f0b7df256f0>, <__main__.superelliptic_drw_form object at 0x7f0b7df25330>, <__main__.superelliptic_drw_form object at 0x7f0b7df265f0>, <__main__.superelliptic_drw_form object at 0x7f0b7df263e0>] -! -1 -1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[[0] d[x] + V((x^2/y^3) dx) + dV([0]), [0] d[x] + V((x/(x^4*y^2 + y^2)) dx) + dV([0]), [0] d[x] + V((x^4/(x^4*y^2 + y^2)) dx) + dV([0]), [0] d[x] + V((1/(x^8*y - x^4*y + y)) dx) + dV([0]), [0] d[x] + V((x^3/(x^8*y - x^4*y + y)) dx) + dV([0]), [0] d[x] + V((x^6/(x^8*y - x^4*y + y)) dx) + dV([0])] -! -1 -1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: V = GF(p)^3 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV = GF(p)^3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: V.subspace([1, 2, 2], [1, 1, 1]) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized) - 6393 try: --> 6394 basis = [ambient(x) for x in basis] - 6395 except TypeError: - 6396 # That failed, try the ambient vector space instead - -File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in (.0) - 6393 try: --> 6394 basis = [ambient(x) for x in basis] - 6395 except TypeError: - 6396 # That failed, try the ambient vector space instead - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds) - 6280 pass --> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds) - -File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check) - 2095 if isinstance(self, FreeModule_ambient): --> 2096 return self.element_class(self, x, coerce, copy) - 2097 try: - -File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__() - 187 if x != 0: ---> 188 raise TypeError("can't initialize vector from nonzero non-list") - 189 else: - -TypeError: can't initialize vector from nonzero non-list - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized) - 6399 try: --> 6400 basis = [V(x) for x in basis] - 6401 except TypeError: - -File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in (.0) - 6399 try: --> 6400 basis = [V(x) for x in basis] - 6401 except TypeError: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds) - 6280 pass --> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds) - -File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check) - 2095 if isinstance(self, FreeModule_ambient): --> 2096 return self.element_class(self, x, coerce, copy) - 2097 try: - -File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__() - 187 if x != 0: ---> 188 raise TypeError("can't initialize vector from nonzero non-list") - 189 else: - -TypeError: can't initialize vector from nonzero non-list - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [108], in () -----> 1 V.subspace([Integer(1), Integer(2), Integer(2)], [Integer(1), Integer(1), Integer(1)]) - -File /ext/sage/9.7/src/sage/modules/free_module.py:4598, in FreeModule_generic_field.subspace(self, gens, check, already_echelonized) - 4555 def subspace(self, gens, check=True, already_echelonized=False): - 4556 """ - 4557  Return the subspace of ``self`` spanned by the elements of gens. - 4558 - (...) - 4596  ArithmeticError: argument gens (= [[1, 1, 0]]) does not generate a submodule of self - 4597  """ --> 4598 return self.submodule(gens, check=check, already_echelonized=already_echelonized) - -File /ext/sage/9.7/src/sage/modules/free_module.py:1744, in Module_free_ambient.submodule(self, gens, check, already_echelonized) - 1742 if isinstance(gens, Module_free_ambient): - 1743 gens = gens.gens() --> 1744 V = self.span(gens, check=check, already_echelonized=already_echelonized) - 1745 if check: - 1746 if not V.is_submodule(self): - -File /ext/sage/9.7/src/sage/modules/free_module.py:1659, in Module_free_ambient.span(self, gens, base_ring, check, already_echelonized) - 1657 gens = gens.gens() - 1658 if base_ring is None or base_ring is self.base_ring(): --> 1659 return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized) - 1661 # The base ring has changed - 1662 try: - -File /ext/sage/9.7/src/sage/modules/free_module.py:7690, in FreeModule_submodule_field.__init__(self, ambient, gens, check, already_echelonized) - 7688 if is_FreeModule(gens): - 7689 gens = gens.gens() --> 7690 FreeModule_submodule_with_basis_field.__init__(self, ambient, basis=gens, check=check, - 7691  echelonize=not already_echelonized, already_echelonized=already_echelonized) - -File /ext/sage/9.7/src/sage/modules/free_module.py:7491, in FreeModule_submodule_with_basis_field.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized) - 7476 def __init__(self, ambient, basis, check=True, - 7477 echelonize=False, echelonized_basis=None, already_echelonized=False): - 7478 """ - 7479  Create a vector space with given basis. - 7480 - (...) - 7489  [4 5 6] - 7490  """ --> 7491 FreeModule_submodule_with_basis_pid.__init__( - 7492  self, ambient, basis=basis, check=check, echelonize=echelonize, - 7493  echelonized_basis=echelonized_basis, already_echelonized=already_echelonized) - -File /ext/sage/9.7/src/sage/modules/free_module.py:6402, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized) - 6400 basis = [V(x) for x in basis] - 6401 except TypeError: --> 6402 raise TypeError("each element of basis must be in " - 6403 "the ambient vector space") - 6405 if echelonize and not already_echelonized: - 6406 basis = self._echelonized_basis(ambient, basis) - -TypeError: each element of basis must be in the ambient vector space -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.subspace([1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lv[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7le[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lc[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lt[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lo[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lr[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7l([1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l([]), [1, 1, 1])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lv[1, 1, 1])[?7h[?12l[?25h[?25l[?7le[1, 1, 1])[?7h[?12l[?25h[?25l[?7lc[1, 1, 1])[?7h[?12l[?25h[?25l[?7lt[1, 1, 1])[?7h[?12l[?25h[?25l[?7lo[1, 1, 1])[?7h[?12l[?25h[?25l[?7lr[1, 1, 1])[?7h[?12l[?25h[?25l[?7l([1, 1, 1])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: V.subspace(vector([1, 2, 2]), vector([1, 1, 1])) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized) - 6393 try: --> 6394 basis = [ambient(x) for x in basis] - 6395 except TypeError: - 6396 # That failed, try the ambient vector space instead - -File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in (.0) - 6393 try: --> 6394 basis = [ambient(x) for x in basis] - 6395 except TypeError: - 6396 # That failed, try the ambient vector space instead - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds) - 6280 pass --> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds) - -File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check) - 2095 if isinstance(self, FreeModule_ambient): --> 2096 return self.element_class(self, x, coerce, copy) - 2097 try: - -File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__() - 187 if x != 0: ---> 188 raise TypeError("can't initialize vector from nonzero non-list") - 189 else: - -TypeError: can't initialize vector from nonzero non-list - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized) - 6399 try: --> 6400 basis = [V(x) for x in basis] - 6401 except TypeError: - -File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in (.0) - 6399 try: --> 6400 basis = [V(x) for x in basis] - 6401 except TypeError: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds) - 6280 pass --> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds) - -File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check) - 2095 if isinstance(self, FreeModule_ambient): --> 2096 return self.element_class(self, x, coerce, copy) - 2097 try: - -File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__() - 187 if x != 0: ---> 188 raise TypeError("can't initialize vector from nonzero non-list") - 189 else: - -TypeError: can't initialize vector from nonzero non-list - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [109], in () -----> 1 V.subspace(vector([Integer(1), Integer(2), Integer(2)]), vector([Integer(1), Integer(1), Integer(1)])) - -File /ext/sage/9.7/src/sage/modules/free_module.py:4598, in FreeModule_generic_field.subspace(self, gens, check, already_echelonized) - 4555 def subspace(self, gens, check=True, already_echelonized=False): - 4556 """ - 4557  Return the subspace of ``self`` spanned by the elements of gens. - 4558 - (...) - 4596  ArithmeticError: argument gens (= [[1, 1, 0]]) does not generate a submodule of self - 4597  """ --> 4598 return self.submodule(gens, check=check, already_echelonized=already_echelonized) - -File /ext/sage/9.7/src/sage/modules/free_module.py:1744, in Module_free_ambient.submodule(self, gens, check, already_echelonized) - 1742 if isinstance(gens, Module_free_ambient): - 1743 gens = gens.gens() --> 1744 V = self.span(gens, check=check, already_echelonized=already_echelonized) - 1745 if check: - 1746 if not V.is_submodule(self): - -File /ext/sage/9.7/src/sage/modules/free_module.py:1659, in Module_free_ambient.span(self, gens, base_ring, check, already_echelonized) - 1657 gens = gens.gens() - 1658 if base_ring is None or base_ring is self.base_ring(): --> 1659 return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized) - 1661 # The base ring has changed - 1662 try: - -File /ext/sage/9.7/src/sage/modules/free_module.py:7690, in FreeModule_submodule_field.__init__(self, ambient, gens, check, already_echelonized) - 7688 if is_FreeModule(gens): - 7689 gens = gens.gens() --> 7690 FreeModule_submodule_with_basis_field.__init__(self, ambient, basis=gens, check=check, - 7691  echelonize=not already_echelonized, already_echelonized=already_echelonized) - -File /ext/sage/9.7/src/sage/modules/free_module.py:7491, in FreeModule_submodule_with_basis_field.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized) - 7476 def __init__(self, ambient, basis, check=True, - 7477 echelonize=False, echelonized_basis=None, already_echelonized=False): - 7478 """ - 7479  Create a vector space with given basis. - 7480 - (...) - 7489  [4 5 6] - 7490  """ --> 7491 FreeModule_submodule_with_basis_pid.__init__( - 7492  self, ambient, basis=basis, check=check, echelonize=echelonize, - 7493  echelonized_basis=echelonized_basis, already_echelonized=already_echelonized) - -File /ext/sage/9.7/src/sage/modules/free_module.py:6402, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized) - 6400 basis = [V(x) for x in basis] - 6401 except TypeError: --> 6402 raise TypeError("each element of basis must be in " - 6403 "the ambient vector space") - 6405 if echelonize and not already_echelonized: - 6406 basis = self._echelonized_basis(ambient, basis) - -TypeError: each element of basis must be in the ambient vector space -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.subspace(vector([1, 2, 2]), vector([1, 1, 1]))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis() -[?7h[?12l[?25h[?2004l[?7h[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis()[0] -[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 1, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).cordinates[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).cordinates[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() == vector(6*[0]) -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates() == vector(6*[0])[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -[?7h[0, 0, 0, 0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates()[?7h[?12l[?25h[?25l[?7l() == vector(6*[0])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() = 6*[0] -[?7h[?12l[?25h[?2004l Input In [114] - (frobenius_kernel(C, prec=Integer(50))[Integer(0)]**p).coordinates() = Integer(6)*[Integer(0)] - ^ -SyntaxError: cannot assign to function call here. Maybe you meant '==' instead of '='? - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates() = 6*[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= 6*[0][?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() == 6*[0] -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates() == 6*[0][?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() == 6*[0] -[?7h[?12l[?25h[?2004l[ -(0, 0, 0, 0, 1, 0), -(0, 0, 0, 0, 0, 1) -] -[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [117], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :13, in  - -File :36, in __init__(self, C, list_of_fcts, prec) - -TypeError: superelliptic_function.expansion_at_infty() got an unexpected keyword argument 'i' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l(ts.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test: -True -p-th root test: -True ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [1], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :5, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :139, in pth_root(self) - -ValueError: Function is not a p-th power. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004las_cover_test: -True -True -group_action_matrices_test: -True -True -True -dual_element_test: -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -ith_component_test: -True -ith ramification group test: -^Csage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z' - """ -sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z' - """ -^C -KeyboardInterrupt - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/infinity.py:1201, in InfinityRing_class._element_constructor_(self, x) - 1199 try: - 1200 # For example, RealField() implements this --> 1201 if x.is_positive_infinity(): - 1202 return self.gen(0) - -AttributeError: 'int' object has no attribute 'is_positive_infinity' - -During handling of the above exception, another exception occurred: - -KeyboardInterrupt Traceback (most recent call last) -Input In [3], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :13, in  - -File :44, in __init__(self, C, list_of_fcts, prec) - -File :134, in artin_schreier_transform(power_series, prec) - -File :17, in new_reverse(power_series, prec) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1356, in sage.structure.element.Element.__sub__() - 1354 cdef int cl = classify_elements(left, right) - 1355 if HAVE_SAME_PARENT(cl): --> 1356 return (left)._sub_(right) - 1357 if BOTH_ARE_ELEMENT(cl): - 1358 return coercion_model.bin_op(left, right, sub) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:792, in sage.rings.laurent_series_ring_element.LaurentSeries._sub_() - 790 # 1. Special case when one or the other is 0. - 791 if not right: ---> 792 return self.add_bigoh(right.prec()) - 793 if not self: - 794 return -right.add_bigoh(self.prec()) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1334, in sage.rings.laurent_series_ring_element.LaurentSeries.prec() - 1332 8 - 1333 """ --> 1334 return self.__u.prec() + self.__n - 1335 - 1336 def precision_absolute(self): - -File /ext/sage/9.7/src/sage/structure/element.pyx:1241, in sage.structure.element.Element.__add__() - 1239 integer_check_long_py(right, &value, &err) - 1240 if not err: --> 1241 return (left)._add_long(value) - 1242 integer_check_long_py(left, &value, &err) - 1243 if not err: - -File /ext/sage/9.7/src/sage/structure/element.pyx:2388, in sage.structure.element.ModuleElement._add_long() - 2386 if n == 0: - 2387 return self --> 2388 return coercion_model.bin_op(self, n, add) - 2389 - 2390 cpdef _sub_(self, other): - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op() - 1198 # Now coerce to a common parent and do the operation there - 1199 try: --> 1200 xy = self.canonical_coercion(x, y) - 1201 except TypeError: - 1202 self._record_exception() - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion() - 1313 x_elt = x - 1314 if y_map is not None: --> 1315 y_elt = (y_map)._call_(y) - 1316 else: - 1317 y_elt = y - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/infinity.py:1201, in InfinityRing_class._element_constructor_(self, x) - 1198 else: - 1199 try: - 1200 # For example, RealField() implements this --> 1201 if x.is_positive_infinity(): - 1202 return self.gen(0) - 1203 if x.is_negative_infinity(): - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[-1].f.function[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations: -z0^5 - z0 = x^3 + x -z1^5 - z1 = x^2 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS. - AS.at_most_poles AS.cohomology_of_structure_sheaf_basis AS.exponent_of_different AS.genus   - AS.at_most_poles_forms AS.de_rham_basis AS.exponent_of_different_prim AS.group   - AS.base_ring AS.dx AS.fct_field AS.height > - AS.characteristic AS.dx_series AS.functions AS.holomorphic_differentials_basis   - [?7h[?12l[?25h[?25l[?7lat_most_poles - AS.at_most_poles  - - - - [?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis - AS.at_most_poles  AS.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7lexpnent_of_different - AS.cohomology_of_structure_sheaf_basis AS.exponent_of_different [?7h[?12l[?25h[?25l[?7lgenus - AS.exponent_of_different  AS.genus [?7h[?12l[?25h[?25l[?7lith_ramification_gp - cohomology_of_structure_sheaf_basisexpnent_of_different genus ith_ramification_gp - derhambasi exponent_of_different_primgroup jumps -<dx fct_fieldheight lift_o_de_rham - dx_seris functionholomorphic_differentials_basismagical_element [?7h[?12l[?25h[?25l[?7lgenus - AS.genus  AS.ith_ramification_gp [?7h[?12l[?25h[?25l[?7lrop - AS.genus  - AS.group [?7h[?12l[?25h[?25l[?7lheight - - AS.group  - AS.height [?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis - - - AS.height  - AS.holomorphic_differentials_basis [?7h[?12l[?25h[?25l[?7l() - - - - -[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, - (z1) * dx, - (z1^2) * dx, - (z1^3) * dx, - (z1^4) * dx, - (z0) * dx, - (z0*z1) * dx, - (z0*z1^2) * dx, - (z0*z1^3 - x*z1^2) * dx, - (z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx, - (z0^2) * dx, - (z0^2*z1) * dx, - (z0^2*z1^2 - x^2) * dx, - (z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1) * dx, - (z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2) * dx, - (z0^3 - x*z1^2) * dx, - (z0^3*z1 - 2*x*z1^3 + x*z0^2) * dx, - (z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0) * dx, - (x) * dx, - (x*z1) * dx, - (x*z0) * dx, - (x*z0*z1 - x^2) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb.function[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l AS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l=AS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l AS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = AS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[5].cartier().coornates()[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lsage: bbb[9[ -....: [?7h[?12l[?25h[?25l[?7l....:  -....: [?7h[?12l[?25h[?25l[?7l -  - [?7h[?12l[?25h[?25l[?7lbbb = AS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[5].cartier().coornates()[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: bbb[9] -[?7h[?12l[?25h[?2004l[?7h(z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[9].monomials() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [9], in () -----> 1 bbb[Integer(9)].monomials() - -AttributeError: 'as_form' object has no attribute 'monomials' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9].monomials()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lfmonomials()[?7h[?12l[?25h[?25l[?7lomonomials()[?7h[?12l[?25h[?25l[?7lrmonomials()[?7h[?12l[?25h[?25l[?7lmonomials()[?7h[?12l[?25h[?25l[?7l.monomials()[?7h[?12l[?25h[?25l[?7lsage: bbb[9].form.monomials() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [10], in () -----> 1 bbb[Integer(9)].form.monomials() - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement' object has no attribute 'monomials' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9].form.monomials()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lsage: (RxyzQ, Rxyz, x, y, z) = AS.fct_field -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z) = AS.fct_field[?7h[?12l[?25h[?25l[?7lbbb[9].form.monomials()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lxb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lyb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lzb[9].form.monomials()[?7h[?12l[?25h[?25l[?7l(b[9].form.monomials()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().monomials()[?7h[?12l[?25h[?25l[?7lsage: Rxyz(bbb[9].form).monomials() -[?7h[?12l[?25h[?2004l[?7h[z0*z1^4, x*z1^3, x*z0^2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(bbb[9].form).monomials()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmonomials(ccc)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(bbb[9].form).monomials()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmRxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l Rxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l=Rxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l Rxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: m = Rxyz(bbb[9].form).monomials()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = Rxyz(bbb[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: m. - m.abs m.base_extend m.change_ring m.content m.denominator m.divides  - m.add_m_mul_q m.base_ring m.coefficient m.content_ideal m.derivative m.dump  - m.additive_order m.cartesian_product m.coefficients m.degree m.dict m.dumps > - m.args m.category m.constant_coefficient m.degrees m.discriminant m.exponents  - [?7h[?12l[?25h[?25l[?7labs - m.abs  - - - - [?7h[?12l[?25h[?25l[?7lbae_extend - m.abs  m.base_extend [?7h[?12l[?25h[?25l[?7lchang_rig - m.base_extend  m.change_ring [?7h[?12l[?25h[?25l[?7lontent - m.change_ring  m.content [?7h[?12l[?25h[?25l[?7ldeominator - m.content  m.denominator [?7h[?12l[?25h[?25l[?7lcotent - m.content  m.denominator [?7h[?12l[?25h[?25l[?7lhange_ring - m.change_ring  m.content [?7h[?12l[?25h[?25l[?7lontent - m.change_ring  m.content [?7h[?12l[?25h[?25l[?7l_ideal - m.content  - m.content_ideal [?7h[?12l[?25h[?25l[?7ldegre - - m.content_ideal  - m.degree [?7h[?12l[?25h[?25l[?7l( - - - - -[?7h[?12l[?25h[?25l[?7l - std_grading= AA AbelianGroup  - x= AS AbelianGroupMorphism  - %%! AS1 AbelianGroupWithValues > - A AS2 AbelianVariety [?7h[?12l[?25h[?25l[?7lz - - - -[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: m.degree(z0) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [14], in () -----> 1 m.degree(z0) - -NameError: name 'z0' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.degree(z0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: m.degree(z[0]) -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.degree(z[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7lsage: m.degree(z[1]) -[?7h[?12l[?25h[?2004l[?7h4 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [17], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -NameError: name 'cartier' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [18], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :16, in cartier(omega) - -NameError: name 'Fxy' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [19], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :17, in cartier(omega) - -File :17, in (.0) - -TypeError: unsupported operand type(s) for -: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' and 'superelliptic_function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z[0] -[?7h[?12l[?25h[?2004l[?7hz0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltz[0][?7h[?12l[?25h[?25l[?7lyz[0][?7h[?12l[?25h[?25l[?7lpz[0][?7h[?12l[?25h[?25l[?7lez[0][?7h[?12l[?25h[?25l[?7ltype(z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: type(z[0]) -[?7h[?12l[?25h[?2004l[?7h -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [22], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :18, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lMultivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [23], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :19, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [24], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :19, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [25], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :19, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basi()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: C.height -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [26], in () -----> 1 C.height - -AttributeError: 'superelliptic' object has no attribute 'height' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l -]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [1], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :19, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [2], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :20, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [3], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :21, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[17;1R^[[18;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;2R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1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-┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [1], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :21, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.x[?7h[?12l[?25h[?25l[?7l C.x[?7h[?12l[?25h[?25l[?7l=C.x[?7h[?12l[?25h[?25l[?7l C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()x[?7h[?12l[?25h[?25l[?7l(x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: f = (C.x)*(C.z[1]) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [2], in () -----> 1 f = (C.x)*(C.z[Integer(1)]) - -NameError: name 'C' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = (C.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7lA.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7lS.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.z[1])[?7h[?12l[?25h[?25l[?7lA.z[1])[?7h[?12l[?25h[?25l[?7lS.z[1])[?7h[?12l[?25h[?25l[?7lsage: f = (AS.x)*(AS.z[1]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = (AS.x)*(AS.z[1])[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lsage: f.substitute({x:x^2, y:x, z[0]:x, z[1]:x}) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [4], in () -----> 1 f.substitute({x:x**Integer(2), y:x, z[Integer(0)]:x, z[Integer(1)]:x}) - -AttributeError: 'as_function' object has no attribute 'substitute' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.substitute({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.substitute({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l = (AS.x)*(AS.z[1])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: f = f.function -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'bad' in str(E.local_data(3))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = f.function[?7h[?12l[?25h[?25l[?7l.substitue({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: f.substitute({x:x^2, y:x, z[0]:x, z[1]:x}) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [6], in () -----> 1 f.substitute({x:x**Integer(2), y:x, z[Integer(0)]:x, z[Integer(1)]:x}) - -NameError: name 'z' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z) = C.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7lA.fct_field[?7h[?12l[?25h[?25l[?7lS.fct_field[?7h[?12l[?25h[?25l[?7lsage: (RxyzQ, Rxyz, x, y, z) = AS.fct_field -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z) = AS.fct_field[?7h[?12l[?25h[?25l[?7lf.substitute({:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: f.substitute({x:x^2, y:x, z[0]:x, z[1]:x}) -[?7h[?12l[?25h[?2004l[?7hx^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [9] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :26 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :14 - omega = AS.holomorphic_differentials_basis()[_sage_const_0 ]: - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnumerator(aaa[0].function)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: num -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(bbb[9].form).monomials()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lnu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Rxyz(num) -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(num)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l{)[?7h[?12l[?25h[?25l[?7l})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l^})[?7h[?12l[?25h[?25l[?7l2})[?7h[?12l[?25h[?25l[?7l,})[?7h[?12l[?25h[?25l[?7l })[?7h[?12l[?25h[?25l[?7ly})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7ly})[?7h[?12l[?25h[?25l[?7l,})[?7h[?12l[?25h[?25l[?7l })[?7h[?12l[?25h[?25l[?7lz})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7l})[?7h[?12l[?25h[?25l[?7l[})[?7h[?12l[?25h[?25l[?7l0})[?7h[?12l[?25h[?25l[?7l]})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l,})[?7h[?12l[?25h[?25l[?7l })[?7h[?12l[?25h[?25l[?7lz})[?7h[?12l[?25h[?25l[?7l[})[?7h[?12l[?25h[?25l[?7l1})[?7h[?12l[?25h[?25l[?7l]})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x}) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [13], in () -----> 1 Rxyz(num).substitute({x:x**Integer(2), y:y, z[Integer(0)]:x, z[Integer(1)]:x}) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[5][?7h[?12l[?25h[?25l[?7l = C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = Rxyz(1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = Rxyz(1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7larent(aaa[0].function)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(a) -[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la = Rxyz(1)[?7h[?12l[?25h[?25l[?7lRxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: a.substitute({x:x^2, y:y, z[0]:x, z[1]:x}) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [16], in () -----> 1 a.substitute({x:x**Integer(2), y:y, z[Integer(0)]:x, z[Integer(1)]:x}) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(a) -[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l({}[?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z = parent(a).gens()[2:] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2:][?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: a.substitute({x:x^2, y:y, z[0]:x, z[1]:x}) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [19], in () -----> 1 a.substitute({x:x**Integer(2), y:y, z[Integer(0)]:x, z[Integer(1)]:x}) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(E.local_data(2))[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: P. = PolynomialRing(GF(p)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP. = PolynomialRing(GF(p))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: P. = PolynomialRing(GF(p), 1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A = P(1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = P(1)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l{)[?7h[?12l[?25h[?25l[?7l})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l^})[?7h[?12l[?25h[?25l[?7l2})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.substitute({x:x^2}) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [23], in () -----> 1 A.substitute({x:x**Integer(2)}) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() - 3537 id_Delete(&to_id, _ring) - 3538 p_Delete(&_p, _ring) --> 3539 raise TypeError("keys do not match self's parent") - 3540 try: - 3541 v = parent.coerce(v) - -TypeError: keys do not match self's parent -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA.base_ring().order()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(A) -[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in X over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2})[?7h[?12l[?25h[?25l[?7lX^2})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:X^2})[?7h[?12l[?25h[?25l[?7lX:X^2})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.substitute({X:X^2}) -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7lA.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7l = P(1)[?7h[?12l[?25h[?25l[?7lP. = PolynomialRing(GF(p), 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lasubstitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2][?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, yy, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2][?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, yy, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lP = PolynomialRing(GF(p))[?7h[?12l[?25h[?25l[?7l, 1)[?7h[?12l[?25h[?25l[?7lA = P(1)[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens[0:1] -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [26], in () -----> 1 x, y = parent(a).gens[Integer(0):Integer(1)] - -TypeError: 'builtin_function_or_method' object is not subscriptable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens[0:1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens[0:2] -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [27], in () -----> 1 x, y = parent(a).gens[Integer(0):Integer(2)] - -TypeError: 'builtin_function_or_method' object is not subscriptable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens[0:2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens[0], parent(a).gens(1) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [28], in () -----> 1 x, y = parent(a).gens[Integer(0)], parent(a).gens(Integer(1)) - -TypeError: 'builtin_function_or_method' object is not subscriptable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens[0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l)[0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens()[0], parent(a).gens()[1] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens()[0], parent(a).gens()[1][?7h[?12l[?25h[?25l[?7l[0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l[:2][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7lA.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7l = P(1)[?7h[?12l[?25h[?25l[?7lP. = PolynomialRing(GF(p), 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lasubstitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: a.substitute({x:x^2, y:y, z[0]:x, z[1]:x}) -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [31], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :31, in cartier(omega) - -File :44, in __add__(self, other) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'form' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [32], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -TypeError: cannot unpack non-iterable as_form object -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(0) * dx -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [33], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :24, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 840 if check: - 841 try: ---> 842 c = base_ring(c) - 843 except TypeError: - 844 p_Delete(&_p, _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num 1 -monomial 1 -(0) * dx -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num z1 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [34], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :24, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 840 if check: - 841 try: ---> 842 c = base_ring(c) - 843 except TypeError: - 844 p_Delete(&_p, _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num 1 -monomials: [1] -monomial 1 -(0) * dx -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num z1 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [35], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :24, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 840 if check: - 841 try: ---> 842 c = base_ring(c) - 843 except TypeError: - 844 p_Delete(&_p, _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.degree(z[1])[?7h[?12l[?25h[?25l[?7lonomials(ccc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2:][?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z[1] -[?7h[?12l[?25h[?2004l[?7hz1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: z[1].monomials() -[?7h[?12l[?25h[?2004l[?7h[z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: Rxyz(z[1]) -[?7h[?12l[?25h[?2004l[?7hz1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num 1 ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [39], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :24, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'monomials' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num 1 -monomials: 1 -monomial 1 -(0) * dx -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num z1 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [40], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :24, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 840 if check: - 841 try: ---> 842 c = base_ring(c) - 843 except TypeError: - 844 p_Delete(&_p, _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num, den 1 1 ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [41], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :24, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'monomials' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num, den 1 1 ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [42], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :25, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'monomials' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num, den 1 1 -monomials: [1] -monomial 1 -(0) * dx -z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num, den z1 1 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [43], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :24, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 840 if check: - 841 try: ---> 842 c = base_ring(c) - 843 except TypeError: - 844 p_Delete(&_p, _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num, den 1 1 -monomials: [1] -monomial 1 -(0) * dx -z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num, den z1 1 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [44], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :25, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 840 if check: - 841 try: ---> 842 c = base_ring(c) - 843 except TypeError: - 844 p_Delete(&_p, _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [1] -monomial 1 -(0) * dx -z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num, den z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [45], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :25, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 840 if check: - 841 try: ---> 842 c = base_ring(c) - 843 except TypeError: - 844 p_Delete(&_p, _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [1] -monomial 1 -(0) * dx -z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)} -num, den z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [46], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :25, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 840 if check: - 841 try: ---> 842 c = base_ring(c) - 843 except TypeError: - 844 p_Delete(&_p, _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: 1 Fraction Field of Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [47], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :27, in cartier(omega) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement' object has no attribute 'monomials' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [1] -monomial 1 -(0) * dx -z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z1^5 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z1^5, x^2] -monomial z1^5 -monomial x^2 -(0) * dx -z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z1^10 - 2*x^2*z1^5 + x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z1^10, x^2*z1^5, x^4] -monomial z1^10 -monomial x^2*z1^5 -monomial x^4 -(1) * dx -z1^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z1^3 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z1^15 + 2*x^2*z1^10 - 2*x^4*z1^5 - x^6 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z1^15, x^2*z1^10, x^4*z1^5, x^6] -monomial z1^15 -monomial x^2*z1^10 -monomial x^4*z1^5 -monomial x^6 -(-2*z1) * dx -z1^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z1^4 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z1^20 + x^2*z1^15 + x^4*z1^10 + x^6*z1^5 + x^8 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z1^20, x^2*z1^15, x^4*z1^10, x^6*z1^5, x^8] -monomial z1^20 -monomial x^2*z1^15 -monomial x^4*z1^10 -monomial x^6*z1^5 -monomial x^8 -(z1^2) * dx -z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^5 - x^3 - x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^5, x^3, x] -monomial z0^5 -monomial x^3 -monomial x -(0) * dx -z0*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^5*z1^5 - x^3*z1^5 - x^2*z0^5 - x*z1^5 + x^5 + x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^5*z1^5, x^3*z1^5, x^2*z0^5, x*z1^5, x^5, x^3] -monomial z0^5*z1^5 -monomial x^3*z1^5 -monomial x^2*z0^5 -monomial x*z1^5 -monomial x^5 -monomial x^3 -(0) * dx -z0*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^5*z1^10 - x^3*z1^10 - 2*x^2*z0^5*z1^5 - x*z1^10 + 2*x^5*z1^5 + x^4*z0^5 + 2*x^3*z1^5 - x^7 - x^5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^5*z1^10, x^3*z1^10, x^2*z0^5*z1^5, x*z1^10, x^5*z1^5, x^4*z0^5, x^3*z1^5, x^7, x^5] -monomial z0^5*z1^10 -monomial x^3*z1^10 -monomial x^2*z0^5*z1^5 -monomial x*z1^10 -monomial x^5*z1^5 -monomial x^4*z0^5 -monomial x^3*z1^5 -monomial x^7 -monomial x^5 -(z0) * dx -z0*z1^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0*z1^3 - x*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^5*z1^15 - x^3*z1^15 + 2*x^2*z0^5*z1^10 - x*z1^15 - 2*x^5*z1^10 - 2*x^4*z0^5*z1^5 - 2*x^3*z1^10 + 2*x^7*z1^5 - x^6*z0^5 - x*z1^10 + 2*x^5*z1^5 + x^9 + 2*x^3*z1^5 + x^7 - x^5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^5*z1^15, x^3*z1^15, x^2*z0^5*z1^10, x*z1^15, x^5*z1^10, x^4*z0^5*z1^5, x^3*z1^10, x^7*z1^5, x^6*z0^5, x*z1^10, x^5*z1^5, x^9, x^3*z1^5, x^7, x^5] -monomial z0^5*z1^15 -monomial x^3*z1^15 -monomial x^2*z0^5*z1^10 -monomial x*z1^15 -monomial x^5*z1^10 -monomial x^4*z0^5*z1^5 -monomial x^3*z1^10 -monomial x^7*z1^5 -monomial x^6*z0^5 -monomial x*z1^10 -monomial x^5*z1^5 -monomial x^9 -monomial x^3*z1^5 -monomial x^7 -monomial x^5 -(-2*z0*z1 + x) * dx -z0*z1^4 + 2*x*z1^3 + 2*x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0*z1^4 + 2*x*z1^3 + 2*x*z0^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^5*z1^20 - x^3*z1^20 + x^2*z0^5*z1^15 - x*z1^20 - x^5*z1^15 + x^4*z0^5*z1^10 - x^3*z1^15 - x^7*z1^10 + x^6*z0^5*z1^5 + 2*x*z1^15 - x^5*z1^10 - x^9*z1^5 + x^8*z0^5 - x^3*z1^10 - x^7*z1^5 - x^11 + 2*x*z0^10 + x^5*z1^5 - x^9 + x^4*z0^5 + x^2*z0^5 - x^5 + 2*x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^5*z1^20, x^3*z1^20, x^2*z0^5*z1^15, x*z1^20, x^5*z1^15, x^4*z0^5*z1^10, x^3*z1^15, x^7*z1^10, x^6*z0^5*z1^5, x*z1^15, x^5*z1^10, x^9*z1^5, x^8*z0^5, x^3*z1^10, x^7*z1^5, x^11, x*z0^10, x^5*z1^5, x^9, x^4*z0^5, x^2*z0^5, x^5, x^3] -monomial z0^5*z1^20 -monomial x^3*z1^20 -monomial x^2*z0^5*z1^15 -monomial x*z1^20 -monomial x^5*z1^15 -monomial x^4*z0^5*z1^10 -monomial x^3*z1^15 -monomial x^7*z1^10 -monomial x^6*z0^5*z1^5 -monomial x*z1^15 -monomial x^5*z1^10 -monomial x^9*z1^5 -monomial x^8*z0^5 -monomial x^3*z1^10 -monomial x^7*z1^5 -monomial x^11 -monomial x*z0^10 -monomial x^5*z1^5 -monomial x^9 -monomial x^4*z0^5 -monomial x^2*z0^5 -monomial x^5 -monomial x^3 -(z0*z1^2 - x*z1 - x + z0) * dx -z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^10 - 2*x^3*z0^5 + x^6 - 2*x*z0^5 + 2*x^4 + x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^10, x^3*z0^5, x^6, x*z0^5, x^4, x^2] -monomial z0^10 -monomial x^3*z0^5 -monomial x^6 -monomial x*z0^5 -monomial x^4 -monomial x^2 -(2) * dx -z0^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0^2*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^10*z1^5 - 2*x^3*z0^5*z1^5 - x^2*z0^10 + x^6*z1^5 - 2*x*z0^5*z1^5 + 2*x^5*z0^5 + 2*x^4*z1^5 - x^8 + 2*x^3*z0^5 + x^2*z1^5 - 2*x^6 - x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^10*z1^5, x^3*z0^5*z1^5, x^2*z0^10, x^6*z1^5, x*z0^5*z1^5, x^5*z0^5, x^4*z1^5, x^8, x^3*z0^5, x^2*z1^5, x^6, x^4] -monomial z0^10*z1^5 -monomial x^3*z0^5*z1^5 -monomial x^2*z0^10 -monomial x^6*z1^5 -monomial x*z0^5*z1^5 -monomial x^5*z0^5 -monomial x^4*z1^5 -monomial x^8 -monomial x^3*z0^5 -monomial x^2*z1^5 -monomial x^6 -monomial x^4 -(2*z1 - 1) * dx -z0^2*z1^2 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0^2*z1^2 - x^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^10*z1^10 - 2*x^3*z0^5*z1^10 - 2*x^2*z0^10*z1^5 + x^6*z1^10 - 2*x*z0^5*z1^10 - x^5*z0^5*z1^5 + x^4*z0^10 + 2*x^4*z1^10 - 2*x^8*z1^5 - x^3*z0^5*z1^5 - 2*x^7*z0^5 + x^2*z1^10 + x^6*z1^5 + x^10 - 2*x^5*z0^5 - 2*x^4*z1^5 + 2*x^8 + x^6 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^10*z1^10, x^3*z0^5*z1^10, x^2*z0^10*z1^5, x^6*z1^10, x*z0^5*z1^10, x^5*z0^5*z1^5, x^4*z0^10, x^4*z1^10, x^8*z1^5, x^3*z0^5*z1^5, x^7*z0^5, x^2*z1^10, x^6*z1^5, x^10, x^5*z0^5, x^4*z1^5, x^8, x^6, x^2] -monomial z0^10*z1^10 -monomial x^3*z0^5*z1^10 -monomial x^2*z0^10*z1^5 -monomial x^6*z1^10 -monomial x*z0^5*z1^10 -monomial x^5*z0^5*z1^5 -monomial x^4*z0^10 -monomial x^4*z1^10 -monomial x^8*z1^5 -monomial x^3*z0^5*z1^5 -monomial x^7*z0^5 -monomial x^2*z1^10 -monomial x^6*z1^5 -monomial x^10 -monomial x^5*z0^5 -monomial x^4*z1^5 -monomial x^8 -monomial x^6 -monomial x^2 -(z0^2 + 2*z1^2 - 2*z1) * dx -z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^10*z1^15 - 2*x^3*z0^5*z1^15 + 2*x^2*z0^10*z1^10 + x^6*z1^15 - 2*x*z0^5*z1^15 - z0^20 + x^5*z0^5*z1^10 - 2*x^4*z0^10*z1^5 + 2*x^4*z1^15 - x^3*z0^15 + 2*x^8*z1^10 + x^3*z0^5*z1^10 - x^7*z0^5*z1^5 + x^2*z1^15 - 2*x^6*z0^10 - x*z0^15 - x^6*z1^10 + 2*x*z0^5*z1^10 - 2*x^10*z1^5 - x^5*z0^5*z1^5 + x^9*z0^5 - 2*x^4*z0^10 + x^8*z1^5 + x^3*z0^5*z1^5 - 2*x^12 - x^7*z0^5 - x^2*z0^10 - 2*x^2*z1^10 + 2*x^6*z1^5 - x^10 - x^5*z0^5 - x^4*z1^5 + x^8 - x^3*z0^5 - 2*x^2*z1^5 - x^6 + x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^10*z1^15, x^3*z0^5*z1^15, x^2*z0^10*z1^10, x^6*z1^15, x*z0^5*z1^15, z0^20, x^5*z0^5*z1^10, x^4*z0^10*z1^5, x^4*z1^15, x^3*z0^15, x^8*z1^10, x^3*z0^5*z1^10, x^7*z0^5*z1^5, x^2*z1^15, x^6*z0^10, x*z0^15, x^6*z1^10, x*z0^5*z1^10, x^10*z1^5, x^5*z0^5*z1^5, x^9*z0^5, x^4*z0^10, x^8*z1^5, x^3*z0^5*z1^5, x^12, x^7*z0^5, x^2*z0^10, x^2*z1^10, x^6*z1^5, x^10, x^5*z0^5, x^4*z1^5, x^8, x^3*z0^5, x^2*z1^5, x^6, x^4] -monomial z0^10*z1^15 -monomial x^3*z0^5*z1^15 -monomial x^2*z0^10*z1^10 -monomial x^6*z1^15 -monomial x*z0^5*z1^15 -monomial z0^20 -monomial x^5*z0^5*z1^10 -monomial x^4*z0^10*z1^5 -monomial x^4*z1^15 -monomial x^3*z0^15 -monomial x^8*z1^10 -monomial x^3*z0^5*z1^10 -monomial x^7*z0^5*z1^5 -monomial x^2*z1^15 -monomial x^6*z0^10 -monomial x*z0^15 -monomial x^6*z1^10 -monomial x*z0^5*z1^10 -monomial x^10*z1^5 -monomial x^5*z0^5*z1^5 -monomial x^9*z0^5 -monomial x^4*z0^10 -monomial x^8*z1^5 -monomial x^3*z0^5*z1^5 -monomial x^12 -monomial x^7*z0^5 -monomial x^2*z0^10 -monomial x^2*z1^10 -monomial x^6*z1^5 -monomial x^10 -monomial x^5*z0^5 -monomial x^4*z1^5 -monomial x^8 -monomial x^3*z0^5 -monomial x^2*z1^5 -monomial x^6 -monomial x^4 -(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx -z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^10*z1^20 - 2*x^3*z0^5*z1^20 + x^2*z0^10*z1^15 + x^6*z1^20 - 2*x*z0^5*z1^20 + z0^20*z1^5 - 2*x^5*z0^5*z1^15 + x^4*z0^10*z1^10 + 2*x^4*z1^20 + x^3*z0^15*z1^5 + x^8*z1^15 - 2*x^3*z0^5*z1^15 - x^2*z0^20 - 2*x^7*z0^5*z1^10 + x^2*z1^20 + 2*x^6*z0^10*z1^5 + x*z0^15*z1^5 + 2*x^6*z1^15 + x*z0^5*z1^15 - x^5*z0^15 + x^10*z1^10 - 2*x^5*z0^5*z1^10 - x^9*z0^5*z1^5 + 2*x^4*z0^10*z1^5 - x^3*z0^15 + 2*x^8*z1^10 + 2*x^3*z0^5*z1^10 + 2*x^12*z1^5 + x^7*z0^5*z1^5 + x^2*z0^10*z1^5 - x^2*z1^15 + 2*x^11*z0^5 - 2*x^6*z0^10 + x*z0^15 - x^6*z1^10 + x^10*z1^5 + x^5*z0^5*z1^5 + x^4*z0^10 - 2*x^4*z1^10 - x^8*z1^5 + x^3*z0^5*z1^5 - 2*x^12 - x^7*z0^5 + 2*x^2*z0^10 + x^2*z1^10 + x^6*z1^5 - x^4*z1^5 - x^8 - 2*x^3*z0^5 + 2*x^6 - x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^10*z1^20, x^3*z0^5*z1^20, x^2*z0^10*z1^15, x^6*z1^20, x*z0^5*z1^20, z0^20*z1^5, x^5*z0^5*z1^15, x^4*z0^10*z1^10, x^4*z1^20, x^3*z0^15*z1^5, x^8*z1^15, x^3*z0^5*z1^15, x^2*z0^20, x^7*z0^5*z1^10, x^2*z1^20, x^6*z0^10*z1^5, x*z0^15*z1^5, x^6*z1^15, x*z0^5*z1^15, x^5*z0^15, x^10*z1^10, x^5*z0^5*z1^10, x^9*z0^5*z1^5, x^4*z0^10*z1^5, x^3*z0^15, x^8*z1^10, x^3*z0^5*z1^10, x^12*z1^5, x^7*z0^5*z1^5, x^2*z0^10*z1^5, x^2*z1^15, x^11*z0^5, x^6*z0^10, x*z0^15, x^6*z1^10, x^10*z1^5, x^5*z0^5*z1^5, x^4*z0^10, x^4*z1^10, x^8*z1^5, x^3*z0^5*z1^5, x^12, x^7*z0^5, x^2*z0^10, x^2*z1^10, x^6*z1^5, x^4*z1^5, x^8, x^3*z0^5, x^6, x^4] -monomial z0^10*z1^20 -monomial x^3*z0^5*z1^20 -monomial x^2*z0^10*z1^15 -monomial x^6*z1^20 -monomial x*z0^5*z1^20 -monomial z0^20*z1^5 -monomial x^5*z0^5*z1^15 -monomial x^4*z0^10*z1^10 -monomial x^4*z1^20 -monomial x^3*z0^15*z1^5 -monomial x^8*z1^15 -monomial x^3*z0^5*z1^15 -monomial x^2*z0^20 -monomial x^7*z0^5*z1^10 -monomial x^2*z1^20 -monomial x^6*z0^10*z1^5 -monomial x*z0^15*z1^5 -monomial x^6*z1^15 -monomial x*z0^5*z1^15 -monomial x^5*z0^15 -monomial x^10*z1^10 -monomial x^5*z0^5*z1^10 -monomial x^9*z0^5*z1^5 -monomial x^4*z0^10*z1^5 -monomial x^3*z0^15 -monomial x^8*z1^10 -monomial x^3*z0^5*z1^10 -monomial x^12*z1^5 -monomial x^7*z0^5*z1^5 -monomial x^2*z0^10*z1^5 -monomial x^2*z1^15 -monomial x^11*z0^5 -monomial x^6*z0^10 -monomial x*z0^15 -monomial x^6*z1^10 -monomial x^10*z1^5 -monomial x^5*z0^5*z1^5 -monomial x^4*z0^10 -monomial x^4*z1^10 -monomial x^8*z1^5 -monomial x^3*z0^5*z1^5 -monomial x^12 -monomial x^7*z0^5 -monomial x^2*z0^10 -monomial x^2*z1^10 -monomial x^6*z1^5 -monomial x^4*z1^5 -monomial x^8 -monomial x^3*z0^5 -monomial x^6 -monomial x^4 -(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx -z0^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0^3 - x*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^15 + 2*x^3*z0^10 - 2*x^6*z0^5 + 2*x*z0^10 - x*z1^10 - x^9 + x^4*z0^5 + 2*x^3*z1^5 + 2*x^7 - 2*x^2*z0^5 + x^5 - x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^15, x^3*z0^10, x^6*z0^5, x*z0^10, x*z1^10, x^9, x^4*z0^5, x^3*z1^5, x^7, x^2*z0^5, x^5, x^3] -monomial z0^15 -monomial x^3*z0^10 -monomial x^6*z0^5 -monomial x*z0^10 -monomial x*z1^10 -monomial x^9 -monomial x^4*z0^5 -monomial x^3*z1^5 -monomial x^7 -monomial x^2*z0^5 -monomial x^5 -monomial x^3 -(-x + z0) * dx -z0^3*z1 - 2*x*z1^3 + x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0^3*z1 - 2*x*z1^3 + x*z0^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^15*z1^5 + 2*x^3*z0^10*z1^5 - x^2*z0^15 - 2*x^6*z0^5*z1^5 + 2*x*z0^10*z1^5 - 2*x*z1^15 - 2*x^5*z0^10 - x^9*z1^5 + x^4*z0^5*z1^5 + 2*x^8*z0^5 - 2*x^3*z0^10 + x^3*z1^10 + 2*x^7*z1^5 - 2*x^2*z0^5*z1^5 + x^11 - x^6*z0^5 + x*z0^10 + x^5*z1^5 - 2*x^9 - x^3*z1^5 + x^7 - 2*x^2*z0^5 - 2*x^5 + x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^15*z1^5, x^3*z0^10*z1^5, x^2*z0^15, x^6*z0^5*z1^5, x*z0^10*z1^5, x*z1^15, x^5*z0^10, x^9*z1^5, x^4*z0^5*z1^5, x^8*z0^5, x^3*z0^10, x^3*z1^10, x^7*z1^5, x^2*z0^5*z1^5, x^11, x^6*z0^5, x*z0^10, x^5*z1^5, x^9, x^3*z1^5, x^7, x^2*z0^5, x^5, x^3] -monomial z0^15*z1^5 -monomial x^3*z0^10*z1^5 -monomial x^2*z0^15 -monomial x^6*z0^5*z1^5 -monomial x*z0^10*z1^5 -monomial x*z1^15 -monomial x^5*z0^10 -monomial x^9*z1^5 -monomial x^4*z0^5*z1^5 -monomial x^8*z0^5 -monomial x^3*z0^10 -monomial x^3*z1^10 -monomial x^7*z1^5 -monomial x^2*z0^5*z1^5 -monomial x^11 -monomial x^6*z0^5 -monomial x*z0^10 -monomial x^5*z1^5 -monomial x^9 -monomial x^3*z1^5 -monomial x^7 -monomial x^2*z0^5 -monomial x^5 -monomial x^3 -(-x*z1 + z0*z1 - 2*x) * dx -z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: z0^15*z1^10 + 2*x^3*z0^10*z1^10 - 2*x^2*z0^15*z1^5 - 2*x^6*z0^5*z1^10 + 2*x*z0^10*z1^10 - x*z1^20 + x^5*z0^10*z1^5 + x^4*z0^15 - x^9*z1^10 + x^4*z0^5*z1^10 - x^8*z0^5*z1^5 + x^3*z0^10*z1^5 - x^3*z1^15 + 2*x^7*z0^10 + 2*x^7*z1^10 - 2*x^2*z0^5*z1^10 + 2*x^11*z1^5 - 2*x^6*z0^5*z1^5 + 2*x*z0^10*z1^5 - 2*x^10*z0^5 + 2*x^5*z0^10 + x^5*z1^10 + x^9*z1^5 - x^13 + x^8*z0^5 - 2*x^3*z0^10 - x^3*z1^10 + 2*x^7*z1^5 + x^2*z0^5*z1^5 + 2*x^11 + 2*x^6*z0^5 + x^5*z1^5 - x^9 - x^4*z0^5 + 2*x^3*z1^5 - 2*x^2*z0^5 + 2*x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [z0^15*z1^10, x^3*z0^10*z1^10, x^2*z0^15*z1^5, x^6*z0^5*z1^10, x*z0^10*z1^10, x*z1^20, x^5*z0^10*z1^5, x^4*z0^15, x^9*z1^10, x^4*z0^5*z1^10, x^8*z0^5*z1^5, x^3*z0^10*z1^5, x^3*z1^15, x^7*z0^10, x^7*z1^10, x^2*z0^5*z1^10, x^11*z1^5, x^6*z0^5*z1^5, x*z0^10*z1^5, x^10*z0^5, x^5*z0^10, x^5*z1^10, x^9*z1^5, x^13, x^8*z0^5, x^3*z0^10, x^3*z1^10, x^7*z1^5, x^2*z0^5*z1^5, x^11, x^6*z0^5, x^5*z1^5, x^9, x^4*z0^5, x^3*z1^5, x^2*z0^5, x^3] -monomial z0^15*z1^10 -monomial x^3*z0^10*z1^10 -monomial x^2*z0^15*z1^5 -monomial x^6*z0^5*z1^10 -monomial x*z0^10*z1^10 -monomial x*z1^20 -monomial x^5*z0^10*z1^5 -monomial x^4*z0^15 -monomial x^9*z1^10 -monomial x^4*z0^5*z1^10 -monomial x^8*z0^5*z1^5 -monomial x^3*z0^10*z1^5 -monomial x^3*z1^15 -monomial x^7*z0^10 -monomial x^7*z1^10 -monomial x^2*z0^5*z1^10 -monomial x^11*z1^5 -monomial x^6*z0^5*z1^5 -monomial x*z0^10*z1^5 -monomial x^10*z0^5 -monomial x^5*z0^10 -monomial x^5*z1^10 -monomial x^9*z1^5 -monomial x^13 -monomial x^8*z0^5 -monomial x^3*z0^10 -monomial x^3*z1^10 -monomial x^7*z1^5 -monomial x^2*z0^5*z1^5 -monomial x^11 -monomial x^6*z0^5 -monomial x^5*z1^5 -monomial x^9 -monomial x^4*z0^5 -monomial x^3*z1^5 -monomial x^2*z0^5 -monomial x^3 -(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx -x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den x 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [x] -monomial x -(0) * dx -x*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den x*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: x*z1^5 - x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [x*z1^5, x^3] -monomial x*z1^5 -monomial x^3 -(0) * dx -x*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den x*z0 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: x*z0^5 - x^4 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [x*z0^5, x^4, x^2] -monomial x*z0^5 -monomial x^4 -monomial x^2 -(-1) * dx -x*z0*z1 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2} -num, den x*z0*z1 - x^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -aaa: x*z0^5*z1^5 - x^4*z1^5 - x^3*z0^5 - x^2*z1^5 + x^6 + x^4 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -monomials: [x*z0^5*z1^5, x^4*z1^5, x^3*z0^5, x^2*z1^5, x^6, x^4, x^2] -monomial x*z0^5*z1^5 -monomial x^4*z1^5 -monomial x^3*z0^5 -monomial x^2*z1^5 -monomial x^6 -monomial x^4 -monomial x^2 -(-z1 + 1) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(0) * dx -z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(0) * dx -z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(1) * dx -z1^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(-2*z1) * dx -z1^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(z1^2) * dx -z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(0) * dx -z0*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(0) * dx -z0*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(z0) * dx -z0*z1^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(-2*z0*z1 + x) * dx -z0*z1^4 + 2*x*z1^3 + 2*x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(z0*z1^2 - x*z1 - x + z0) * dx -z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(2) * dx -z0^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(2*z1 - 1) * dx -z0^2*z1^2 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(z0^2 + 2*z1^2 - 2*z1) * dx -z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx -z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx -z0^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(-x + z0) * dx -z0^3*z1 - 2*x*z1^3 + x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(-x*z1 + z0*z1 - 2*x) * dx -z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx -x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(0) * dx -x*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(0) * dx -x*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(-1) * dx -x*z0*z1 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 -(-z1 + 1) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(0) * dx -(0) * dx -(1) * dx -(-2*z1) * dx -(z1^2) * dx -(0) * dx -(0) * dx -(z0) * dx -(-2*z0*z1 + x) * dx -(z0*z1^2 - x*z1 - x + z0) * dx -(2) * dx -(2*z1 - 1) * dx -(z0^2 + 2*z1^2 - 2*z1) * dx -(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx -(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx -(-x + z0) * dx -(-x*z1 + z0*z1 - 2*x) * dx -(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx -(0) * dx -(0) * dx -(-1) * dx -(-z1 + 1) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7lS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, - (z1) * dx, - (z1^2) * dx, - (z1^3) * dx, - (z1^4) * dx, - (z0) * dx, - (z0*z1) * dx, - (z0*z1^2) * dx, - (z0*z1^3 - x*z1^2) * dx, - (z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx, - (z0^2) * dx, - (z0^2*z1) * dx, - (z0^2*z1^2 - x^2) * dx, - (z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1) * dx, - (z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2) * dx, - (z0^3 - x*z1^2) * dx, - (z0^3*z1 - 2*x*z1^3 + x*z0^2) * dx, - (z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0) * dx, - (x) * dx, - (x*z1) * dx, - (x*z0) * dx, - (x*z0*z1 - x^2) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(0) * dx -(0) * dx -(1) * dx -(-2*z1) * dx -(z1^2) * dx -(0) * dx -(0) * dx -(z0) * dx -(-2*z0*z1 + x) * dx -(z0*z1^2 - x*z1 - x + z0) * dx -(2) * dx -(2*z1 - 1) * dx -(z0^2 + 2*z1^2 - 2*z1) * dx -(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx -(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx -(-x + z0) * dx -(-x*z1 + z0*z1 - 2*x) * dx -(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx -(0) * dx -(0) * dx -(-1) * dx -(-z1 + 1) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(0) * dx -(0) * dx -(1) * dx -(-2*z1) * dx -(z1^2) * dx -(0) * dx -(0) * dx -(z0) * dx -(-2*z0*z1 + x) * dx -(z0*z1^2 - x*z1 - x + z0) * dx -(2) * dx -(2*z1 - 1) * dx -(z0^2 + 2*z1^2 - 2*z1) * dx -(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx -(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx -(-x + z0) * dx -(-x*z1 + z0*z1 - 2*x) * dx -(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx -(0) * dx -(0) * dx -(-1) * dx -(-z1 + 1) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0] -[0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 4 4 0 0] -[2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 3 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] -[1 4 0 2 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 1 0] -[4 4 3 0 2 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 4] -[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0] -[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 3 4 0 0] -[0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 1 0 0 4 1 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h22 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: bbb -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, - (z1) * dx, - (z1^2) * dx, - (z1^3) * dx, - (z1^4) * dx, - (z0) * dx, - (z0*z1) * dx, - (z0*z1^2) * dx, - (z0*z1^3 - x*z1^2) * dx, - (z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx, - (z0^2) * dx, - (z0^2*z1) * dx, - (z0^2*z1^2 - x^2) * dx, - (z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1) * dx, - (z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2) * dx, - (z0^3 - x*z1^2) * dx, - (z0^3*z1 - 2*x*z1^3 + x*z0^2) * dx, - (z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0) * dx, - (x) * dx, - (x*z1) * dx, - (x*z0) * dx, - (x*z0*z1 - x^2) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.function[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[9].form.monomials()[?7h[?12l[?25h[?25l[?7l0catier().coordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].cartier().coordinates()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier().coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[0 0 1 0 0 0 0 0 0 0 2 4 0 1 4 0 0 0 0 0 4 1] -[0 0 0 3 0 0 0 0 0 0 0 2 3 4 4 0 0 0 0 0 0 4] -[0 0 0 0 1 0 0 0 0 0 0 0 2 0 3 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 4 0 0 0 0] -[0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 1 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 1 3 1 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 1 4 0 0 0 0 0 4 3 4 0 0 0 0] -[0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 4 1 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0] -[0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l4 ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [59], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :26, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :13, in  - -File :17, in cartier_matrix(AS) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'genus' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 with the equation: - z^5 - z = x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l4 -4 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltests.sage')[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') - tensor tests.sage text3d  - tensor_signed tetrahedron  - tests text  - - [?7h[?12l[?25h[?25l[?7l(sts.sage') - - -[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004lCartier test: -Increase precision. -Increase precision. ---------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [63], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :155, in cartier_matrix(self) - -File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__() - 1502 raise IndexError("value does not have the right number of columns") - 1503 elif single_col and row_list_len != len(value_list): --> 1504 raise IndexError("value does not have the right number of rows") - 1505 else: - 1506 if row_list_len != len(value_list): - -IndexError: value does not have the right number of rows -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004lCartier test: -Increase precision. -Increase precision. ---------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [64], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :155, in cartier_matrix(self) - -File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__() - 1502 raise IndexError("value does not have the right number of columns") - 1503 elif single_col and row_list_len != len(value_list): --> 1504 raise IndexError("value does not have the right number of rows") - 1505 else: - 1506 if row_list_len != len(value_list): - -IndexError: value does not have the right number of rows -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7load('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004lCartier test: -True -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = E.frobenius_matrix_hypellfrob()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: M = matrix(QQ, [[1, 1], [0, 0]]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(QQ, [[1, 1], [0, 0]])[?7h[?12l[?25h[?25l[?7l.jordan_form()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.image() -[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field -Basis matrix: -[1 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.image()[?7h[?12l[?25h[?25l[?7lsage: M -[?7h[?12l[?25h[?2004l[?7h[1 1] -[0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.image()[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.kernel() -[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field -Basis matrix: -[0 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.kernel()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7limag()[?7h[?12l[?25h[?25l[?7lmage()[?7h[?12l[?25h[?25l[?7lsage: M.image() -[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field -Basis matrix: -[1 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.image()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltimage()[?7h[?12l[?25h[?25l[?7lrimage()[?7h[?12l[?25h[?25l[?7laimage()[?7h[?12l[?25h[?25l[?7lnimage()[?7h[?12l[?25h[?25l[?7lsimage()[?7h[?12l[?25h[?25l[?7lpimage()[?7h[?12l[?25h[?25l[?7loimage()[?7h[?12l[?25h[?25l[?7lsimage()[?7h[?12l[?25h[?25l[?7leimage()[?7h[?12l[?25h[?25l[?7l(image()[?7h[?12l[?25h[?25l[?7l()image()[?7h[?12l[?25h[?25l[?7l().image()[?7h[?12l[?25h[?25l[?7lsage: M.transpose().image() -[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field -Basis matrix: -[1 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.transpose().image()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.transpose().image().basis() -[?7h[?12l[?25h[?2004l[?7h[ -(1, 0) -] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ losage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7ln.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTrue True True -[ -RModule M of dimension 3 over GF(2) -] -{ -[0 0 1] -[1 1 1] -[1 0 0], -[1 1 1] -[0 0 1] -[0 1 0] -} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTrue True True -[ -RModule M of dimension 3 over GF(2) -] -{ -[0 0 1] -[1 1 1] -[1 0 0], -[1 1 1] -[0 0 1] -[0 1 0] -} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRax. = PolynomialRing(Ra)[?7h[?12l[?25h[?25l[?7l. =PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: R. = PolynomialRing(GF(3)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l-, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.height[?7h[?12l[?25h[?25l[?7ldx.cartier()[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(1, n):[?7h[?12l[?25h[?25l[?7l =a[n]*x^ + a[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(1, n):[?7h[?12l[?25h[?25l[?7l =a[n]*x^ + a[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7luperelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, y/x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [5], in () -----> 1 f = superelliptic_function(C, y/x) - -NameError: name 'y' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, y/x)[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lR. = PoynomalRing(GF(3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,> = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7l > = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7ly> = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx. = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7ly. = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rxy. = PolynomialRing(GF(3), 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lf = superelliptic_functio(C, y/x)[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, y/x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldimension_of_RHS = p*gY + (len(list_of_m) - 1)*(p-1) + sum(sum(i*alpha(i, m, p) for i in range(1, p)) for m in list_of_m)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, y/x)[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn() -[?7h[?12l[?25h[?2004l[?7h((-x^2 - 1)/(x*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expnsion_at_infty()[1][?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().pth_root()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l/*(C.dx)[?7h[?12l[?25h[?25l[?7lC*(C.dx)[?7h[?12l[?25h[?25l[?7l.*(C.dx)[?7h[?12l[?25h[?25l[?7ly*(C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y*(C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*(C.dx)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x)^2/(C.y)*(C.dx) -[?7h[?12l[?25h[?2004l[?7h(x^2/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^2/(C.y)*(C.dx)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).expansi[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^2/(C.y)*(C.dx).expansi[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^2/(C.y)*(C.dx)).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-4 + 1 + O(t^6) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() - - - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: C. -[?7h[?12l[?25h[?2004l Input In [11] - C. - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l/C.x).coordinates()[?7h[?12l[?25h[?25l[?7l/C.x).coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^.cordinates()[?7h[?12l[?25h[?25l[?7l(.cordinates()[?7h[?12l[?25h[?25l[?7l().cordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).cordinates()[?7h[?12l[?25h[?25l[?7l1).cordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y)^(-1) -[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + 2*x))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)^(-1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)).diffn() -[?7h[?12l[?25h[?2004l[?7h((-1)/(x^3*y - x*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l1C.x[?7h[?12l[?25h[?25l[?7l/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((1/C.x).difn()[?7h[?12l[?25h[?25l[?7l)(1/C.x).difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/C.x).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l^).difn()[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^.difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).difn()[?7h[?12l[?25h[?25l[?7l1).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l((C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l*((C.x)^(-1)).difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7lx)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l.)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l.)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7lx)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l(*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l-*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l2*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l()*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x)^(-2)*((C.x)^(-1)).diffn() -[?7h[?12l[?25h[?2004l[?7h((-1)/x^4) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7lfff.cartier()[?7h[?12l[?25h[?25l[?7l = x^3 - x + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff = superellitptic_function(C, y/x^2) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [15], in () -----> 1 ff = superellitptic_function(C, y/x**Integer(2)) - -NameError: name 'superellitptic_function' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = superellitptic_function(C, y/x^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lptic_function(C, y/x^2)[?7h[?12l[?25h[?25l[?7lsage: ff = superelliptic_function(C, y/x^2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = superelliptic_function(C, y/x^2)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.dicriminant()%8[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn() -[?7h[?12l[?25h[?2004l[?7h(1/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ losage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [1], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :43, in  - -File :75, in coordinates(self) - -File :113, in degree_of_rational_fctn(f, F) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in PolynomialRing(base_ring, *args, **kwds) - 52 r""" - 53 Return the globally unique univariate or multivariate polynomial - 54 ring with given properties and variable name or names. - (...) - 551  TypeError: unable to convert 'x' to an integer - 552 """ - 553 if not ring.is_Ring(base_ring): ---> 554 raise TypeError("base_ring {!r} must be a ring".format(base_ring)) - 556 n = -1 # Unknown number of variables - 557 names = None # Unknown variable names - -TypeError: base_ring 3 must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [2], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :11, in  - -TypeError: bad operand type for unary -: 'superelliptic_function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [3], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :11, in  - -File /ext/sage/9.7/src/sage/rings/integer.pyx:1769, in sage.rings.integer.Integer.__add__() - 1767 return y - 1768 --> 1769 return coercion_model.bin_op(left, right, operator.add) - 1770 - 1771 cpdef _add_(self, right): - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() - 1246 # We should really include the underlying error. - 1247 # This causes so much headache. --> 1248 raise bin_op_exception(op, x, y) - 1249 - 1250 cpdef canonical_coercion(self, x, y): - -TypeError: unsupported operand parent(s) for +: 'Integer Ring' and '' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: C.one -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: loa -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [5], in () -----> 1 loa - -NameError: name 'loa' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lloa[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lloa[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [8], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :16, in  - -NameError: name 'quo_rem' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) -(2*x^15 + 2*x^13 + x^12 + x^10 + 2*x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2, 2*x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) -(2*x^15 + 2*x^13 + x^12 + x^10 + 2*x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2, 2*x) -(2*x^12 + x^10 + x^9 + x^8 + 2*x^7 + x^6 + x^5 + x^4 + x^2 + 2*x + 1, x^2 + x + 2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) -[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega -[?7h[?12l[?25h[?2004l[?7h((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.xpansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^(-2)*((C.x)^(-1)).diffn()[?7h[?12l[?25h[?25l[?7l)^(-2)*((C.x)^(-1)).diffn()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()y[?7h[?12l[?25h[?25l[?7l(y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: (C.x)^(11)/(C.y)^3*C.dx -[?7h[?12l[?25h[?2004l[?7h(x^11/y^3) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(1)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(11)/(C.y)^3*C.dx).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t^-40 + O(t^-30) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(11)/(C.y)^3*C.dx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7l(C.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(11)/(C.y)^3*C.dx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7lm((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l1((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l ((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l=((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l ((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7lsage: om1 = ((C.x)^(11)/(C.y)^3*C.dx) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((C.x)^(11)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: om1.is_regular_on_U - om1.is_regular_on_U0  - om1.is_regular_on_Uinfty - - - [?7h[?12l[?25h[?25l[?7l0 - om1.is_regular_on_U0  - - [?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.is_regular_on_U0() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lom1.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1 -[?7h[?12l[?25h[?2004l[?7h(x^11/y^3) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lth_component[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(0) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(1) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.jth_component(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(2) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.jth_component(2)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.cartier() -[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1 -[?7h[?12l[?25h[?2004l[?7h(x^11/y^3) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7ljth_component(2)[?7h[?12l[?25h[?25l[?7lth_component(2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(3) -[?7h[?12l[?25h[?2004l[?7hx^11 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens()[0], parent(a).gens()[1][?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l11.[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x^11.quo_rem(x^3 - x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [24], in () -----> 1 x**Integer(11).quo_rem(x**Integer(3) - x) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:592, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__pow__() - 590 cdef long e - 591 try: ---> 592 e = ee - 593 except OverflowError: - 594 return Polynomial.__pow__(self, ee, modulus) - -TypeError: an integer is required -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^11.quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^1.quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(11).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: (x^11).quo_rem(x^3 - x) -[?7h[?12l[?25h[?2004l[?7h(x^8 + x^6 + x^4 + x^2 + 1, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = Ra.gens()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^11, x^3 - x) -[?7h[?12l[?25h[?2004l[?7h[x^2, 0, x^2 + 1, x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lheight[?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) -[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation: - z^3 - z = x^4 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.cartier_matrix() -[?7h[?12l[?25h[?2004l[?7h[0 0 0] -[0 0 0] -[0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: (AS.x)^(-1)*AS.dx -[?7h[?12l[?25h[?2004l[?7h(1/x) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x)^(-1)*AS.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x)^(-1)*AS.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((AS.x)^(-1)*AS.dx).cartier() -[?7h[?12l[?25h[?2004l[?7h(1/x) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lor  i range(1, n):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for b in AS.holomorphic_differentials_basis(): -....: [?7h[?12l[?25h[?25l[?7lprint(ffff.cartier())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(b.cartier()) -....: [?7h[?12l[?25h[?25l[?7lsage: for b in AS.holomorphic_differentials_basis(): -....:  print(b.cartier()) -....:  -[?7h[?12l[?25h[?2004l(0) * dx -(0) * dx -(0) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: AS.cartier_matrix() -[?7h[?12l[?25h[?2004l[?7h[0 0 0 1] -[0 0 0 0] -[0 2 0 0] -[0 0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc.monomials()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr_kernel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [36], in () -----> 1 cartier_kernel(AS) - -File :16, in cartier_kernel(C, prec) - -TypeError: as_cover.cartier_matrix() got an unexpected keyword argument 'prec' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: AS.cartier_matrix() -[?7h[?12l[?25h[?2004l[?7h[0 0 0 1] -[0 0 0 0] -[0 2 0 0] -[0 0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [39], in () -----> 1 cartier_kernel(AS) - -File :24, in cartier_kernel(C, prec) - -File :23, in __add__(self, other) - -AttributeError: 'as_form' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS) -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (x) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS) -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (x) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS) -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (x) * dx, (x^3) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (x) * dx, (x^3) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (x) * dx, (x^3) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (x^2 + z0) * dx, (x) * dx, (x^3) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7l(ests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -superelliptic p rank test: ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category() - 838 try: ---> 839 return self.__cached_methods[name] - 840 except KeyError: - -KeyError: 'p' - -During handling of the above exception, another exception occurred: - -AttributeError Traceback (most recent call last) -Input In [51], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :5, in  - -File /ext/sage/9.7/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__() - 831 AttributeError: 'PrimeNumbers_with_category' object has no attribute 'sadfasdf' - 832 """ ---> 833 return self.getattr_from_category(name) - 834 - 835 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category() - 846 cls = self._category.parent_class - 847 ---> 848 attr = getattr_from_other_class(self, cls, name) - 849 self.__cached_methods[name] = attr - 850 return attr - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class() - 354 dummy_error_message.cls = type(self) - 355 dummy_error_message.name = name ---> 356 raise AttributeError(dummy_error_message) - 357 cdef PyObject* attr = instance_getattr(cls, name) - 358 if attr is NULL: - -AttributeError: 'HyperellipticCurve_FiniteField_with_category' object has no attribute 'p' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -superelliptic p rank test: -2 ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [52], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :6, in  - -NameError: name 'superelliptic_curve' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -superelliptic p rank test: -2 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [53], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :170, in p_rank(self) - -File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse) - 920 n = ring - 921 ring = ZZ ---> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1) - -File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__() - 318 """ - 319 if cls.classcall is not None: ---> 320 return cls.classcall(cls, *args, **kwds) - 321 else: - 322 # Fast version of type.__call__(cls, *args, **kwds) - -File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds) - 516 """ - 517 Normalize the arguments to call the ``__init__`` constructor. - 518 - (...) - 558  False - 559 """ - 560 if base_ring not in _Rings: ---> 561 raise TypeError("base_ring (=%s) must be a ring"%base_ring) - 562 nrows = int(nrows) - 563 if ncols is None: - -TypeError: base_ring (=3) must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^11.quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: x -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(f^2)[?7h[?12l[?25h[?25l[?7larent(A)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(x) -[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 67 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?superelliptic_cech[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: ?superelliptic -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -OSError Traceback (most recent call last) -Input In [56], in () -----> 1 get_ipython().run_line_magic('pinfo', 'superelliptic') - -File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:2305, in InteractiveShell.run_line_magic(self, magic_name, line, _stack_depth) - 2303 kwargs['local_ns'] = self.get_local_scope(stack_depth) - 2304 with self.builtin_trap: --> 2305 result = fn(*args, **kwargs) - 2306 return result - -File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/magics/namespace.py:58, in NamespaceMagics.pinfo(self, parameter_s, namespaces) - 56 self.psearch(oname) - 57 else: ----> 58 self.shell._inspect('pinfo', oname, detail_level=detail_level, - 59  namespaces=namespaces) - -File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:1685, in InteractiveShell._inspect(self, meth, oname, namespaces, **kw) - 1683 pmethod(info.obj, oname, formatter) - 1684 elif meth == 'pinfo': --> 1685 pmethod( - 1686  info.obj, - 1687  oname, - 1688  formatter, - 1689  info, - 1690  enable_html_pager=self.enable_html_pager, - 1691  **kw, - 1692  ) - 1693 else: - 1694 pmethod(info.obj, oname) - -File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:698, in Inspector.pinfo(self, obj, oname, formatter, info, detail_level, enable_html_pager, omit_sections) - 665 def pinfo( - 666 self, - 667 obj, - (...) - 673 omit_sections=(), - 674 ): - 675 """Show detailed information about an object. - 676 - 677  Optional arguments: - (...) - 696  - omit_sections: set of section keys and titles to omit - 697  """ ---> 698 info = self._get_info( - 699  obj, oname, formatter, info, detail_level, omit_sections=omit_sections - 700  ) - 701 if not enable_html_pager: - 702 del info['text/html'] - -File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:591, in Inspector._get_info(self, obj, oname, formatter, info, detail_level, omit_sections) - 571 def _get_info( - 572 self, obj, oname="", formatter=None, info=None, detail_level=0, omit_sections=() - 573 ): - 574 """Retrieve an info dict and format it. - 575 - 576  Parameters - (...) - 588  Titles or keys to omit from output (can be set, tuple, etc., anything supporting `in`) - 589  """ ---> 591 info = self.info(obj, oname=oname, info=info, detail_level=detail_level) - 593 _mime = { - 594 'text/plain': [], - 595 'text/html': '', - 596 } - 598 def append_field(bundle, title:str, key:str, formatter=None): - -File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:762, in Inspector.info(self, obj, oname, info, detail_level) - 760 ds += "\nDocstring:\n" + obj.__doc__ - 761 else: ---> 762 ds = getdoc(obj) - 763 if ds is None: - 764 ds = '' - -File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__() - 389 True - 390 """ ---> 391 return self.get_object()(*args, **kwds) - 392 - 393 def __repr__(self): - -File /ext/sage/9.7/src/sage/misc/sageinspect.py:2107, in sage_getdoc(obj, obj_name, embedded) - 2105 r = sage_getdoc_original(obj) - 2106 s = sage.misc.sagedoc.format(r, embedded=embedded) --> 2107 f = sage_getfile(obj) - 2108 if f and os.path.exists(f): - 2109 from sage.doctest.control import skipfile - -File /ext/sage/9.7/src/sage/misc/sageinspect.py:1414, in sage_getfile(obj) - 1412 # No go? fall back to inspect. - 1413 try: --> 1414 sourcefile = inspect.getabsfile(obj) - 1415 except TypeError: # this happens for Python builtins - 1416 return '' - -File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:844, in getabsfile(object, _filename) - 839 """Return an absolute path to the source or compiled file for an object. - 840 - 841 The idea is for each object to have a unique origin, so this routine - 842 normalizes the result as much as possible.""" - 843 if _filename is None: ---> 844 _filename = getsourcefile(object) or getfile(object) - 845 return os.path.normcase(os.path.abspath(_filename)) - -File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:817, in getsourcefile(object) - 813 def getsourcefile(object): - 814 """Return the filename that can be used to locate an object's source. - 815  Return None if no way can be identified to get the source. - 816  """ ---> 817 filename = getfile(object) - 818 all_bytecode_suffixes = importlib.machinery.DEBUG_BYTECODE_SUFFIXES[:] - 819 all_bytecode_suffixes += importlib.machinery.OPTIMIZED_BYTECODE_SUFFIXES[:] - -File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:785, in getfile(object) - 783 return module.__file__ - 784 if object.__module__ == '__main__': ---> 785 raise OSError('source code not available') - 786 raise TypeError('{!r} is a built-in class'.format(object)) - 787 if ismethod(object): - -OSError: source code not available -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(E.local_data(2))[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: superelliptic - superelliptic superelliptic_drw_form - superelliptic/ superelliptic_form  - superelliptic_cech superelliptic_function - - [?7h[?12l[?25h[?25l[?7l - superelliptic  - - - [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l - superelliptic superelliptic_drw_form - superelliptic/ superelliptic_form  - superelliptic_cech superelliptic_function[?7h[?12l[?25h[?25l[?7ll - - -[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -superelliptic p rank test: -2 -[ 0 39 0] -[19 0 29] -[ 0 21 0] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [57], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :8, in  - -File :170, in p_rank(self) - -File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse) - 920 n = ring - 921 ring = ZZ ---> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1) - -File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__() - 318 """ - 319 if cls.classcall is not None: ---> 320 return cls.classcall(cls, *args, **kwds) - 321 else: - 322 # Fast version of type.__call__(cls, *args, **kwds) - -File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds) - 516 """ - 517 Normalize the arguments to call the ``__init__`` constructor. - 518 - (...) - 558  False - 559 """ - 560 if base_ring not in _Rings: ---> 561 raise TypeError("base_ring (=%s) must be a ring"%base_ring) - 562 nrows = int(nrows) - 563 if ncols is None: - -TypeError: base_ring (=3) must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus() -[?7h[?12l[?25h[?2004l[?7h3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: identity_matrix(3) -[?7h[?12l[?25h[?2004l[?7h[1 0 0] -[0 1 0] -[0 0 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -superelliptic p rank test: -2 -[ 0 39 0] -[19 0 29] -[ 0 21 0] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [60], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :8, in  - -File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse) - 920 n = ring - 921 ring = ZZ ---> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1) - -File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__() - 318 """ - 319 if cls.classcall is not None: ---> 320 return cls.classcall(cls, *args, **kwds) - 321 else: - 322 # Fast version of type.__call__(cls, *args, **kwds) - -File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds) - 516 """ - 517 Normalize the arguments to call the ``__init__`` constructor. - 518 - (...) - 558  False - 559 """ - 560 if base_ring not in _Rings: ---> 561 raise TypeError("base_ring (=%s) must be a ring"%base_ring) - 562 nrows = int(nrows) - 563 if ncols is None: - -TypeError: base_ring (=2*x^18 + x^15 + x^14 + x^11) must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lidentity_matrix(3)[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ltity_matrix(3)[?7h[?12l[?25h[?25l[?7lsage: identity_matrix(3) -[?7h[?12l[?25h[?2004l[?7h[1 0 0] -[0 1 0] -[0 0 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgX = (two_gX_minus_2+2)/2[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7h2*x^18 + x^15 + x^14 + x^11 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhight[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus() -[?7h[?12l[?25h[?2004l[?7h3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -superelliptic p rank test: -2 -[ 0 39 0] -[19 0 29] -[ 0 21 0] -[1 0 0] -[0 1 0] -[0 0 1] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [64], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :170, in p_rank(self) - -File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse) - 920 n = ring - 921 ring = ZZ ---> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1) - -File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__() - 318 """ - 319 if cls.classcall is not None: ---> 320 return cls.classcall(cls, *args, **kwds) - 321 else: - 322 # Fast version of type.__call__(cls, *args, **kwds) - -File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds) - 516 """ - 517 Normalize the arguments to call the ``__init__`` constructor. - 518 - (...) - 558  False - 559 """ - 560 if base_ring not in _Rings: ---> 561 raise TypeError("base_ring (=%s) must be a ring"%base_ring) - 562 nrows = int(nrows) - 563 if ncols is None: - -TypeError: base_ring (=3) must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -superelliptic p rank test: -2 -[66 39 0] -[19 66 29] -[ 0 21 66] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [65], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :8, in  - -File :170, in p_rank(self) - -File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse) - 920 n = ring - 921 ring = ZZ ---> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1) - -File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__() - 318 """ - 319 if cls.classcall is not None: ---> 320 return cls.classcall(cls, *args, **kwds) - 321 else: - 322 # Fast version of type.__call__(cls, *args, **kwds) - -File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds) - 516 """ - 517 Normalize the arguments to call the ``__init__`` constructor. - 518 - (...) - 558  False - 559 """ - 560 if base_ring not in _Rings: ---> 561 raise TypeError("base_ring (=%s) must be a ring"%base_ring) - 562 nrows = int(nrows) - 563 if ncols is None: - -TypeError: base_ring (=3) must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -superelliptic p rank test: -2 -[66 39 0] -[19 66 29] -[ 0 21 66] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [66], in () -----> 1 load('tests.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :8, in  - -File :170, in p_rank(self) - -File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse) - 920 n = ring - 921 ring = ZZ ---> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1) - -File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__() - 318 """ - 319 if cls.classcall is not None: ---> 320 return cls.classcall(cls, *args, **kwds) - 321 else: - 322 # Fast version of type.__call__(cls, *args, **kwds) - -File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds) - 516 """ - 517 Normalize the arguments to call the ``__init__`` constructor. - 518 - (...) - 558  False - 559 """ - 560 if base_ring not in _Rings: ---> 561 raise TypeError("base_ring (=%s) must be a ring"%base_ring) - 562 nrows = int(nrows) - 563 if ncols is None: - -TypeError: base_ring (=3) must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?superelliptic[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: ?identity_matrix -[?7h[?12l[?25h[?2004l[?1049h[?1h= Signature: identity_matrix(ring, n=0, sparse=False) -Docstring:  - This function is available as identity_matrix(...) and - matrix.identity(...). - - Return the n x n identity matrix over the given ring. - - The default ring is the integers. - - EXAMPLES: - - sage: M = identity_matrix(QQ, 2); M - [1 0] - [0 1] - sage: M.parent() - Full MatrixSpace of 2 by 2 dense matrices over Rational Field - sage: M = identity_matrix(2); M - [1 0] - [0 1] - sage: M.parent() - Full MatrixSpace of 2 by 2 dense matrices over Integer Ring - sage: M.is_mutable() - True - sage: M = identity_matrix(3, sparse=True); M - [1 0 0] - [0 1 0] -:  [0 0 1] -:  sage: M.parent() -:  Full MatrixSpace of 3 by 3 sparse matrices over Integer Ring -:  sage: M.is_mutable() -:  True -: Init docstring: Initialize self. See help(type(self)) for accurate signature. -: File: /ext/sage/9.7/src/sage/matrix/special.py -: Type: function -:  (END)  (END)  (END)  (END) M The default ring is the integers. -M -M Return the n x n identity matrix over the given ring. -M -M matrix.identity(...). -M This function is available as identity_matrix(...) and -MDocstring:  -MSignature: identity_matrix(ring, n=0, sparse=False) - :  ::ww :  [0 0 1] -:  ::qq [?1l>[?1049l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -superelliptic p rank test: -2 -[66 39 0] -[19 66 29] -[ 0 21 66] -0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.a_number() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7lsage: X -[?7h[?12l[?25h[?2004l[?7hHyperelliptic Curve over Finite Field of size 67 defined by y^2 = x^7 + x^3 + x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lnumber[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: X.a_number() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') -[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx] -a-number test: -True -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [73], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :10, in  - -TypeError: 'function' object cannot be interpreted as an integer -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [74], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds) - 637 from .misc_c import prod as c_prod - 638 if hasattr(expression, 'prod'): ---> 639 return expression.prod(*args, **kwds) - 640 elif len(args) <= 1: - 641 return c_prod(expression, *args) - -TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [75], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds) - 637 from .misc_c import prod as c_prod - 638 if hasattr(expression, 'prod'): ---> 639 return expression.prod(*args, **kwds) - 640 elif len(args) <= 1: - 641 return c_prod(expression, *args) - -TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [76], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds) - 637 from .misc_c import prod as c_prod - 638 if hasattr(expression, 'prod'): ---> 639 return expression.prod(*args, **kwds) - 640 elif len(args) <= 1: - 641 return c_prod(expression, *args) - -TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [77], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds) - 637 from .misc_c import prod as c_prod - 638 if hasattr(expression, 'prod'): ---> 639 return expression.prod(*args, **kwds) - 640 elif len(args) <= 1: - 641 return c_prod(expression, *args) - -TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(0, 0, 0, 0, 0, 0, 0) -(0, 0, 0, 0, 0, 0, 0) x^7 -x^7 ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [78], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :23, in  - -AttributeError: 'as_cover' object has no attribute 'a_number' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(0, 0, 0, 0, 0, 0, 0) -(0, 0, 0, 0, 0, 0, 0) x^7 -x^7 -x^7 -2 -(0, 0, 0, 0, 0, 0, 1) -(0, 0, 0, 0, 0, 0, 1) x^7 -x^7 -x^7 -2 -(0, 0, 0, 0, 0, 0, 2) -(0, 0, 0, 0, 0, 0, 2) x^7 -x^7 -x^7 -2 -(0, 0, 0, 0, 0, 1, 0) -(0, 0, 0, 0, 0, 1, 0) x^7 -x^7 + x^5 -x^7 + x^5 -3 -(0, 0, 0, 0, 0, 1, 1) -(0, 0, 0, 0, 0, 1, 1) x^7 -x^7 + x^5 -x^7 + x^5 -3 -(0, 0, 0, 0, 0, 1, 2) -(0, 0, 0, 0, 0, 1, 2) x^7 -x^7 + x^5 -x^7 + x^5 -3 -(0, 0, 0, 0, 0, 2, 0) -(0, 0, 0, 0, 0, 2, 0) x^7 -x^7 + 2*x^5 -x^7 + 2*x^5 -3 -(0, 0, 0, 0, 0, 2, 1) -(0, 0, 0, 0, 0, 2, 1) x^7 -x^7 + 2*x^5 -x^7 + 2*x^5 -3 -(0, 0, 0, 0, 0, 2, 2) -(0, 0, 0, 0, 0, 2, 2) x^7 -x^7 + 2*x^5 -x^7 + 2*x^5 -3 -(0, 0, 0, 0, 1, 0, 0) -(0, 0, 0, 0, 1, 0, 0) x^7 -x^7 + x^4 -x^7 + x^4 -2 -(0, 0, 0, 0, 1, 0, 1) -(0, 0, 0, 0, 1, 0, 1) x^7 -x^7 + x^4 -x^7 + x^4 -2 -(0, 0, 0, 0, 1, 0, 2) -(0, 0, 0, 0, 1, 0, 2) x^7 -x^7 + x^4 -x^7 + x^4 -2 -(0, 0, 0, 0, 1, 1, 0) -(0, 0, 0, 0, 1, 1, 0) x^7 -x^7 + x^5 + x^4 -x^7 + x^5 + x^4 -3 -(0, 0, 0, 0, 1, 1, 1) -(0, 0, 0, 0, 1, 1, 1) x^7 -x^7 + x^5 + x^4 -^Csage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z' - """ -sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z' - """ ---------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [79], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :22, in  - -File :44, in __init__(self, C, list_of_fcts, prec) - -File :167, in artin_schreier_transform(power_series, prec) - -File :12, in new_reverse(power_series, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1829 if x: - 1830 raise ValueError("must not specify %s keyword and positional argument" % name) --> 1831 a = self(kwds[name]) - 1832 del kwds[name] - 1833 try: - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1850 x = x[0] - 1851 --> 1852 return self.__u(*x)*(x[0]**self.__n) - 1853 - 1854 def __pari__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__() - 363 x[0] = a - 364 x = tuple(x) ---> 365 return self.__f(x) - 366 - 367 def _unsafe_mutate(self, i, value): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:332, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__call__() - 330 nmod_poly_compose(&t.x, &self.x, &y.x) - 331 return t ---> 332 return Polynomial.__call__(self, *x, **kwds) - 333 - 334 @coerce_binop - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() - 896 return result - 897 pol._compiled = CompiledPolynomialFunction(pol.list()) ---> 898 return pol._compiled.eval(a) - 899 - 900 def compose_trunc(self, Polynomial other, long n): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval() - 123 cdef object temp - 124 try: ---> 125 pd_eval(self._dag, x, self._coeffs) #see further down - 126 temp = self._dag.value #for an explanation - 127 pd_clean(self._dag) #of these 3 lines - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - - [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (42 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (41 times)] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) ---> 509 self.value = self.left.value * self.right.value + coeffs[self.index] - 510 pd_clean(self.left) - 511 pd_clean(self.right) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__() - 1512 cdef int cl = classify_elements(left, right) - 1513 if HAVE_SAME_PARENT(cl): --> 1514 return (left)._mul_(right) - 1515 if BOTH_ARE_ELEMENT(cl): - 1516 return coercion_model.bin_op(left, right, mul) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_() - 911 cdef LaurentSeries right = right_r - 912 return type(self)(self._parent, ---> 913 self.__u * right.__u, - 914 self.__n + right.__n) - 915 - -File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__() - 1512 cdef int cl = classify_elements(left, right) - 1513 if HAVE_SAME_PARENT(cl): --> 1514 return (left)._mul_(right) - 1515 if BOTH_ARE_ELEMENT(cl): - 1516 return coercion_model.bin_op(left, right, mul) - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_() - 538 """ - 539 prec = self._mul_prec(right_r) ---> 540 return PowerSeries_poly(self._parent, - 541 self.__f * (right_r).__f, - 542 prec=prec, - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() - 42 ValueError: series has negative valuation - 43 """ ----> 44 R = parent._poly_ring() - 45 if isinstance(f, Element): - 46 if (f)._parent is R: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) - 958 pass - 959 return False ---> 961 def _poly_ring(self): - 962 """ - 963  Return the underlying polynomial ring used to represent elements of - 964  this power series ring. - (...) - 970  Univariate Polynomial Ring in t over Integer Ring - 971  """ - 972 return self.__poly_ring - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lx^7 -x^7 -2 -x^7 -x^7 -2 -x^7 -x^7 -2 -x^7 + x^5 -x^7 + x^5 -3 -x^7 + x^5 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [80], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :21, in  - -File :313, in a_number(self) - -File :155, in cartier_matrix(self, prec) - -File :70, in coordinates(self, basis) - -File :137, in holomorphic_differentials_basis(self, threshold) - -File :423, in holomorphic_combinations(S) - -File :45, in __add__(self, other) - -File :10, in __init__(self, C, g) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:647, in PolynomialRing(base_ring, *args, **kwds) - 644 raise TypeError("variable names specified twice inconsistently: %r and %r" % (names, kwnames)) - 646 if multivariate or len(names) != 1: ---> 647 return _multi_variate(base_ring, names, **kwds) - 648 else: - 649 return _single_variate(base_ring, names, **kwds) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:762, in _multi_variate(base_ring, names, sparse, order, implementation) - 760 from sage.rings.polynomial.term_order import TermOrder - 761 n = len(names) ---> 762 order = TermOrder(order, n) - 764 # "implementation" must be last - 765 key = [base_ring, names, n, order, implementation] - -File /ext/sage/9.7/src/sage/rings/polynomial/term_order.py:796, in TermOrder.__init__(self, name, n, force) - 794 self._singular_str = singular_name_mapping.get(name,name) - 795 self._macaulay2_str = macaulay2_name_mapping.get(name,name) ---> 796 self._magma_str = magma_name_mapping.get(name,name) - 797 else: # len(block_names) > 1, and hence block order represented by a string - 798 length = 0 - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lx^7 -x^7 4 -x^7 -x^7 4 -x^7 -x^7 4 -x^7 + x^5 -x^7 + x^5 3 -x^7 + x^5 -x^7 + x^5 3 -x^7 + x^5 -x^7 + x^5 3 -x^7 + 2*x^5 -x^7 + 2*x^5 3 -x^7 + 2*x^5 -x^7 + 2*x^5 3 -x^7 + 2*x^5 -x^7 + 2*x^5 3 -x^7 + x^4 -x^7 + x^4 4 -x^7 + x^4 -x^7 + x^4 4 -x^7 + x^4 -x^7 + x^4 4 -x^7 + x^5 + x^4 -x^7 + x^5 + x^4 3 -x^7 + x^5 + x^4 -x^7 + x^5 + x^4 3 -x^7 + x^5 + x^4 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [81], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :21, in  - -File :313, in a_number(self) - -File :155, in cartier_matrix(self, prec) - -File :139, in cartier(self) - -File :60, in cartier(self) - -File :15, in __add__(self, other) - -File :217, in reduction(C, g) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:649, in PolynomialRing(base_ring, *args, **kwds) - 647 return _multi_variate(base_ring, names, **kwds) - 648 else: ---> 649 return _single_variate(base_ring, names, **kwds) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:683, in _single_variate(base_ring, name, sparse, implementation, order) - 681 # "implementation" must be last - 682 key = [base_ring, name, sparse, implementation] ---> 683 R = _get_from_cache(key) - 684 if R is not None: - 685 return R - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:668, in _get_from_cache(key) - 666 def _get_from_cache(key): - 667 key = tuple(key) ---> 668 return _cache.get(key) - -File /ext/sage/9.7/src/sage/misc/weak_dict.pyx:662, in sage.misc.weak_dict.WeakValueDictionary.get() - 660 - 661 """ ---> 662 cdef PyObject * wr = PyDict_GetItemWithError(self, k) - 663 if wr == NULL: - 664 return d - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:783, in FractionField_generic.__hash__(self) - 769 """ - 770 Compute the hash of ``self``. - 771 - (...) - 779  True - 780 """ - 781 # to avoid having exactly the same hash as the base ring, - 782 # we change this hash using a random number ---> 783 return hash(self._R) ^ 147068341996611 - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lx^7 4 -x^7 4 -x^7 4 -x^7 + x^5 3 -x^7 + x^5 3 -x^7 + x^5 3 -x^7 + 2*x^5 3 -x^7 + 2*x^5 3 -x^7 + 2*x^5 3 -x^7 + x^4 4 -x^7 + x^4 4 -x^7 + x^4 4 -x^7 + x^5 + x^4 3 -x^7 + x^5 + x^4 3 -x^7 + x^5 + x^4 3 -x^7 + 2*x^5 + x^4 3 -x^7 + 2*x^5 + x^4 3 -x^7 + 2*x^5 + x^4 3 -x^7 + 2*x^4 4 -x^7 + 2*x^4 4 -x^7 + 2*x^4 4 -x^7 + x^5 + 2*x^4 3 -x^7 + x^5 + 2*x^4 3 -x^7 + x^5 + 2*x^4 3 -x^7 + 2*x^5 + 2*x^4 3 -x^7 + 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2*x^4 + x^2 3 -x^7 + x^5 + 2*x^4 + x^2 3 -x^7 + 2*x^5 + 2*x^4 + x^2 3 -x^7 + 2*x^5 + 2*x^4 + x^2 3 -x^7 + 2*x^5 + 2*x^4 + x^2 3 -x^7 + x^2 4 -x^7 + x^2 4 -x^7 + x^2 4 -x^7 + x^5 + x^2 3 -x^7 + x^5 + x^2 3 -x^7 + x^5 + x^2 3 -x^7 + 2*x^5 + x^2 3 -x^7 + 2*x^5 + x^2 3 -x^7 + 2*x^5 + x^2 3 -x^7 + x^4 + x^2 4 -x^7 + x^4 + x^2 4 -x^7 + x^4 + x^2 4 -x^7 + x^5 + x^4 + x^2 3 -x^7 + x^5 + x^4 + x^2 3 -x^7 + x^5 + x^4 + x^2 3 -x^7 + 2*x^5 + x^4 + x^2 3 -x^7 + 2*x^5 + x^4 + x^2 3 -x^7 + 2*x^5 + x^4 + x^2 3 -x^7 + 2*x^4 + x^2 4 -x^7 + 2*x^4 + x^2 4 -x^7 + 2*x^4 + x^2 4 -x^7 + x^5 + 2*x^4 + x^2 3 -x^7 + x^5 + 2*x^4 + x^2 3 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [82], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :44, in __init__(self, C, list_of_fcts, prec) - -File :167, in artin_schreier_transform(power_series, prec) - -File :12, in new_reverse(power_series, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1829 if x: - 1830 raise ValueError("must not specify %s keyword and positional argument" % name) --> 1831 a = self(kwds[name]) - 1832 del kwds[name] - 1833 try: - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1850 x = x[0] - 1851 --> 1852 return self.__u(*x)*(x[0]**self.__n) - 1853 - 1854 def __pari__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__() - 363 x[0] = a - 364 x = tuple(x) ---> 365 return self.__f(x) - 366 - 367 def _unsafe_mutate(self, i, value): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:332, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__call__() - 330 nmod_poly_compose(&t.x, &self.x, &y.x) - 331 return t ---> 332 return Polynomial.__call__(self, *x, **kwds) - 333 - 334 @coerce_binop - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() - 896 return result - 897 pol._compiled = CompiledPolynomialFunction(pol.list()) ---> 898 return pol._compiled.eval(a) - 899 - 900 def compose_trunc(self, Polynomial other, long n): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval() - 123 cdef object temp - 124 try: ---> 125 pd_eval(self._dag, x, self._coeffs) #see further down - 126 temp = self._dag.value #for an explanation - 127 pd_clean(self._dag) #of these 3 lines - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - - [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (9 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (8 times)] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) ---> 509 self.value = self.left.value * self.right.value + coeffs[self.index] - 510 pd_clean(self.left) - 511 pd_clean(self.right) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__() - 1512 cdef int cl = classify_elements(left, right) - 1513 if HAVE_SAME_PARENT(cl): --> 1514 return (left)._mul_(right) - 1515 if BOTH_ARE_ELEMENT(cl): - 1516 return coercion_model.bin_op(left, right, mul) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_() - 911 cdef LaurentSeries right = right_r - 912 return type(self)(self._parent, ---> 913 self.__u * right.__u, - 914 self.__n + right.__n) - 915 - -File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__() - 1512 cdef int cl = classify_elements(left, right) - 1513 if HAVE_SAME_PARENT(cl): --> 1514 return (left)._mul_(right) - 1515 if BOTH_ARE_ELEMENT(cl): - 1516 return coercion_model.bin_op(left, right, mul) - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_() - 538 """ - 539 prec = self._mul_prec(right_r) ---> 540 return PowerSeries_poly(self._parent, - 541 self.__f * (right_r).__f, - 542 prec=prec, - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() - 42 ValueError: series has negative valuation - 43 """ ----> 44 R = parent._poly_ring() - 45 if isinstance(f, Element): - 46 if (f)._parent is R: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) - 958 pass - 959 return False ---> 961 def _poly_ring(self): - 962 """ - 963  Return the underlying polynomial ring used to represent elements of - 964  this power series ring. - (...) - 970  Univariate Polynomial Ring in t over Integer Ring - 971  """ - 972 return self.__poly_ring - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.a_number()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 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((C.y)^3/(C.x)^4).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-1 + O(t^19) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^3/(C.x)^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y)^3/(C.x)^4[?7h[?12l[?25h[?25l[?7l(C.y)^3/(C.x)^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^3/(C.x)^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7lf((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l=((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7lsage: ff = ((C.y)^3/(C.x)^4) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ff -[?7h[?12l[?25h[?2004l[?7h((x^2 + 2)/x^3)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff[?7h[?12l[?25h[?25l[?7l = ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: ff = ((C.y)^3/(C.x)^2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ((C.y)^3/(C.x)^2)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^-1 + 2*t^3 + 2*t^7 + t^11 + O(t^15) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ff -[?7h[?12l[?25h[?2004l[?7h((x^2 + 2)/x)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.base_ring[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.base_ring[?7h[?12l[?25h[?25l[?7lfrobenus_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis()[0] -[?7h[?12l[?25h[?2004l[?7h(1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50) -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = PolynomialRing(ZZ)[?7h[?12l[?25h[?25l[?7lsage: R. = PolynomialRing(ZZ) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff[?7h[?12l[?25h[?25l[?7l = superelliptic_function(C, y/x)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^n + a[0][?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3-x[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: f = x^3 - x -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = PolynomialRing(ZZ)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = hypellfrob(p, 1, f)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 1, f)[?7h[?12l[?25h[?25l[?7l3, 1, f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = hypellfrob(3, 1, f) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [105], in () -----> 1 M = hypellfrob(Integer(3), Integer(1), f) - -NameError: name 'hypellfrob' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrom sage.schemes.hyperelliptic_curves.hypellfrob import hypellfrob[?7h[?12l[?25h[?25l[?7lsage: from sage.schemes.hyperelliptic_curves.hypellfrob import hypellfrob -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrom sage.schemes.hyperelliptic_curves.hypellfrob import hypellfrob[?7h[?12l[?25h[?25l[?7lM = hypellfrob(3, 1, f)[?7h[?12l[?25h[?25l[?7lsage: M = hypellfrob(3, 1, f) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [107], in () -----> 1 M = hypellfrob(Integer(3), Integer(1), f) - -File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hypellfrob.pyx:238, in sage.schemes.hyperelliptic_curves.hypellfrob.hypellfrob() - 236 bound = (len(Q) - 1) * (2*N - 1) - 237 if p <= bound: ---> 238 raise ValueError("In the current implementation, p must be greater " - 239 "than (2g+1)(2N-1) = %s" % bound) - 240 - -ValueError: In the current implementation, p must be greater than (2g+1)(2N-1) = 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.discriminant().factor()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lbase_rng[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C. - C.a_number C.basis_of_cohomology C.degrees_de_rham0  - C.base_ring C.cartier_matrix C.degrees_de_rham1  - C.basis_de_rham_degrees C.characteristic C.degrees_holomorphic_differentials > - C.basis_holomorphic_differentials_degree C.de_rham_basis C.dr_frobenius_matrix  - [?7h[?12l[?25h[?25l[?7la_number - C.a_number  - - - - [?7h[?12l[?25h[?25l[?7lbasis_of_cohomology - C.a_number  C.basis_of_cohomology [?7h[?12l[?25h[?25l[?7l() - - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.basis_of_cohomology() -[?7h[?12l[?25h[?2004l[?7h[2/x*y] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg = (C.y)/(C.x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - - [?7h[?12l[?25h[?25l[?7lgg = (C.y)/(C.x)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7log^8*[?7h[?12l[?25h[?25l[?7lmg^8*[?7h[?12l[?25h[?25l[?7l g^8*[?7h[?12l[?25h[?25l[?7l=g^8*[?7h[?12l[?25h[?25l[?7l g^8*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lfn[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = gg^8*gg.diffn() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lom = gg^8*gg.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion_at_ifty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t^-10 + 2*t^-6 + t^-2 + O(1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 30) -[?7h[?12l[?25h[?2004l[?7h2*t^-10 + 2*t^-6 + t^-2 + t^2 + 2*t^6 + t^10 + O(t^20) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lsage: v -[?7h[?12l[?25h[?2004l[?7h1/x^2*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lY[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lv)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: C.y*v*(v - C.y) -[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om -[?7h[?12l[?25h[?2004l[?7h((-x^10 + x^6 + x^4 - 1)/(x^5*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y*v*(v - C.y)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l.C.dx[?7h[?12l[?25h[?25l[?7lxC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.xC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l.C.dx[?7h[?12l[?25h[?25l[?7lyC.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l()^C.dx[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l-C.dx[?7h[?12l[?25h[?25l[?7l1C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l()*C.dx[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.y)^(-1)*C.dx -[?7h[?12l[?25h[?2004l[?7h(1/(x*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l1(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l (C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l=(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l (C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = (C.x*C.y)^(-1)*C.dx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = (C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.jth_component(3[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + O(t^12) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[1] -3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y*v*(v - C.y)[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y*v*(v - C.y)[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -[1] -3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^3 - x^2 - x + 1)/(x^3*y)) dx -[1] -3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -[1] -3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -[1] -3*X^18 + 2*X^16 - X^15 + 2*X^14 + 3*X^13 + 2*X^12 - 3*X^11 + 2*X^10 - X^9 + 2*X^8 + 6*X^7 + 2*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -[1] -3*X^18 + 2*X^16 - 2*X^15 + 2*X^14 + 6*X^13 + 2*X^12 - 6*X^11 + 2*X^10 - 2*X^9 + 2*X^8 + 12*X^7 + 2*X^6 - 12*X^5 + 2*X^4 + 4*X^3 + 2*X^2 - 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -[1] -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: (-10)%3 -[?7h[?12l[?25h[?2004l[?7h2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-10)%3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: (3/2)%9 -[?7h[?12l[?25h[?2004l[?7h6 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3/2)%9[?7h[?12l[?25h[?25l[?7lC.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x/C.y).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1621228612.factor()[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 19/3-4 -[?7h[?12l[?25h[?2004l[?7h7/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l19/3-4[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 17/3-4 -[?7h[?12l[?25h[?2004l[?7h5/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l17/3-4[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 13/3-4 -[?7h[?12l[?25h[?2004l[?7h1/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l13/3-4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 11/3-4 -[?7h[?12l[?25h[?2004l[?7h-1/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7/3-3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 7/3-4 -[?7h[?12l[?25h[?2004l[?7h-5/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5/3-3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 5/3-4 -[?7h[?12l[?25h[?2004l[?7h-7/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -[1] -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -[1] -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -[0] -[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor m in range(1, p^2):[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f2.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-11 + 2*t^-7 + 2*t^-3 + t + 2*t^5 + O(t^9) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: f2 -[?7h[?12l[?25h[?2004l[?7h(x^8/(x^4 + x^2 + 1))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2[?7h[?12l[?25h[?25l[?7l1 = superelliptic_function(C_super, 1)[?7h[?12l[?25h[?25l[?7lsage: f1 -[?7h[?12l[?25h[?2004l[?7h((x^10 + 2*x^2 + 2)/(x^6 + 2*x^4))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.y)/(C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRHS = ceil(m*(k+1)/p) - ceil(m*k/p)[?7h[?12l[?25h[?25l[?7lxy. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. = PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(3)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.y)/(C.x)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp = 5[?7h[?12l[?25h[?25l[?7lrint(LHS == RHS)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l8)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: print((x^8).quo_rem(x^4 + x^2 + 1)) -[?7h[?12l[?25h[?2004l(x^4 + 2*x^2, x^2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2/(C.y)*(C.dx)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7lg(C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l (C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l=(C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l (C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [26], in () -----> 1 gg = (C.x)**Integer(2)*C.y/((C.y)**Integer(4) + (C.y)**Integer(2) + Integer(1)) - -File :38, in __add__(self, other) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -[1] -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [1], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :14, in  - -NameError: name 'g' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7lor m in range(1, p^2):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: forma -[?7h[?12l[?25h[?2004l[?7h((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: forma.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t^-8 + 2*t^-4 + O(t^2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: forma.expansion_at_infty(prec=30) -[?7h[?12l[?25h[?2004l[?7h2*t^-8 + 2*t^-4 + 2*t^4 + 2*t^8 + O(t^22) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: forma -[?7h[?12l[?25h[?2004l[?7h((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [6] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :25 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :14 - forma2 = ((xx**_sage_const_4 + xx**_sage_const_2 + C.one)/(xx**_sage_const_6 *C.y)) C.dx - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [7], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :16, in  - -NameError: name 'g' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: forma1 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [8], in () -----> 1 forma1 - -NameError: name 'forma1' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: forma2 -[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)/(x^6*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: forma2.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^4 + t^8 + O(t^14) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: forma2 -[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)/(x^6*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [12], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :16, in  - -NameError: name 'g' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [13], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File :38, in __add__(self, other) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx^11)quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^10 - x^6 + 1).quo_rem(x^2 - 1) -[?7h[?12l[?25h[?2004l[?7h(x^8 + x^6, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^10 - x^6 + 1).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l^).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l8).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l+).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7lx).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l^).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l6).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - 1)[?7h[?12l[?25h[?25l[?7l3 - 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lsage: (x^8+x^6).quo_rem(x^3 - x) -[?7h[?12l[?25h[?2004l[?7h(x^5 + 2*x^3 + 2*x, 2*x^2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^11, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc_expansion(x^11, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l8, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7l+, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l6, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^8 + x^6, x^3 - x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [17], in () -----> 1 adic_expansion(x**Integer(8) + x**Integer(6), x**Integer(3) - x) - -NameError: name 'adic_expansion' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lfty/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft - drafty/draft.sage drafty/draft4.sage - drafty/draft2.sage drafty/draft5.sage - drafty/draft3.sage drafty/draft6.sage - - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage - drafty/draft.sage  - - - [?7h[?12l[?25h[?25l[?7l2.sage - drafty/draft.sage  - drafty/draft2.sage[?7h[?12l[?25h[?25l[?7l3 - - drafty/draft2.sage - drafty/draft3.sage[?7h[?12l[?25h[?25l[?7l4 - drafty/draft4.sage - - drafty/draft3.sage[?7h[?12l[?25h[?25l[?7l5 - drafty/draft4.sage - drafty/draft5.sage[?7h[?12l[?25h[?25l[?7l' - - - -[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) -[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7ladic_expansion(x^8 + x^6, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^8 + x^6, x^3 - x) -[?7h[?12l[?25h[?2004l[?7h[x^2, 2*x, 2*x^2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx^11/(C.y)^3*C.dx -[?7h[?12l[?25h[?2004l[?7h(x^10/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^11/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^11/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xx^9*C.y*C.y*C.y.diffn() -[?7h[?12l[?25h[?2004l[?7h((x^12 - x^10)/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^8+x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7ld(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7li(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7lc(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7l_(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7le(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7lx(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7lp(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7la(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7ln(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7ls(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7li(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7lo(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7ln(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^9*(x^3-x)^2 - x^4 - x^2 - 1, x^3 - x) -[?7h[?12l[?25h[?2004l[?7h[1, 0, 1, x, 2*x, x^2 + 2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ losage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l11/3-4[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 19/3-4 -[?7h[?12l[?25h[?2004l[?7h7/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l19/3-4[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l/3-4[?7h[?12l[?25h[?25l[?7lsage: 17/3-4 -[?7h[?12l[?25h[?2004l[?7h5/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l17/3-4[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/3-4[?7h[?12l[?25h[?25l[?7lsage: 13/3-4 -[?7h[?12l[?25h[?2004l[?7h1/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l13/3-4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/3-4[?7h[?12l[?25h[?25l[?7lsage: 11/3-4 -[?7h[?12l[?25h[?2004l[?7h-1/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7/3-4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3-4[?7h[?12l[?25h[?25l[?7lsage: 7/3-4 -[?7h[?12l[?25h[?2004l[?7h-5/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5/3-4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3-4[?7h[?12l[?25h[?25l[?7lsage: 5/3-4 -[?7h[?12l[?25h[?2004l[?7h-7/3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma2[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: forma -[?7h[?12l[?25h[?2004l[?7h((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7lsage: forma.expansion_at_infty(prec=30) -[?7h[?12l[?25h[?2004l[?7h2*t^-8 + 2*t^-4 + 2*t^4 + 2*t^8 + t^16 + t^20 + O(t^22) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [11], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :25, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :31, in  - -File /ext/sage/9.7/src/sage/structure/element.pyx:4496, in sage.structure.element.coerce_binop.new_method() - 4494 return method(self, other, *args, **kwargs) - 4495 else: --> 4496 a, b = coercion_model.canonical_coercion(self, other) - 4497 if a is self: - 4498 return method(a, b, *args, **kwargs) - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1393, in sage.structure.coerce.CoercionModel.canonical_coercion() - 1391 self._record_exception() - 1392 --> 1393 raise TypeError("no common canonical parent for objects with parents: '%s' and '%s'"%(xp, yp)) - 1394 - 1395 - -TypeError: no common canonical parent for objects with parents: 'Univariate Polynomial Ring in x over Finite Field of size 3' and 'Univariate Polynomial Ring in X over Rational Field' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^8+x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^7+x).quo_rem(x^3 - x) -[?7h[?12l[?25h[?2004l[?7h(x^4 + x^2 + 1, 2*x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lff.cartier()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: ffffff = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffffff.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-11 + t^-7 + 2*t^-3 + 2*t + t^5 + O(t^9) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffffff.coordinates() -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7l(x^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lffffff = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: fg = (xx^7+xx)/yy -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg = (xx^7+xx)/yy[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fg.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-11 + t^-7 + 2*t^-3 + 2*t + t^5 + O(t^9) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7linates[?7h[?12l[?25h[?25l[?7l*()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fg.coordinates() -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (xx^7+xx)/yy[?7h[?12l[?25h[?25l[?7lfffff.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7l(x^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: (x^7+x).quo_rem(x^3 - x) -[?7h[?12l[?25h[?2004l[?7h(x^4 + x^2 + 1, 2*x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = (xx^7+xx)/yy[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fg = xx*yy/(xx^3 - xx) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg = xx*yy/(xx^3 - xx)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: fg.coordinates() -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: fg.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l-10)%3[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - 1[?7h[?12l[?25h[?25l[?7l2 - 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (-x^6 - 1).quo_rem(x^2 - 1) -[?7h[?12l[?25h[?2004l[?7h(2*x^4 + 2*x^2 + 2, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1;3S[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) -[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: G = 2*x^9*(x^3 - x)+2*x^4+2*x^2+2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG = 2*x^9*(x^3 - x)+2*x^4+2*x^2+2[?7h[?12l[?25h[?25l[?7lsage: G -[?7h[?12l[?25h[?2004l[?7h2*x^12 + x^10 + 2*x^4 + 2*x^2 + 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^9*(x^3-x)^2 - x^4 - x^2 - 1, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion(x^9*(x^3-x)^2 - x^4 - x^2 - 1, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lG, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(G, x^3 - x) -[?7h[?12l[?25h[?2004l[?7h[2, 0, 2, x, x^2 + 2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lsage: G -[?7h[?12l[?25h[?2004l[?7h2*x^12 + x^10 + 2*x^4 + 2*x^2 + 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l = 2*x^9*(x^3 - x)+2*x^4+2*x^2+2[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0].function).denominator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7lsage: G1 = G - 2*x^4 + 2*x^6\ -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG1 = G - 2*x^4 + 2*x^6\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(G, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(G1, x^3 - x) -[?7h[?12l[?25h[?2004l[?7h[2, 0, 1, 0, x^2 + 2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(G1, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l4, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7l+, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l2, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^4 + x^2, x^3 - x) -[?7h[?12l[?25h[?2004l[?7h[x, 2*x^2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lGx9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l x9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l=x9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l x9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l* + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l( + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7lx + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l^ + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l3 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l- + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7lx + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l() + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: G = x^9*(x^3 - x) + x^4 + x^2 + 1 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG = x^9*(x^3 - x) + x^4 + x^2 + 1[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lsage: G(x+1) - G -[?7h[?12l[?25h[?2004l[?7h2*x^3 + 2*x + 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG(x+1) - G[?7h[?12l[?25h[?25l[?7l1 = G2*x^4 + 2*x^6\[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2x4 + 2x2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: G1 = 2*x^4 + 2*x^2 + 2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG1 = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lsage: G1(x+1) - G -[?7h[?12l[?25h[?2004l[?7h2*x^12 + x^10 + x^4 + 2*x^3 + x^2 + 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG1(x+1) - G[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: G1(x+1) - G1 -[?7h[?12l[?25h[?2004l[?7h2*x^3 + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l = len(Ifactors)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^3/(x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+1)^2) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [15], in () -----> 1 g = yy**Integer(3)/(xx*(xx+Integer(1))**Integer(2)) - -File :38, in __add__(self, other) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+1)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)^2)[?7h[?12l[?25h[?25l[?7lC)^2)[?7h[?12l[?25h[?25l[?7l.)^2)[?7h[?12l[?25h[?25l[?7lo)^2)[?7h[?12l[?25h[?25l[?7ln)^2)[?7h[?12l[?25h[?25l[?7le)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l.coordinates)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l2*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx^2*(xx+C.one)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx - yy/(xx+1) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [20], in () -----> 1 g = yy/xx - yy/(xx+Integer(1)) - -File :38, in __add__(self, other) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx - yy/(xx+1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC1)[?7h[?12l[?25h[?25l[?7l.1)[?7h[?12l[?25h[?25l[?7l.o1)[?7h[?12l[?25h[?25l[?7ln1)[?7h[?12l[?25h[?25l[?7le1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx - yy/(xx+C.one) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7h(1/(x^2 + x))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^5 + 2*t^9 + t^17 + O(t^25) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx^2*(xx+C.one)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + x^2))*y^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^3 + t^7 + t^15 + 2*t^19 + O(t^23) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + 2*x^2 + x))*y^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lini[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx^2*(xx+C.one)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l+ y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-y^3/(x^2*(x+C.one) + y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l y^3/(x^2*(x+C.one) + y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = - yy^3/(xx^2*(xx+C.one)) + yy^3/(xx*(xx+C.one)^2) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [38], in () -----> 1 g = - yy**Integer(3)/(xx**Integer(2)*(xx+C.one)) + yy**Integer(3)/(xx*(xx+C.one)**Integer(2)) - -TypeError: bad operand type for unary -: 'superelliptic_function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = - yy^3/(xx^2*(xx+C.one)) + yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l()y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l(()y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l(y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()-[?7h[?12l[?25h[?25l[?7lyy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l. = PolynomialRing(ZZ)[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7llRing(ZZ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: R. = PolynomialRing(GF(3)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: g = 2*x^4 + 2*x^2 + 2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g -[?7h[?12l[?25h[?2004l[?7h2*x^3 + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^(f.degree())*f(1/x)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: g = x^4 +x^2 + 1 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1) - g[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g -[?7h[?12l[?25h[?2004l[?7hx^3 + 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = x^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = x^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx - yy/(xx+C.one) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7l/(x+C.one)[?7h[?12l[?25h[?25l[?7l/(x+C.one)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^/(x+C.one)[?7h[?12l[?25h[?25l[?7l2/(x+C.one)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()&[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * y/x - yy/(xx+C.one) * yy^2/xx^2 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [9], in () -----> 1 g = yy**Integer(2)/(xx+C.one)**Integer(2) * y/x - yy/(xx+C.one) * yy**Integer(2)/xx**Integer(2) - -NameError: name 'y' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * y/x - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l.expansion_at_ifty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t^-1 + 2*t + 2*t^5 + t^7 + t^9 + t^11 + t^13 + 2*t^15 + 2*t^17 + O(t^19) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g - yy/xxx -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [14], in () -----> 1 g - yy/xxx - -NameError: name 'xxx' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - yy/xxx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g - yy/xx -[?7h[?12l[?25h[?2004l[?7h(1/(x + 1))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - yy/xx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g - y/x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - yy/xxx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y/x[?7h[?12l[?25h[?25l[?7l+ y/x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g + yy/xx -[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg + yy/xx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g + y/x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (g + yy/xx).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t + t^3 + 2*t^5 + t^9 + t^13 + 2*t^17 + O(t^21) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgy/x[?7h[?12l[?25h[?25l[?7lgy/x[?7h[?12l[?25h[?25l[?7l y/x[?7h[?12l[?25h[?25l[?7l=y/x[?7h[?12l[?25h[?25l[?7l y/x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg = yy/xx - yy/(xx + C.one) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = yy/xx - yy/(xx + C.one)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + yy/xx[?7h[?12l[?25h[?25l[?7l=^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly^2/(x+1)^2 \cdot y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^2/(x+1)^2 \cdot y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx+1)^2 \cdot y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l* y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ly/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7lC) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l.) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7lo) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7ln) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7le) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l* y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+1)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [21], in () -----> 1 g = yy**Integer(2)/(xx+Integer(1))**Integer(2) * yy/xx - yy/(xx+C.one) * yy**Integer(2)/xx**Integer(2) - -File :38, in __add__(self, other) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+1)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7lC)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l.)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7lo)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7ln)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7le)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lordinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l+/xx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7lsage: g + yy/xx -[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg + yy/xx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g + y/x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (g + yy/xx).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t + t^3 + 2*t^5 + t^9 + t^13 + 2*t^17 + O(t^21) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g + yy/xx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: (x+1)^5 - x^5 -[?7h[?12l[?25h[?2004l[?7h2*x^4 + x^3 + x^2 + 2*x + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) -[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l 2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l=2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l 2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* (x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = 2*x^4 + x^3 + x^2 + 2*x - x^3* (x^3 - x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*x^4 + x^3 + x^2 + 2*x - x^3* (x^3 - x)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^4 + x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lic_expansion(x^4 + x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lg, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x) -[?7h[?12l[?25h[?2004l[?7h[2, x + 1, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: yy/xx -[?7h[?12l[?25h[?2004l[?7h1/x*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^/x[?7h[?12l[?25h[?25l[?7l3/x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgy^3/x^3[?7h[?12l[?25h[?25l[?7l y^3/x^3[?7h[?12l[?25h[?25l[?7l=y^3/x^3[?7h[?12l[?25h[?25l[?7l y^3/x^3[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/xx^3 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/xx^3[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[0, 0, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^3 + O(t^23) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) -[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/xx^3[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/xx^3 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/xx^3[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-3 + t + 2*t^5 + 2*t^9 + t^13 + O(t^17) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates() -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7h((x^2 + 2)/x^2)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = hypellfrob(3, 1, f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R9 = Integers(9) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - - [?7h[?12l[?25h[?25l[?7lM = hypellfrob(3, 1, f)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lmatrix(QQ, [[1, 1], [0, 0]])[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l7]][?7h[?12l[?25h[?25l[?7l,]][?7h[?12l[?25h[?25l[?7l ]][?7h[?12l[?25h[?25l[?7l4]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l[[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l3]][?7h[?12l[?25h[?25l[?7l,]][?7h[?12l[?25h[?25l[?7l ]][?7h[?12l[?25h[?25l[?7l4]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[7, 4], [3, 4]]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3 -[?7h[?12l[?25h[?2004l[?7h[1 6] -[0 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l.transpose().image().basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.determinant() -[?7h[?12l[?25h[?2004l[?7h7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.determinant()[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l8]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[7, 4], [3, 8]]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[7, 4], [3, 8]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3 -[?7h[?12l[?25h[?2004l[?7h[4 4] -[3 5] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[7, 4], [3, 8]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[7, 4], [3, 4]]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3 -[?7h[?12l[?25h[?2004l[?7h[1 6] -[0 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^9*C.y*C.y*C.y.diffn()[?7h[?12l[?25h[?25l[?7lsage: x -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lsage: (x+1)^5 - x^5 -[?7h[?12l[?25h[?2004l[?7h2*x^4 + x^3 + x^2 + 2*x + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2+2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = yy/xx - yy/(xx + C.one)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2x^4 + x^3 + x^2 + 2x + x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l* (x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x + x^3*(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x^4 + x^3 + x^2 + 2*x + x^3*(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = 2*x^4 + x^3 + x^2 + 2*x + x^3*(x^3 - x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = 2*x^4 + x^3 + x^2 + 2*x + x^3*(x^3 - x)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: gg -[?7h[?12l[?25h[?2004l[?7hx^6 + x^4 + x^3 + x^2 + 2*x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [54], in () -----> 1 adic_expansion(g, x**Integer(3) - x) - -File :17, in adic_expansion(g, h) - -AttributeError: 'superelliptic_function' object has no attribute 'degree' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(gg, x^3 - x) -[?7h[?12l[?25h[?2004l[?7h[1, 1, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l4], [3, 4])[?7h[?12l[?25h[?25l[?7l,], [3, 4])[?7h[?12l[?25h[?25l[?7l ], [3, 4])[?7h[?12l[?25h[?25l[?7l4], [3, 4])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l6]])[?7h[?12l[?25h[?25l[?7l,]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7l3]])[?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[4, 4], [6, 4]]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3 -[?7h[?12l[?25h[?2004l[?7h[1 0] -[0 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM - iden[?7h[?12l[?25h[?25l[?7l1M - iden[?7h[?12l[?25h[?25l[?7l M - iden[?7h[?12l[?25h[?25l[?7l=M - iden[?7h[?12l[?25h[?25l[?7l M - iden[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(3) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [58], in () -----> 1 M1 = M - identity_matrix(Integer(3)) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1358, in sage.structure.element.Element.__sub__() - 1356 return (left)._sub_(right) - 1357 if BOTH_ARE_ELEMENT(cl): --> 1358 return coercion_model.bin_op(left, right, sub) - 1359 - 1360 try: - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() - 1246 # We should really include the underlying error. - 1247 # This causes so much headache. --> 1248 raise bin_op_exception(op, x, y) - 1249 - 1250 cpdef canonical_coercion(self, x, y): - -TypeError: unsupported operand parent(s) for -: 'Full MatrixSpace of 2 by 2 dense matrices over Ring of integers modulo 9' and 'Full MatrixSpace of 3 by 3 dense matrices over Integer Ring' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lG3)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7lR3)[?7h[?12l[?25h[?25l[?7l93)[?7h[?12l[?25h[?25l[?7l,3)[?7h[?12l[?25h[?25l[?7l 3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(R9, 3) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [59], in () -----> 1 M1 = M - identity_matrix(R9, Integer(3)) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1358, in sage.structure.element.Element.__sub__() - 1356 return (left)._sub_(right) - 1357 if BOTH_ARE_ELEMENT(cl): --> 1358 return coercion_model.bin_op(left, right, sub) - 1359 - 1360 try: - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() - 1246 # We should really include the underlying error. - 1247 # This causes so much headache. --> 1248 raise bin_op_exception(op, x, y) - 1249 - 1250 cpdef canonical_coercion(self, x, y): - -TypeError: unsupported operand parent(s) for -: 'Full MatrixSpace of 2 by 2 dense matrices over Ring of integers modulo 9' and 'Full MatrixSpace of 3 by 3 dense matrices over Ring of integers modulo 9' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(R9, 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(R9, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(R9, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1.kernel() -[?7h[?12l[?25h[?2004lsage/matrix/matrix_modn_dense_template.pxi:1: DeprecationWarning: invalid escape sequence '\Z' - """ -sage/matrix/matrix_modn_dense_template.pxi:1: DeprecationWarning: invalid escape sequence '\Z' - """ ---------------------------------------------------------------------------- -NotImplementedError Traceback (most recent call last) -Input In [61], in () -----> 1 M1.kernel() - -File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:5032, in sage.matrix.matrix2.Matrix.left_kernel() - 5030 - 5031 tm = verbose("computing left kernel for %sx%s matrix" % (self.nrows(), self.ncols()),level=1) --> 5032 K = self.transpose().right_kernel(*args, **kwds) - 5033 self.cache('left_kernel', K) - 5034 verbose("done computing left kernel for %sx%s matrix" % (self.nrows(), self.ncols()),level=1,t=tm) - -File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:4870, in sage.matrix.matrix2.Matrix.right_kernel() - 4868 - 4869 # Go get the kernel matrix, this is where it all happens --> 4870 M = self.right_kernel_matrix(*args, **kwds) - 4871 - 4872 ambient = R**self.ncols() - -File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:1897, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.right_kernel_matrix() - 1895 """ - 1896 if self.fetch('in_echelon_form') is None: --> 1897 self = self.echelon_form(algorithm=algorithm) - 1898 - 1899 cdef Py_ssize_t r = self.rank() - -File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:7729, in sage.matrix.matrix2.Matrix.echelon_form() - 7727 v = E.echelonize(cutoff=cutoff, **kwds) - 7728 else: --> 7729 v = E.echelonize(algorithm = algorithm, cutoff=cutoff, **kwds) - 7730 E.set_immutable() # so we can cache the echelon form. - 7731 self.cache('echelon_form', E) - -File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:1725, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.echelonize() - 1723 - 1724 if not self.base_ring().is_field(): --> 1725 raise NotImplementedError("Echelon form not implemented over '%s'."%self.base_ring()) - 1726 - 1727 if algorithm == 'linbox': - -NotImplementedError: Echelon form not implemented over 'Ring of integers modulo 9'. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1.kernel()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: M1 -[?7h[?12l[?25h[?2004l[?7h[3 4] -[6 3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.kernel()[?7h[?12l[?25h[?25l[?7lsage: M1.kernel() - M1.C M1.QR M1.add_multiple_of_row M1.adjoint_classical  - M1.H M1.T M1.add_to_entry M1.adjugate  - M1.LLL_gram M1.act_on_polynomial M1.additive_order M1.anticommutator > - M1.LU M1.add_multiple_of_column M1.adjoint M1.antitranspose  - [?7h[?12l[?25h[?25l[?7lC - M1.C  - - - - [?7h[?12l[?25h[?25l[?7lQR - M1.C  M1.QR [?7h[?12l[?25h[?25l[?7ladd_multiple_of_row - M1.QR  M1.add_multiple_of_row [?7h[?12l[?25h[?25l[?7ljoint_classical - M1.add_multiple_of_row  M1.adjoint_classical [?7h[?12l[?25h[?25l[?7lpply_map - QRadd_multiple_of_rowjoint_classical pply_map  - Tadd_to_entryjugat pply_morphism -<acton_polynomialdditive_order ntcommutatos_bipartite_graph - add_multiple_of_columnjoint ntitransposes_sum_of_permutations[?7h[?12l[?25h[?25l[?7lugment -add_multiple_of_rowjoint_classical pply_map ugment  -add_to_entryjugat pply_morphismutomorphism_of_rows_and_columns -dditive_order ntcommutatos_bipartite_graphbase_extend  -joint ntitransposes_sum_of_permutationsbase_ring [?7h[?12l[?25h[?25l[?7lblock_ldlt -joint_classical pply_map ugment block_ldlt -jugat pply_morphismutomorphism_of_rows_and_columnsblock_sum  -ntcommutatos_bipartite_graphbase_extend crtesian_product -ntitransposes_sum_of_permutationsbase_ring ctgory [?7h[?12l[?25h[?25l[?7lchange_ring -pply_map ugment block_ldltchange_ring -pply_morphismutomorphism_of_rows_and_columnsblock_sum characteristic_polynomial -s_bipartite_graphbase_extend crtesian_productharpoly  -s_sum_of_permutationsbase_ring ctgory holesk[?7h[?12l[?25h[?25l[?7loefficiet -ugment block_ldltchange_ringoefficiet -utomorphism_of_rows_and_columnsblock_sum characteristic_polynomialoefficients  -base_extend crtesian_productharpoly olumn  -base_ring ctgory holeskolumn_ambient_module[?7h[?12l[?25h[?25l[?7lr - - - - -[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1.rank() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NotImplementedError Traceback (most recent call last) -Input In [63], in () -----> 1 M1.rank() - -File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:2159, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.rank() - 2157 # linbox is very buggy for p=2, but this code should never - 2158 # be called since p=2 is handled via M4RI --> 2159 return Matrix_dense.rank(self) - 2160 - 2161 def determinant(self): - -File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:4643, in sage.matrix.matrix0.Matrix.rank() - 4641 if self._nrows == 0 or self._ncols == 0: - 4642 return 0 --> 4643 r = len(self.pivots()) - 4644 self.cache('rank', r) - 4645 return r - -File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:4600, in sage.matrix.matrix0.Matrix.pivots() - 4598 x = self.fetch('pivots') - 4599 if not x is None: return tuple(x) --> 4600 self.echelon_form() - 4601 x = self.fetch('pivots') - 4602 if x is None: - -File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:7727, in sage.matrix.matrix2.Matrix.echelon_form() - 7725 E = self.__copy__() - 7726 if algorithm == 'default': --> 7727 v = E.echelonize(cutoff=cutoff, **kwds) - 7728 else: - 7729 v = E.echelonize(algorithm = algorithm, cutoff=cutoff, **kwds) - -File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:1725, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.echelonize() - 1723 - 1724 if not self.base_ring().is_field(): --> 1725 raise NotImplementedError("Echelon form not implemented over '%s'."%self.base_ring()) - 1726 - 1727 if algorithm == 'linbox': - -NotImplementedError: Echelon form not implemented over 'Ring of integers modulo 9'. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1.rank()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: M1 -[?7h[?12l[?25h[?2004l[?7h[3 4] -[6 3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lorma.expansionat_infty(prec=30)[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l m in range(1, p^2):[?7h[?12l[?25h[?25l[?7lalista2:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lrange(0, 10):[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for a in range(3): -....: [?7h[?12l[?25h[?25l[?7lf += a[i]*x^i[?7h[?12l[?25h[?25l[?7lor B in range(-10, 30):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb0, 10):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:  for b in range(3): -....: [?7h[?12l[?25h[?25l[?7lfor k in range(1, p-1):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:  for c in range(3): -....: [?7h[?12l[?25h[?25l[?7lpass[?7h[?12l[?25h[?25l[?7lrint(e, f, g)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lif not(LHS == RHS):[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:  if 0 == 1: -....: [?7h[?12l[?25h[?25l[?7lprint(m, k)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print(1) -....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(3): -....:  for b in range(3): -....:  for c in range(3): -....:  if 0 == 1: -....:  print(1) -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7list_of_m = [m for m in list_of_m if m%p != 0][?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista = ['a', 'b','c'][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: lista = [] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = [][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: licznik = 0 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicznik = 0[?7h[?12l[?25h[?25l[?7lsta =[][?7h[?12l[?25h[?25l[?7lsage: for a in range(3): -....:  for b in range(3): -....:  for c in range(3): -....:  if 0 == 1: -....:  print(1)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = d/(e*g)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l -....: [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 + 3*a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l....:  M = matrix(R9, [[1 + 3*a, 1+3*b], [3*c, 1+3*d]]) -....: [?7h[?12l[?25h[?25l[?7lif e == 3:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lind[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldetity_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lntity_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:  if M^3 == identity_matrix(R9, 2): -....: [?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l....:  licznik += 1 -....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(3): -....:  for b in range(3): -....:  for c in range(3): -....:  for d in range(3): -....:  M = matrix(R9, [[1 + 3*a, 1+3*b], [3*c, 1+3*d]]) -....:  if M^3 == identity_matrix(R9, 2): -....:  licznik += 1 -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 3^4 -[?7h[?12l[?25h[?2004l[?7h81 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicznik = 0[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnik = 0[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7lsage: licznik -[?7h[?12l[?25h[?2004l[?7h27 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1[?7h[?12l[?25h[?25l[?7lsage: M -[?7h[?12l[?25h[?2004l[?7h[7 7] -[6 7] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg[?7h[?12l[?25h[?25l[?7l = yy^3/xx^3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2*x^4 + x^3 + x^2 + 2*x - x^3* (x^3 - x)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+ x^3 + x^2 + 2*x - x^3* (x^3 - x)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*x^2 + 2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx^2 + 2[?7h[?12l[?25h[?25l[?7lsage: g = 2*x^4 + 2*x^2 + 2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx+1) - g[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g -[?7h[?12l[?25h[?2004l[?7h2*x^3 + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: v = yy/xx^2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lsage: yy*v^2 - yy^2*v -[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lhy*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7l y*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7l=y*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7l y*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7lsage: h = yy*v^2 - yy^2*v -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh = yy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: h.coordinates() -[?7h[?12l[?25h[?2004l[?7h[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: yx = yy/xx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyx = yy/xx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: yx^8*yx.diffn() -[?7h[?12l[?25h[?2004l[?7h((-x^10 + x^6 + x^4 - 1)/(x^5*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh.coordinates()[?7h[?12l[?25h[?25l[?7lsage: h -[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy^3/xx^3[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2(x+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g1 = g + yy/xx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg1 = g + yy/xx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: g1 -[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g1.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t + t^3 + 2*t^5 + t^9 + t^13 + 2*t^17 + O(t^21) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ M = msasage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lmatrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7l, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7lQ, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7lQ, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l-], [6, 4])[?7h[?12l[?25h[?25l[?7l1], [6, 4])[?7h[?12l[?25h[?25l[?7l,], [6, 4])[?7h[?12l[?25h[?25l[?7l ], [6, 4])[?7h[?12l[?25h[?25l[?7l-], [6, 4])[?7h[?12l[?25h[?25l[?7l1], [6, 4])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l1]])[?7h[?12l[?25h[?25l[?7l,]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7l0]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = matrix(QQ, [[-1, -1], [1, 0]]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(QQ, [[-1, -1], [1, 0]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3 -[?7h[?12l[?25h[?2004l[?7h[1 0] -[0 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = M - identity_matrix(R9, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l - identity_matrix(R9, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lQ, 2)[?7h[?12l[?25h[?25l[?7lQ, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(QQ, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(QQ, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.rank()[?7h[?12l[?25h[?25l[?7lkernel()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1.kernel() -[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 0 over Rational Field -Basis matrix: -[] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l11/3-4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicznik[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l1y)[?7h[?12l[?25h[?25l[?7l/y)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, superelliptic_function(C, 1/y)) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [6], in () -----> 1 AS = as_cover(C, superelliptic_function(C, Integer(1)/y)) - -NameError: name 'y' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, superelliptic_function(C, 1/y))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsuper)[?7h[?12l[?25h[?25l[?7lsupe)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)^(-1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, (C.y)^(-1)) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [7], in () -----> 1 AS = as_cover(C, (C.y)**(-Integer(1))) - -File :6, in __init__(self, C, list_of_fcts, prec) - -TypeError: object of type 'superelliptic_function' has no len() -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, (C.y)^(-1))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[(C.y)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.y)^(-1)]) -[?7h[?12l[?25h[?2004lno 0 -th root; divide by 1 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [8], in () -----> 1 AS = as_cover(C, [(C.y)**(-Integer(1))]) - -File :44, in __init__(self, C, list_of_fcts, prec) - -ValueError: not enough values to unpack (expected 4, got 2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lC.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly)^3/(C.)^4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l(-1)[?7h[?12l[?25h[?25l[?7l(-1)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.p_rank() -[?7h[?12l[?25h[?2004lHyperelliptic Curve over Finite Field of size 3 defined by y^2 = x^3 + 2*x -[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))". Alternatively, "R. = QQ[]; WeierstrassForm(v^2 - (u^4 - 1), transformation=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lTru[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1))) -[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 4*x over Multivariate Polynomial Ring in u, v over Rational Field -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7lG[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7lF[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l(; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l3; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l(); ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l()[; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: R. = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1))) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ZeroDivisionError Traceback (most recent call last) -Input In [13], in () -----> 1 R = GF(Integer(3))['u, v']; (u, v,) = R._first_ngens(2); EllipticCurve(WeierstrassForm(v**Integer(2) - (u**Integer(4) - Integer(1)))) - -File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__() - 389 True - 390 """ ---> 391 return self.get_object()(*args, **kwds) - 392 - 393 def __repr__(self): - -File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:499, in WeierstrassForm(polynomial, variables, transformation) - 497 return WeierstrassForm_P1xP1(polynomial, variables) - 498 if polygon is polar_P2_112_polytope(): ---> 499 return WeierstrassForm_P2_112(polynomial, variables) - 500 raise ValueError('Newton polytope is not contained in a reflexive polygon') - -File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:1078, in WeierstrassForm_P2_112(polynomial, variables) - 1076 delta = _partial_discriminant(polynomial, y, t) - 1077 Q = invariant_theory.binary_quartic(delta, x, z) --> 1078 g2 = Q.EisensteinD() - 1079 g3 = -Q.EisensteinE() - 1080 return (-g2/4, -g3/4) - -File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__() - 2297 if self.cache is None: - 2298 f = self.f --> 2299 self.cache = f(self._instance) - 2300 return self.cache - 2301 - -File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1480, in BinaryQuartic.EisensteinD(self) - 1455 @cached_method - 1456 def EisensteinD(self): - 1457 r""" - 1458  One of the Eisenstein invariants of a binary quartic. - 1459 - (...) - 1478  3*a2^2 - 4*a1*a3 + a0*a4 - 1479  """ --> 1480 a = self.scaled_coeffs() - 1481 assert len(a) == 5 - 1482 return a[0]*a[4]+3*a[2]**2-4*a[1]*a[3] - -File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1452, in BinaryQuartic.scaled_coeffs(self) - 1425 """ - 1426 The coefficients of a binary quartic. - 1427 - (...) - 1449  (a0, a1, a2, a3, a4) - 1450 """ - 1451 coeff = self.coeffs() --> 1452 return (coeff[0], coeff[1]/4, coeff[2]/6, coeff[3]/4, coeff[4]) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() - 1740 - 1741 try: --> 1742 return coercion_model.bin_op(left, right, truediv) - 1743 except TypeError: - 1744 return NotImplemented - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op() - 1194 return (action)._act_(x, y) - 1195 else: --> 1196 return (action)._act_(y, x) - 1197 - 1198 # Now coerce to a common parent and do the operation there - -File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_() - 492 if self.S_precomposition is not None: - 493 x = self.S_precomposition._call_(x) ---> 494 return self._action._act_(g, x) - 495 - 496 def domain(self): - -File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_() - 492 if self.S_precomposition is not None: - 493 x = self.S_precomposition._call_(x) ---> 494 return self._action._act_(g, x) - 495 - 496 def domain(self): - -File /ext/sage/9.7/src/sage/categories/action.pyx:407, in sage.categories.action.InverseAction._act_() - 405 if self.S_precomposition is not None: - 406 x = self.S_precomposition(x) ---> 407 return self._action._act_(~g, x) - 408 - 409 def codomain(self): - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2821, in sage.rings.finite_rings.integer_mod.IntegerMod_int.__invert__() - 2819 x = self.__modulus.inverses[self.ivalue] - 2820 if x is None: --> 2821 raise ZeroDivisionError(f"inverse of Mod({self}, {self.__modulus.sageInteger}) does not exist") - 2822 else: - 2823 return x - -ZeroDivisionError: inverse of Mod(0, 3) does not exist -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 1)[?7h[?12l[?25h[?25l[?7l+ 1)[?7h[?12l[?25h[?25l[?7lsage: R. = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1))) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ZeroDivisionError Traceback (most recent call last) -Input In [14], in () -----> 1 R = GF(Integer(3))['u, v']; (u, v,) = R._first_ngens(2); EllipticCurve(WeierstrassForm(v**Integer(2) - (u**Integer(4) + Integer(1)))) - -File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__() - 389 True - 390 """ ---> 391 return self.get_object()(*args, **kwds) - 392 - 393 def __repr__(self): - -File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:499, in WeierstrassForm(polynomial, variables, transformation) - 497 return WeierstrassForm_P1xP1(polynomial, variables) - 498 if polygon is polar_P2_112_polytope(): ---> 499 return WeierstrassForm_P2_112(polynomial, variables) - 500 raise ValueError('Newton polytope is not contained in a reflexive polygon') - -File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:1078, in WeierstrassForm_P2_112(polynomial, variables) - 1076 delta = _partial_discriminant(polynomial, y, t) - 1077 Q = invariant_theory.binary_quartic(delta, x, z) --> 1078 g2 = Q.EisensteinD() - 1079 g3 = -Q.EisensteinE() - 1080 return (-g2/4, -g3/4) - -File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__() - 2297 if self.cache is None: - 2298 f = self.f --> 2299 self.cache = f(self._instance) - 2300 return self.cache - 2301 - -File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1480, in BinaryQuartic.EisensteinD(self) - 1455 @cached_method - 1456 def EisensteinD(self): - 1457 r""" - 1458  One of the Eisenstein invariants of a binary quartic. - 1459 - (...) - 1478  3*a2^2 - 4*a1*a3 + a0*a4 - 1479  """ --> 1480 a = self.scaled_coeffs() - 1481 assert len(a) == 5 - 1482 return a[0]*a[4]+3*a[2]**2-4*a[1]*a[3] - -File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1452, in BinaryQuartic.scaled_coeffs(self) - 1425 """ - 1426 The coefficients of a binary quartic. - 1427 - (...) - 1449  (a0, a1, a2, a3, a4) - 1450 """ - 1451 coeff = self.coeffs() --> 1452 return (coeff[0], coeff[1]/4, coeff[2]/6, coeff[3]/4, coeff[4]) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() - 1740 - 1741 try: --> 1742 return coercion_model.bin_op(left, right, truediv) - 1743 except TypeError: - 1744 return NotImplemented - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op() - 1194 return (action)._act_(x, y) - 1195 else: --> 1196 return (action)._act_(y, x) - 1197 - 1198 # Now coerce to a common parent and do the operation there - -File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_() - 492 if self.S_precomposition is not None: - 493 x = self.S_precomposition._call_(x) ---> 494 return self._action._act_(g, x) - 495 - 496 def domain(self): - -File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_() - 492 if self.S_precomposition is not None: - 493 x = self.S_precomposition._call_(x) ---> 494 return self._action._act_(g, x) - 495 - 496 def domain(self): - -File /ext/sage/9.7/src/sage/categories/action.pyx:407, in sage.categories.action.InverseAction._act_() - 405 if self.S_precomposition is not None: - 406 x = self.S_precomposition(x) ---> 407 return self._action._act_(~g, x) - 408 - 409 def codomain(self): - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2821, in sage.rings.finite_rings.integer_mod.IntegerMod_int.__invert__() - 2819 x = self.__modulus.inverses[self.ivalue] - 2820 if x is None: --> 2821 raise ZeroDivisionError(f"inverse of Mod({self}, {self.__modulus.sageInteger}) does not exist") - 2822 else: - 2823 return x - -ZeroDivisionError: inverse of Mod(0, 3) does not exist -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lQQ[]; ElliptcCurve(WierstassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7lsage: R. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1))) -[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 4*x over Multivariate Polynomial Ring in u, v over Rational Field -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7lsage: R. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 2))) -[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 8*x over Multivariate Polynomial Ring in u, v over Rational Field -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 2)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l/))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7lsage: R. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1/2))) -[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 2*x over Multivariate Polynomial Ring in u, v over Rational Field -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1/2)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l+))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: R. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1))) -[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + (-4)*x over Multivariate Polynomial Ring in u, v over Rational Field -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7lG[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7lF[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l([]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l3[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l)[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7lsage: R. = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1))) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ZeroDivisionError Traceback (most recent call last) -Input In [19], in () -----> 1 R = GF(Integer(3))['u, v']; (u, v,) = R._first_ngens(2); EllipticCurve(WeierstrassForm(v**Integer(2) - (u**Integer(4) + Integer(1)))) - -File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__() - 389 True - 390 """ ---> 391 return self.get_object()(*args, **kwds) - 392 - 393 def __repr__(self): - -File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:499, in WeierstrassForm(polynomial, variables, transformation) - 497 return WeierstrassForm_P1xP1(polynomial, variables) - 498 if polygon is polar_P2_112_polytope(): ---> 499 return WeierstrassForm_P2_112(polynomial, variables) - 500 raise ValueError('Newton polytope is not contained in a reflexive polygon') - -File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:1078, in WeierstrassForm_P2_112(polynomial, variables) - 1076 delta = _partial_discriminant(polynomial, y, t) - 1077 Q = invariant_theory.binary_quartic(delta, x, z) --> 1078 g2 = Q.EisensteinD() - 1079 g3 = -Q.EisensteinE() - 1080 return (-g2/4, -g3/4) - -File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__() - 2297 if self.cache is None: - 2298 f = self.f --> 2299 self.cache = f(self._instance) - 2300 return self.cache - 2301 - -File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1480, in BinaryQuartic.EisensteinD(self) - 1455 @cached_method - 1456 def EisensteinD(self): - 1457 r""" - 1458  One of the Eisenstein invariants of a binary quartic. - 1459 - (...) - 1478  3*a2^2 - 4*a1*a3 + a0*a4 - 1479  """ --> 1480 a = self.scaled_coeffs() - 1481 assert len(a) == 5 - 1482 return a[0]*a[4]+3*a[2]**2-4*a[1]*a[3] - -File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1452, in BinaryQuartic.scaled_coeffs(self) - 1425 """ - 1426 The coefficients of a binary quartic. - 1427 - (...) - 1449  (a0, a1, a2, a3, a4) - 1450 """ - 1451 coeff = self.coeffs() --> 1452 return (coeff[0], coeff[1]/4, coeff[2]/6, coeff[3]/4, coeff[4]) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() - 1740 - 1741 try: --> 1742 return coercion_model.bin_op(left, right, truediv) - 1743 except TypeError: - 1744 return NotImplemented - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op() - 1194 return (action)._act_(x, y) - 1195 else: --> 1196 return (action)._act_(y, x) - 1197 - 1198 # Now coerce to a common parent and do the operation there - -File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_() - 492 if self.S_precomposition is not None: - 493 x = self.S_precomposition._call_(x) ---> 494 return self._action._act_(g, x) - 495 - 496 def domain(self): - -File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_() - 492 if self.S_precomposition is not None: - 493 x = self.S_precomposition._call_(x) ---> 494 return self._action._act_(g, x) - 495 - 496 def domain(self): - -File /ext/sage/9.7/src/sage/categories/action.pyx:407, in sage.categories.action.InverseAction._act_() - 405 if self.S_precomposition is not None: - 406 x = self.S_precomposition(x) ---> 407 return self._action._act_(~g, x) - 408 - 409 def codomain(self): - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2821, in sage.rings.finite_rings.integer_mod.IntegerMod_int.__invert__() - 2819 x = self.__modulus.inverses[self.ivalue] - 2820 if x is None: --> 2821 raise ZeroDivisionError(f"inverse of Mod({self}, {self.__modulus.sageInteger}) does not exist") - 2822 else: - 2823 return x - -ZeroDivisionError: inverse of Mod(0, 3) does not exist -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.p_rank()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l4, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l-, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l^, 2)[?7h[?12l[?25h[?25l[?7l3, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.p_rank()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_rank()[?7h[?12l[?25h[?25l[?7lsage: C.p_rank() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [3], in () -----> 1 C.p_rank() - -File :176, in p_rank(self) - -File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1889, in HyperellipticCurve_finite_field.p_rank(self) - 1855 r""" - 1856 INPUT: - 1857 - (...) - 1880  0 - 1881 """ - 1882 #We use caching here since Hasse Witt is needed to compute p_rank. So if the Hasse Witt - 1883 #is already computed it is stored in list A. If it was not cached (i.e. A is empty), we simply - 1884 #compute it. If it is cached then we need to make sure that we have the correct one. So check - (...) - 1887 # However, it seems a waste of time to manually analyse the cache - 1888 # -- See Trac Ticket #11115 --> 1889 N, E = self._Hasse_Witt_cached() - 1890 if E != self: - 1891 self._Hasse_Witt_cached.clear_cache() - -File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__() - 2297 if self.cache is None: - 2298 f = self.f --> 2299 self.cache = f(self._instance) - 2300 return self.cache - 2301 - -File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1727, in HyperellipticCurve_finite_field._Hasse_Witt_cached(self) - 1647 r""" - 1648 This is where Hasse_Witt is actually computed. - 1649 - (...) - 1712  0 - 1713 """ - 1714 # If Cartier Matrix is already cached for this curve, use that or evaluate it to get M, - 1715 #Coeffs, genus, Fq=base field of self, p=char(Fq). This is so we have one less matrix to - 1716 #compute. - (...) - 1725 #that don't accept arguments. Anyway, the easiest is to call - 1726 #the cached method and simply see whether the data belong to self. --> 1727 M, Coeffs, g, Fq, p, E = self._Cartier_matrix_cached() - 1728 if E != self: - 1729 self._Cartier_matrix_cached.clear_cache() - -File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__() - 2297 if self.cache is None: - 2298 f = self.f --> 2299 self.cache = f(self._instance) - 2300 return self.cache - 2301 - -File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1523, in HyperellipticCurve_finite_field._Cartier_matrix_cached(self) - 1521 #this implementation is for odd degree only, even degree will be handled later. - 1522 if d%2 == 0: --> 1523 raise ValueError("In this implementation the degree of f must be odd") - 1524 #Compute resultant to make sure no repeated roots - 1525 df=f.derivative() - -ValueError: In this implementation the degree of f must be odd -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.p_rank()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcatier_matrix()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix() -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix() -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lp_ank()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.carti_matrix()[?7h[?12l[?25h[?25l[?7lde_rhambsis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), (((-x^2 - x)/y) dx, 2/x*y, (1/(x*y)) dx)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.dx -[?7h[?12l[?25h[?2004l[?7h1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liC.dx[?7h[?12l[?25h[?25l[?7lsC.dx[?7h[?12l[?25h[?25l[?7liC.dx[?7h[?12l[?25h[?25l[?7lnC.dx[?7h[?12l[?25h[?25l[?7lsC.dx[?7h[?12l[?25h[?25l[?7ltC.dx[?7h[?12l[?25h[?25l[?7laC.dx[?7h[?12l[?25h[?25l[?7lnC.dx[?7h[?12l[?25h[?25l[?7lceC.dx[?7h[?12l[?25h[?25l[?7lisinstance(C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: isinstance(C.dx,superelliptic_form) -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint((x^8).quo_rem(x^4 + x^2 + 1))[?7h[?12l[?25h[?25l[?7larent)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [2], in () -----> 1 patch(C) - -File :5, in patch(C) - -NameError: name 'self' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lsage: patch(C) -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C).genus() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7luperelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C).genus()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltch(C).genus()[?7h[?12l[?25h[?25l[?7lsage: patch(C).genus() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C).genus()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().genus()[?7h[?12l[?25h[?25l[?7lsage: patch(C) -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(E.local_data(2))[?7h[?12l[?25h[?25l[?7let*list2)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x -....: [?7h[?12l[?25h[?25l[?7l( -)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x -....: ) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [10], in () -----> 1 second_patch(C.x - 2 ) - -File :19, in second_patch(argument) - -NameError: name 'y' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x -....: )[?7h[?12l[?25h[?25l[?7l( -[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [11], in () -----> 1 second_patch(C.x) - -File :19, in second_patch(argument) - -NameError: name 'y' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [13], in () -----> 1 second_patch(C.x) - -File :20, in second_patch(argument) - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2409 if type(exp) is not Integer: - 2410 try: --> 2411 exp = Integer(exp) - 2412 except TypeError: - 2413 try: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__() - 656 otmp = getattr(x, "_integer_", None) - 657 if otmp is not None: ---> 658 set_from_Integer(self, otmp(the_integer_ring)) - 659 return - 660 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion() - 1389 if self.degree() > 0: - 1390 raise TypeError("cannot convert nonconstant polynomial") --> 1391 return R(self.get_coeff_c(0)) - 1392 - 1393 _real_double_ = _scalar_conversion - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1690 """ - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - 1694 - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1618 Section._update_slots(self, _slots) - 1619 --> 1620 cpdef Element _call_(self, _x): - 1621 """ - 1622 Applies the section. - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7lsage: C. -[?7h[?12l[?25h[?2004l Input In [14] - C. - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lsage: C.x -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lC.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l().pth_root([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7l=(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7lsage: g = (C.x).function -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [17], in () -----> 1 g(x = x+Integer(1), y = y+Integer(1)) - -NameError: name 'y' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y = C.fct_field -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lg(x = +1, y=y+1)[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1) -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lFxy, Ry, x,y= C.fct_field[?7h[?12l[?25h[?25l[?7lg(x = +1, y=y+1)[?7h[?12l[?25h[?25l[?7l =(C.x).function[?7h[?12l[?25h[?25l[?7lsage: g = (C.x).function -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lFxy, Ry, x,y= C.fct_field[?7h[?12l[?25h[?25l[?7lg(x = +1, y=y+1)[?7h[?12l[?25h[?25l[?7l =(C.x).function[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2410 try: --> 2411 exp = Integer(exp) - 2412 except TypeError: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__() - 657 if otmp is not None: ---> 658 set_from_Integer(self, otmp(the_integer_ring)) - 659 return - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion() - 828 if self.__denominator.is_one(): ---> 829 return R(self.__numerator) - 830 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_() - 12065 """ -> 12066 cpdef Element _call_(self, x): - 12067 """ - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_() - 12090 else: -> 12091 raise TypeError("not a constant polynomial") - 12092 - -TypeError: not a constant polynomial - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2413 try: --> 2414 n = Rational(exp) - 2415 except TypeError: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_() - 783 """ ---> 784 return self._conversion(QQ) - 785 - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion() - 828 if self.__denominator.is_one(): ---> 829 return R(self.__numerator) - 830 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_() - 174 from sage.rings.rational_field import QQ ---> 175 return self._scalar_conversion(QQ) - 176 - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion() - 104 return R(self.constant_coefficient()) ---> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}") - 106 - -TypeError: unable to convert non-constant polynomial x + 1 to Rational Field - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [22], in () -----> 1 second_patch(C.x) - -File :20, in second_patch(argument) - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2414 n = Rational(exp) - 2415 except TypeError: --> 2416 raise TypeError("{} is neither an integer nor a rational".format(exp)) - 2417 num = n.numerator() - 2418 den = n.denominator() - -TypeError: x + 1 is neither an integer nor a rational -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2410 try: --> 2411 exp = Integer(exp) - 2412 except TypeError: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__() - 657 if otmp is not None: ---> 658 set_from_Integer(self, otmp(the_integer_ring)) - 659 return - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion() - 104 return R(self.constant_coefficient()) ---> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}") - 106 - -TypeError: unable to convert non-constant polynomial x + 1 to Integer Ring - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2413 try: --> 2414 n = Rational(exp) - 2415 except TypeError: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_() - 174 from sage.rings.rational_field import QQ ---> 175 return self._scalar_conversion(QQ) - 176 - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion() - 104 return R(self.constant_coefficient()) ---> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}") - 106 - -TypeError: unable to convert non-constant polynomial x + 1 to Rational Field - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [24], in () -----> 1 second_patch(C.x) - -File :20, in second_patch(argument) - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2414 n = Rational(exp) - 2415 except TypeError: --> 2416 raise TypeError("{} is neither an integer nor a rational".format(exp)) - 2417 num = n.numerator() - 2418 den = n.denominator() - -TypeError: x + 1 is neither an integer nor a rational -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: x+1 -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()x[?7h[?12l[?25h[?25l[?7l(x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l().pth_root([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7l=(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7lsage: g = (C.x).function -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = Rxy(g) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = Rxy(g)[?7h[?12l[?25h[?25l[?7l(x= x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+1) - g[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g(x+1, y+1) -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1, y+1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx+1, y+1)[?7h[?12l[?25h[?25l[?7l x+1, y+1)[?7h[?12l[?25h[?25l[?7l=x+1, y+1)[?7h[?12l[?25h[?25l[?7l x+1, y+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly+1)[?7h[?12l[?25h[?25l[?7l y+1)[?7h[?12l[?25h[?25l[?7l=y+1)[?7h[?12l[?25h[?25l[?7l y+1)[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1) -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7l+1, y+1)[?7h[?12l[?25h[?25l[?7l = Rxy(g)[?7h[?12l[?25h[?25l[?7l(C.x).function[?7h[?12l[?25h[?25l[?7lx+1[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7lx+1[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004lx ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [31], in () -----> 1 second_patch(C.x) - -File :21, in second_patch(argument) - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2409 if type(exp) is not Integer: - 2410 try: --> 2411 exp = Integer(exp) - 2412 except TypeError: - 2413 try: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__() - 656 otmp = getattr(x, "_integer_", None) - 657 if otmp is not None: ---> 658 set_from_Integer(self, otmp(the_integer_ring)) - 659 return - 660 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion() - 1389 if self.degree() > 0: - 1390 raise TypeError("cannot convert nonconstant polynomial") --> 1391 return R(self.get_coeff_c(0)) - 1392 - 1393 _real_double_ = _scalar_conversion - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1690 """ - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - 1694 - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1618 Section._update_slots(self, _slots) - 1619 --> 1620 cpdef Element _call_(self, _x): - 1621 """ - 1622 Applies the section. - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004lx Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [33], in () -----> 1 second_patch(C.x) - -File :21, in second_patch(argument) - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2409 if type(exp) is not Integer: - 2410 try: --> 2411 exp = Integer(exp) - 2412 except TypeError: - 2413 try: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__() - 656 otmp = getattr(x, "_integer_", None) - 657 if otmp is not None: ---> 658 set_from_Integer(self, otmp(the_integer_ring)) - 659 return - 660 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion() - 1389 if self.degree() > 0: - 1390 raise TypeError("cannot convert nonconstant polynomial") --> 1391 return R(self.get_coeff_c(0)) - 1392 - 1393 _real_double_ = _scalar_conversion - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1690 """ - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - 1694 - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1618 Section._update_slots(self, _slots) - 1619 --> 1620 cpdef Element _call_(self, _x): - 1621 """ - 1622 Applies the section. - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: --> 1654 raise ValueError("not constant") - 1655 ans = IntegerMod_int.__new__(IntegerMod_int) - 1656 ans._parent = self.codomain() - -ValueError: not constant -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Fxy -[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lFxy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgC.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7lFC.x.function[?7h[?12l[?25h[?25l[?7lxC.x.function[?7h[?12l[?25h[?25l[?7lyC.x.function[?7h[?12l[?25h[?25l[?7l(C.x.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = Fxy(C.x.function) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = Fxy(C.x.function)[?7h[?12l[?25h[?25l[?7l(x= x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+1, y+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7l( = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1) -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lsage: g.subs({x:x+1, y:y+1}) -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcond_patch(C.x)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2410 try: --> 2411 exp = Integer(exp) - 2412 except TypeError: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__() - 657 if otmp is not None: ---> 658 set_from_Integer(self, otmp(the_integer_ring)) - 659 return - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion() - 828 if self.__denominator.is_one(): ---> 829 return R(self.__numerator) - 830 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_() - 12065 """ -> 12066 cpdef Element _call_(self, x): - 12067 """ - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_() - 12090 else: -> 12091 raise TypeError("not a constant polynomial") - 12092 - -TypeError: not a constant polynomial - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2413 try: --> 2414 n = Rational(exp) - 2415 except TypeError: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_() - 783 """ ---> 784 return self._conversion(QQ) - 785 - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion() - 828 if self.__denominator.is_one(): ---> 829 return R(self.__numerator) - 830 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_() - 174 from sage.rings.rational_field import QQ ---> 175 return self._scalar_conversion(QQ) - 176 - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion() - 104 return R(self.constant_coefficient()) ---> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}") - 106 - -TypeError: unable to convert non-constant polynomial x + 1 to Rational Field - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [39], in () -----> 1 second_patch(C.x) - -File :20, in second_patch(argument) - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2414 n = Rational(exp) - 2415 except TypeError: --> 2416 raise TypeError("{} is neither an integer nor a rational".format(exp)) - 2417 num = n.numerator() - 2418 den = n.denominator() - -TypeError: x + 1 is neither an integer nor a rational -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2410 try: --> 2411 exp = Integer(exp) - 2412 except TypeError: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__() - 657 if otmp is not None: ---> 658 set_from_Integer(self, otmp(the_integer_ring)) - 659 return - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion() - 828 if self.__denominator.is_one(): ---> 829 return R(self.__numerator) - 830 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_() - 12065 """ -> 12066 cpdef Element _call_(self, x): - 12067 """ - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_() - 12090 else: -> 12091 raise TypeError("not a constant polynomial") - 12092 - -TypeError: not a constant polynomial - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2413 try: --> 2414 n = Rational(exp) - 2415 except TypeError: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_() - 783 """ ---> 784 return self._conversion(QQ) - 785 - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion() - 828 if self.__denominator.is_one(): ---> 829 return R(self.__numerator) - 830 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_() - 174 from sage.rings.rational_field import QQ ---> 175 return self._scalar_conversion(QQ) - 176 - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion() - 104 return R(self.constant_coefficient()) ---> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}") - 106 - -TypeError: unable to convert non-constant polynomial x + 1 to Rational Field - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [41], in () -----> 1 second_patch(C.x) - -File :20, in second_patch(argument) - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2414 n = Rational(exp) - 2415 except TypeError: --> 2416 raise TypeError("{} is neither an integer nor a rational".format(exp)) - 2417 num = n.numerator() - 2418 den = n.denominator() - -TypeError: x + 1 is neither an integer nor a rational -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(z[0])[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: type(x+1) -[?7h[?12l[?25h[?2004l[?7h -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(x+1)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2410 try: --> 2411 exp = Integer(exp) - 2412 except TypeError: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__() - 657 if otmp is not None: ---> 658 set_from_Integer(self, otmp(the_integer_ring)) - 659 return - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion() - 828 if self.__denominator.is_one(): ---> 829 return R(self.__numerator) - 830 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_() - 12065 """ -> 12066 cpdef Element _call_(self, x): - 12067 """ - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_() - 12090 else: -> 12091 raise TypeError("not a constant polynomial") - 12092 - -TypeError: not a constant polynomial - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2413 try: --> 2414 n = Rational(exp) - 2415 except TypeError: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_() - 783 """ ---> 784 return self._conversion(QQ) - 785 - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion() - 828 if self.__denominator.is_one(): ---> 829 return R(self.__numerator) - 830 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_() - 174 from sage.rings.rational_field import QQ ---> 175 return self._scalar_conversion(QQ) - 176 - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion() - 104 return R(self.constant_coefficient()) ---> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}") - 106 - -TypeError: unable to convert non-constant polynomial x + 1 to Rational Field - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [43], in () -----> 1 second_patch(C.x) - -File :20, in second_patch(argument) - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__() - 2414 n = Rational(exp) - 2415 except TypeError: --> 2416 raise TypeError("{} is neither an integer nor a rational".format(exp)) - 2417 num = n.numerator() - 2418 den = n.denominator() - -TypeError: x + 1 is neither an integer nor a rational -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C) -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: patch(patch(C)) -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(patch(C))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lpatch(patch(C))[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x) -[?7h[?12l[?25h[?2004l[?7h1/x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lesecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lcsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7losecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lnsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7ldsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7l_second_patch(C.x)[?7h[?12l[?25h[?25l[?7lpsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lasecond_patch(C.x)[?7h[?12l[?25h[?25l[?7ltsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lcsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lhsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7l(second_patch(C.x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: second_patch(second_patch(C.x)) -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(second_patch(C.x))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ldx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(second_patch(C.dx)) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'superelliptic_function' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [53], in () -----> 1 second_patch(second_patch(C.dx)) - -File :26, in second_patch(argument) - -File :7, in __init__(self, C, g) - -File :245, in reduction_form(C, g) - -File :216, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert 2/x^2/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(second_patch(C.dx))[?7h[?12l[?25h[?25l[?7lsage: second_patch(second_patch(C.dx)) -[?7h[?12l[?25h[?2004l[?7h1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(second_patch(C.dx))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.dx) -[?7h[?12l[?25h[?2004l[?7h((-1)/x^2) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7lheight[?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?7h[(1/y) dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = supeelliptc(x^4 - x^3 + x, 2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l1 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l1 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^11 - x^3 + x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^11 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.holomophic_dfferentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (x/y) dx, (x^2/y) dx, (x^3/y) dx, (x^4/y) dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7lg.sage')[?7h[?12l[?25h[?25l[?7lu.sage')[?7h[?12l[?25h[?25l[?7ll.sage')[?7h[?12l[?25h[?25l[?7la.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7l .sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l_.sage')[?7h[?12l[?25h[?25l[?7lo.sage')[?7h[?12l[?25h[?25l[?7ln.sage')[?7h[?12l[?25h[?25l[?7l_.sage')[?7h[?12l[?25h[?25l[?7lU.sage')[?7h[?12l[?25h[?25l[?7l0.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: regula - regular_form - regulator  - - - [?7h[?12l[?25h[?25l[?7lr_form - regular_form - - [?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - - [?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*C.dx).form -[?7h[?12l[?25h[?2004l[?7h1/y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - [?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbn((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lo((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7le((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7ln((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lo((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lm((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7li((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7ln((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7la((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lt((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lo((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lr((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l(((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: denominator(((C.y)^(-1)*C.dx).form) == y -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldenominator(((C.y)^(-1)*C.dx).form) == y[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7ldenominator(((C.y)^(-1)*C.dx).form) == y[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [66], in () -----> 1 regular_form((C.y)**(-Integer(1))*C.dx) - -File :8, in regular_form(omega) - -ValueError: too many values to unpack (expected 2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx) -[?7h[?12l[?25h[?2004l1 -[?7h((x^9 + x^7 - x^5 + x^3 - x)/y, (x^10 + x^8 - x^6 + x^4 + x^2 + 1)/y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx) -[?7h[?12l[?25h[?2004l1 -[?7h(x^9 + x^7 - x^5 + x^3 - x, x^10 + x^8 - x^6 + x^4 + x^2 + 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = supeelliptc(x^11 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^11 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7l^3 + x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x, 2)[?7h[?12l[?25h[?25l[?7l- x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx) -[?7h[?12l[?25h[?2004l1 -[?7h(0, -1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx) -[?7h[?12l[?25h[?2004l1 0 2 -[?7h(0, -1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx) -[?7h[?12l[?25h[?2004l1 0 2 -[?7h(0, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx) -[?7h[?12l[?25h[?2004l[?7h(0, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx) -[?7h[?12l[?25h[?2004l[?7h(0, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(3):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.subs({x:x+1, y:y+1})[?7h[?12l[?25h[?25l[?7l = Fxy(C..function)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: g = x^3 + 2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x^3 + 2[?7h[?12l[?25h[?25l[?7l.subs({x:x+1, y:y+1})[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.lift() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [82], in () -----> 1 g.lift() - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'lift' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(x+1)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: type(g) -[?7h[?12l[?25h[?2004l[?7h -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(g)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltyp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(patch(C))[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrent(x)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(g) -[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.lift() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [85], in () -----> 1 g.lift() - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'lift' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(ZZ) -[?7h[?12l[?25h[?2004l[?7hx^3 + 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(ZZ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(ZZ) + 3 -[?7h[?12l[?25h[?2004l[?7hx^3 + 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(ZZ) + 3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l) + 3[?7h[?12l[?25h[?25l[?7l) + 3[?7h[?12l[?25h[?25l[?7lI) + 3[?7h[?12l[?25h[?25l[?7ln) + 3[?7h[?12l[?25h[?25l[?7lt) + 3[?7h[?12l[?25h[?25l[?7le) + 3[?7h[?12l[?25h[?25l[?7lg) + 3[?7h[?12l[?25h[?25l[?7le) + 3[?7h[?12l[?25h[?25l[?7lr) + 3[?7h[?12l[?25h[?25l[?7ls) + 3[?7h[?12l[?25h[?25l[?7l(() + 3[?7h[?12l[?25h[?25l[?7l9) + 3[?7h[?12l[?25h[?25l[?7l(()) + 3[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) + 3 -[?7h[?12l[?25h[?2004l[?7hx^3 + 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9)) + 3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) + 9 -[?7h[?12l[?25h[?2004l[?7hx^3 + 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9)) + 9[?7h[?12l[?25h[?25l[?7l = x^3 + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: g = x + 2*y -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x + 2*y[?7h[?12l[?25h[?25l[?7l.change_ring(Integers(9)) + 9[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lZZ) + 3[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(ZZ) -[?7h[?12l[?25h[?2004l[?7hx + 2*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(ZZ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lI)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l9))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l) + 9[?7h[?12l[?25h[?25l[?7l() + 9[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) + 9 -[?7h[?12l[?25h[?2004l[?7hx + 2*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9)) + 9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) -[?7h[?12l[?25h[?2004l[?7hx + 2*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7l = x + 2*y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx + 2*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x + 2*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = (x + 2*y)/(-8*x+1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (x + 2*y)/(-8*x+1)[?7h[?12l[?25h[?25l[?7l.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lge_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) -[?7h[?12l[?25h[?2004lsage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z' - """ -sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z' - """ ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 379 try: ---> 380 z = integer_ring.Z(value) - 381 except (TypeError, ValueError): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1619 --> 1620 cpdef Element _call_(self, _x): - 1621 """ - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1651 if nmod_poly_degree(x._denom) != 0: --> 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: - -ValueError: not integral - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [95], in () -----> 1 g.change_ring(Integers(Integer(9))) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3377, in sage.rings.polynomial.polynomial_element.Polynomial.change_ring() - 3375 return self.map_coefficients(R) - 3376 else: --> 3377 return self._parent.change_ring(R)(self.list(copy=False)) - 3378 - 3379 cpdef dict _mpoly_dict_recursive(self, tuple variables=None, base_ring=None): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:416, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds) - 414 C = self.element_class - 415 if isinstance(x, (list, tuple)): ---> 416 return C(self, x, check=check, is_gen=False, construct=construct) - 417 if isinstance(x, range): - 418 return C(self, list(x), check=check, is_gen=False, - 419 construct=construct) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:106, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__() - 104 k = parent._base - 105 if check: ---> 106 lst = [k(i) for i in x] - 107 else: - 108 lst = x - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) - 1143 """ - 1144 TESTS:: - 1145 - (...) - 1182  True - 1183 """ - 1184 try: --> 1185 return integer_mod.IntegerMod(self, x) - 1186 except (NotImplementedError, PariError): - 1187 raise TypeError("error coercing to finite field") - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() - 199 return a - 200 t = modulus.element_class() ---> 201 return t(parent, value) - 202 - 203 - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:388, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 386 value = py_scalar_to_element(value) - 387 if isinstance(value, Element) and value.parent().is_exact(): ---> 388 value = sage.rings.rational_field.QQ(value) - 389 z = value % self.__modulus.sageInteger - 390 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 536 """ - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - 540 def __reduce__(self): - -File /ext/sage/9.7/src/sage/rings/rational.pyx:691, in sage.rings.rational.Rational.__set_value() - 689 - 690 else: ---> 691 raise TypeError("unable to convert {!r} to a rational".format(x)) - 692 - 693 cdef void set_from_mpq(Rational self, mpq_t value): - -TypeError: unable to convert x/(x + 1) to a rational -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 379 try: ---> 380 z = integer_ring.Z(value) - 381 except (TypeError, ValueError): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1619 --> 1620 cpdef Element _call_(self, _x): - 1621 """ - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1651 if nmod_poly_degree(x._denom) != 0: --> 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: - -ValueError: not integral - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [96], in () -----> 1 g.change_ring(Integers(Integer(9))) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3377, in sage.rings.polynomial.polynomial_element.Polynomial.change_ring() - 3375 return self.map_coefficients(R) - 3376 else: --> 3377 return self._parent.change_ring(R)(self.list(copy=False)) - 3378 - 3379 cpdef dict _mpoly_dict_recursive(self, tuple variables=None, base_ring=None): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:416, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds) - 414 C = self.element_class - 415 if isinstance(x, (list, tuple)): ---> 416 return C(self, x, check=check, is_gen=False, construct=construct) - 417 if isinstance(x, range): - 418 return C(self, list(x), check=check, is_gen=False, - 419 construct=construct) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:106, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__() - 104 k = parent._base - 105 if check: ---> 106 lst = [k(i) for i in x] - 107 else: - 108 lst = x - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) - 1143 """ - 1144 TESTS:: - 1145 - (...) - 1182  True - 1183 """ - 1184 try: --> 1185 return integer_mod.IntegerMod(self, x) - 1186 except (NotImplementedError, PariError): - 1187 raise TypeError("error coercing to finite field") - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() - 199 return a - 200 t = modulus.element_class() ---> 201 return t(parent, value) - 202 - 203 - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:388, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 386 value = py_scalar_to_element(value) - 387 if isinstance(value, Element) and value.parent().is_exact(): ---> 388 value = sage.rings.rational_field.QQ(value) - 389 z = value % self.__modulus.sageInteger - 390 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 536 """ - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - 540 def __reduce__(self): - -File /ext/sage/9.7/src/sage/rings/rational.pyx:691, in sage.rings.rational.Rational.__set_value() - 689 - 690 else: ---> 691 raise TypeError("unable to convert {!r} to a rational".format(x)) - 692 - 693 cdef void set_from_mpq(Rational self, mpq_t value): - -TypeError: unable to convert x/(x + 1) to a rational -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sag')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/rgular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7ld.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7la.sage')[?7h[?12l[?25h[?25l[?7lf.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft.sage') -[?7h[?12l[?25h[?2004l(y, -x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(y, -x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.holomophic_dfferentials_basis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?7h[(1/y) dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7leC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lcC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7loC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lnC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7ldC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7l_C.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lpC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7laC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7ltC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lcC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lhC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7l(C.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.holomorphic_differentials_basis()[0]) -[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(g)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltch(patch(C))[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C) -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?identity_matrix[?7h[?12l[?25h[?25l[?7lsuperelliptic[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lsage: ?second_patch -[?7h[?12l[?25h[?2004lSignature: second_patch(argument) -Init docstring: Initialize self. See help(type(self)) for accurate signature. -File: Dynamically generated function. No source code available. -Type: function -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld_patch[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: help(second_patch) -[?7h[?12l[?25h[?2004l[?1049h[?1h= Help on function second_patch in module __main__: - -second_patch(argument) -(END)  (END)  ::qq [?1l>[?1049l -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?second_patch[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: ?regula - regular_form - regulator  - - - [?7h[?12l[?25h[?25l[?7lr_form - regular_form - - [?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7lsage: ?regular_form -[?7h[?12l[?25h[?2004lSignature: regular_form(omega) -Docstring: -Given a form omega regular on U0, present it as P(x, y) dx + Q(x, y) -dy for some polynomial P, Q. - The output is A(x)*y, B(x), where omega = A(x) y dx + B(x) dy -Init docstring: Initialize self. See help(type(self)) for accurate signature. -File: Dynamically generated function. No source code available. -Type: function -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 dx -3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3 -f2 ((-x^6 - 1)/(x^2*y - y)) dx -((x^4 + x^2 + 1)/(x^6*y)) dx -[0] -[0] -t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25) -((x^10 - x^6 + 1)/(x^2*y - y)) dx -(x^7 + x, 0) -((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx -((-x^6 - 1)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l?regular_form[?7h[?12l[?25h[?25l[?7lhelp(second_patch)[?7h[?12l[?25h[?25l[?7l?second_patch[?7h[?12l[?25h[?25l[?7lpath(C)[?7h[?12l[?25h[?25l[?7l?seond_patch[?7h[?12l[?25h[?25l[?7lhelp(second_patch)[?7h[?12l[?25h[?25l[?7l?regular_form[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -I-search:[?7h[?12l[?25h[?25l[?7lload('init.sage') -l[?7h[?12l[?25h[?25l[?7l -;[?7h[?12l[?25h[?25l[?7lload('init.sage') -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -False -(y, -x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -((2*x^3 + 1)/y) dx (1/y) dx -(y, -x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -((2*x^3 + 1)/y) dx (1/y) dx -3*x^3 + 1 1 -(y, -x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -((2*x^3 + 1)/y) dx (1/y) dx -1 1 -(y, -x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -((-2*x^3 + 1)/y) dx (1/y) dx -1 1 -(y, -x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -1 1 -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -False -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.dx == C.dx -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx == C.dx[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx == C.dx[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C == C -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7licznik[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: omega = C.de - C.de_rham_basis C.degrees_de_rham1  - C.degrees_de_rham0 C.degrees_holomorphic_differentials - - - [?7h[?12l[?25h[?25l[?7l_rham_basis - C.de_rham_basis  - - [?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega = C.de_rham_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - - [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7licznik[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt - lift  - lift_form_to_drw - lift_to_sl2z  -  - [?7h[?12l[?25h[?25l[?7l - lift  - - - [?7h[?12l[?25h[?25l[?7l_form_to_drw - lift  - lift_form_to_drw[?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [24], in () -----> 1 lift_form_to_drw(omega) - -File :29, in lift_form_to_drw(omega) - -File :5, in regular_form(omega) - -AttributeError: 'list' object has no attribute 'curve' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7lomega = C.derham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: omega = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7llift_form_todrw(omega)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [26], in () -----> 1 lift_form_to_drw(omega) - -File :29, in lift_form_to_drw(omega) - -File :10, in regular_form(omega) - -AttributeError: 'superelliptic_cech' object has no attribute 'form' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7lomega = C.derham_basis()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: omega = C.holomorphic_differentials_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.holomorphic_differentials_basis()[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.holomorphic_differentials_basis()[0][?7h[?12l[?25h[?25l[?7llift_form_t_drw(omega)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega) -[?7h[?12l[?25h[?2004l(1/y) dx (1/y) dx -y dx + x dy -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R = Integers(25) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR = Integers(25)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R(2^5) -[?7h[?12l[?25h[?2004l[?7h7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(2^5)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R(7^5) -[?7h[?12l[?25h[?2004l[?7h7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(7^5)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R(2^25) -[?7h[?12l[?25h[?2004l[?7h7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(3):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lin range(3):[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l):[?7h[?12l[?25h[?25l[?7l2):[?7h[?12l[?25h[?25l[?7l5):[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: for a in range(25): -....: [?7h[?12l[?25h[?25l[?7lif m%p != 0:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la not in lista2:[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7land[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:  if a%5 == 2 and a^5 == 1: -....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lan[?7h[?12l[?25h[?25l[?7land[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l -....: [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print(a) -....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(25): -....:  if a%5 == 2 and a^5%25 == 1: -....:  print(a) -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in range(25): -....:  if a%5 == 2 and a^5%25 == 1: -....:  print(a)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^5%25 = 1:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()%25 = 1:[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -....:  -....:  print(a)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l print(a) - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l() -....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(25): -....:  if a%5 == 2 and (a^5)%25 == 1: -....:  print(a) -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in range(25): -....:  if a%5 == 2 and (a^5)%25 == 1: -....:  print(a)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7la:[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(a) -....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(25): -....:  if a%5 == 2 and (a^5)%25 == a: -....:  print(a) -....:  -[?7h[?12l[?25h[?2004l7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(2^25)[?7h[?12l[?25h[?25l[?7l(2^25)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laR(2)[?7h[?12l[?25h[?25l[?7l R(2)[?7h[?12l[?25h[?25l[?7l=R(2)[?7h[?12l[?25h[?25l[?7l R(2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a = R(2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = R(2)[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.lift() -[?7h[?12l[?25h[?2004l[?7h2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(g)[?7h[?12l[?25h[?25l[?7lextE.local_data(2))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -UnboundLocalError Traceback (most recent call last) -Input In [40], in () -----> 1 teichmuller(C.x + Integer(2)*C.y) - -File :22, in teichmuller(fct) - -UnboundLocalError: local variable 'fct1' referenced before assignment -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [42], in () -----> 1 teichmuller(C.x + Integer(2)*C.y) - -File :22, in teichmuller(fct) - -TypeError: unsupported operand type(s) for -: 'PolynomialRing_field_with_category.element_class' and 'superelliptic_function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [44], in () -----> 1 teichmuller(C.x + Integer(2)*C.y) - -File :24, in teichmuller(fct) - -File :24, in teichmuller(fct) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.fraction_field_FpT.FpTElement' object has no attribute 'lift' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [46], in () -----> 1 teichmuller(C.x + Integer(2)*C.y) - -File :18, in teichmuller(fct) - -AttributeError: 'superelliptic' object has no attribute 'base_field' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [48], in () -----> 1 teichmuller(C.x + Integer(2)*C.y) - -File :23, in teichmuller(fct) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:6094, in sage.rings.polynomial.polynomial_element.Polynomial.monomial_coefficient() - 6092 """ - 6093 if not m.parent() is self._parent: --> 6094 raise TypeError("monomial must have same parent as self.") - 6095 - 6096 d = m.degree() - -TypeError: monomial must have same parent as self. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [50], in () -----> 1 teichmuller(C.x + Integer(2)*C.y) - -File :26, in teichmuller(fct) - -File :26, in teichmuller(fct) - -File /ext/sage/9.7/src/sage/rings/integer.pyx:1769, in sage.rings.integer.Integer.__add__() - 1767 return y - 1768 --> 1769 return coercion_model.bin_op(left, right, operator.add) - 1770 - 1771 cpdef _add_(self, right): - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() - 1246 # We should really include the underlying error. - 1247 # This causes so much headache. --> 1248 raise bin_op_exception(op, x, y) - 1249 - 1250 cpdef canonical_coercion(self, x, y): - -TypeError: unsupported operand parent(s) for +: 'Integer Ring' and '' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l[?7h) failed: NameError: name 'f0' is not defined> -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l[?7hx + 32*y + V(2*x^2*y + 4*x^4 + 4*x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC == C[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [57], in () -----> 1 teichmuller(C.x + Integer(2)*C.y) - -File :43, in teichmuller(fct) - -File :43, in teichmuller(fct) - -File :38, in teichmuller(fct) - -File :6, in __init__(self, C, f0, f1) - -File :23, in reduce_rational_fct(fct, p) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'monomials' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l[?7hx + 7*y + V(2*x^2*y + 4*x^4 + 4*x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx -(1/y) dx (1/y) dx -(y, x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l == C[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(2^25)[?7h[?12l[?25h[?25l[?7lx. = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l. = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l4))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(4)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l == C[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l+, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l1, 3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 3) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 3)[?7h[?12l[?25h[?25l[?7l.dx == C.dx[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lsmooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp_rank()[?7h[?12l[?25h[?25l[?7lsage: C.p_rank() - C.p_rank  - C.polynomial - - - [?7h[?12l[?25h[?25l[?7l - -[?7h[?12l[?25h[?25l[?7l - C.a_number C.basis_of_cohomology C.degrees_de_rham0  - C.base_ring C.cartier_matrix C.degrees_de_rham1  - C.basis_de_rham_degrees C.characteristic C.degrees_holomorphic_differentials > - C.basis_holomorphic_differentials_degree C.de_rham_basis C.dr_frobenius_matrix [?7h[?12l[?25h[?25l[?7lgenus() - - - -[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + 1, 2)[?7h[?12l[?25h[?25l[?7l4 + 1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 + 1, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - [?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 + 1, 2)[?7h[?12l[?25h[?25l[?7l.gens()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 + x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 + x, 2)[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.y)^(-1)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(25):[?7h[?12l[?25h[?25l[?7l =x^3 - x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: f = AS.magical_element()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7lsage: f -[?7h[?12l[?25h[?2004l[?7hx^5 + x^4 + z0*z1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.valuation() -[?7h[?12l[?25h[?2004l[?7h-13 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.y)^(-1)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different - AS.exponent_of_different  - AS.exponent_of_different_prim - - - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - AS.exponent_of_different  - - [?7h[?12l[?25h[?25l[?7l_prim - AS.exponent_of_different  - AS.exponent_of_different_prim[?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim() -[?7h[?12l[?25h[?2004l[?7h13 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lf.valuation()[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.valuation()[?7h[?12l[?25h[?25l[?7l = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf + z0^2[?7h[?12l[?25h[?25l[?7l1f + z0^2[?7h[?12l[?25h[?25l[?7l f + z0^2[?7h[?12l[?25h[?25l[?7l=f + z0^2[?7h[?12l[?25h[?25l[?7l f + z0^2[?7h[?12l[?25h[?25l[?7lsage: f1 = f + z0^2 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [6], in () -----> 1 f1 = f + z0**Integer(2) - -NameError: name 'z0' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f + z0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f + z0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2[?7h[?12l[?25h[?25l[?7lSz0^2[?7h[?12l[?25h[?25l[?7l.z0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = f + AS.z[0]^2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f + AS.z[0]^2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.valuation() -[?7h[?12l[?25h[?2004l[?7h-20 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim() -[?7h[?12l[?25h[?2004l[?7h13 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfAS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l1AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l=AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7lAS.z[1]+x^4[?7h[?12l[?25h[?25l[?7lSAS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l.AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7lzAS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l0AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[]AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[] AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l+AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])+x^4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = AS.z[0]*(AS.z[0] + AS.z[1])+x^4 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [12], in () -----> 1 f1 = AS.z[Integer(0)]*(AS.z[Integer(0)] + AS.z[Integer(1)])+x**Integer(4) - -File :23, in __add__(self, other) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.polynomial.polynomial_gf2x.Polynomial_GF2X' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = AS.z[0]*(AS.z[0] + AS.z[1])+x^4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f1 -[?7h[?12l[?25h[?2004l[?7hx^5 + x^4 + z0^2 + z0*z1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7l = AS.z[0]*(AS.z[0] + AS.z[1])+x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAx^4[?7h[?12l[?25h[?25l[?7lSx^4[?7h[?12l[?25h[?25l[?7l.x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = AS.z[0]*(AS.z[0] + AS.z[1])+AS.x^4 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = AS.z[0]*(AS.z[0] + AS.z[1])+AS.x^4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lluation()[?7h[?12l[?25h[?25l[?7lsage: f1.valuation() -[?7h[?12l[?25h[?2004l[?7h-13 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(4))[?7h[?12l[?25h[?25l[?7l. = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx>[?7h[?12l[?25h[?25l[?7l = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lsage: R. = PolynomialRing(GF(3)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1.valuation()[?7h[?12l[?25h[?25l[?7l = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^3 - x[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f = x^3 + 2*x - 1 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.holomorphic_differentials_basis()[0])[?7h[?12l[?25h[?25l[?7ltr(E.local_data(2))[?7h[?12l[?25h[?25l[?7lstr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]"[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: str(f).replace("x", "[x]") -[?7h[?12l[?25h[?2004l[?7h'[x]^3 + 2*[x] + 2' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y) -[?7h[?12l[?25h[?2004l[?7h[x] + V(0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [6] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :26 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :14 - return "[" + str(t) "] + " + str(f0).replace("x", "[x]").replace("y", "[y]") + " + V(" + str(f1) + ")" - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.lift()[?7h[?12l[?25h[?25l[?7l = R(2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_witt(C, C.x, 0, C.y) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_witt(C, C.x, 0, C.y)[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h[x] + 0 + V(x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_witt(C, C.x, 0, C.y)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x, 0, C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(), 0, C.y)[?7h[?12l[?25h[?25l[?7l()^, 0, C.y)[?7h[?12l[?25h[?25l[?7l2, 0, C.y)[?7h[?12l[?25h[?25l[?7l , 0, C.y)[?7h[?12l[?25h[?25l[?7l+, 0, C.y)[?7h[?12l[?25h[?25l[?7l , 0, C.y)[?7h[?12l[?25h[?25l[?7lC, 0, C.y)[?7h[?12l[?25h[?25l[?7l., 0, C.y)[?7h[?12l[?25h[?25l[?7ly, 0, C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_witt(C, (C.x)^2 + C.y, 0, C.y) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_witt(C, (C.x)^2 + C.y, 0, C.y)[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h[x^2 + x] + 0 + V(x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd .. -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status -On branch master -Your branch is up to date with 'origin/master'. - -Changes not staged for commit: - (use "git add ..." to update what will be committed) - (use "git restore ..." to discard changes in working directory) - modified: sage/.run.term-0.term - modified: sage/as_covers/as_cover_class.sage - modified: sage/as_covers/as_form_class.sage - modified: sage/drafty/draft.sage - modified: sage/drafty/draft2.sage - modified: sage/init.sage - modified: sage/superelliptic/superelliptic_class.sage - modified: sage/superelliptic/superelliptic_form_class.sage - modified: sage/superelliptic/superelliptic_function_class.sage - modified: sage/tests.sage - -Untracked files: - (use "git add ..." to include in what will be committed) - .crystalline_p2.ipynb.sage-jupyter2 - .deRhamComputation.ipynb.sage-jupyter2 - .elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2 - .git.x11-0.term - .superelliptic.ipynb.sage-jupyter2 - .superelliptic_alpha.ipynb.sage-jupyter2 - .superelliptic_arbitrary_field.ipynb.sage-jupyter2 - git.x11 - sage/as_covers/tests/cartier_test.sage - sage/drafty/as_cartier.sage - sage/drafty/better_trace.sage - sage/drafty/cartier_image_representation.sage - sage/drafty/draft4.sage - sage/drafty/draft5.sage - sage/drafty/draft6.sage - sage/drafty/draft7.sage - sage/drafty/lift_to_de_rham.sage - sage/drafty/pole_numbers.sage - sage/drafty/regular_on_U0.sage - sage/drafty/second_patch.sage - sage/drafty/superelliptic_drw.sage - sage/superelliptic/decomposition_into_g0_g8.sage - sage/superelliptic/frobenius_kernel.sage - sage/superelliptic/tests/ - superelliptic_arbitrary_field.ipynb - -no changes added to commit (use "git add" and/or "git commit -a") -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ add sage/drafty/addgit add sage/drafty/superelliptic_drw.sage sage/drafty/superelliptic/decomposition_into_g0_g8.sage -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m "superelliptic de rham witt - poczatek" -[master 856d742] superelliptic de rham witt - poczatek - 12 files changed, 12077 insertions(+), 105 deletions(-) - rewrite sage/drafty/draft.sage (91%) - create mode 100644 sage/drafty/superelliptic_drw.sage - create mode 100644 sage/superelliptic/decomposition_into_g0_g8.sage -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push -Username for 'https://git.wmi.amu.edu.pl': jgarnek -Password for 'https://jgarnek@git.wmi.amu.edu.pl': -Enumerating objects: 31, done. -Counting objects: 3% (1/31) Counting objects: 6% (2/31) Counting objects: 9% (3/31) Counting objects: 12% (4/31) Counting objects: 16% (5/31) Counting objects: 19% (6/31) Counting objects: 22% (7/31) Counting objects: 25% (8/31) Counting objects: 29% (9/31) Counting objects: 32% (10/31) Counting objects: 35% (11/31) Counting objects: 38% (12/31) Counting objects: 41% (13/31) Counting objects: 45% (14/31) Counting objects: 48% (15/31) Counting objects: 51% (16/31) Counting objects: 54% (17/31) Counting objects: 58% (18/31) Counting objects: 61% (19/31) Counting objects: 64% (20/31) Counting objects: 67% (21/31) Counting objects: 70% (22/31) Counting objects: 74% (23/31) Counting objects: 77% (24/31) Counting objects: 80% (25/31) Counting objects: 83% (26/31) Counting objects: 87% (27/31) Counting objects: 90% (28/31) Counting objects: 93% (29/31) Counting objects: 96% (30/31) Counting objects: 100% (31/31) Counting objects: 100% (31/31), done. -Delta compression using up to 4 threads -Compressing objects: 5% (1/18) Compressing objects: 11% (2/18) Compressing objects: 16% (3/18) Compressing objects: 22% (4/18) Compressing objects: 27% (5/18) Compressing objects: 33% (6/18) Compressing objects: 38% (7/18) Compressing objects: 44% (8/18) Compressing objects: 50% (9/18) Compressing objects: 55% (10/18) Compressing objects: 61% (11/18) Compressing objects: 66% (12/18) Compressing objects: 72% (13/18) Compressing objects: 77% (14/18) Compressing objects: 83% (15/18) Compressing objects: 88% (16/18) Compressing objects: 94% (17/18) Compressing objects: 100% (18/18) Compressing objects: 100% (18/18), done. -Writing objects: 5% (1/18) Writing objects: 11% (2/18) Writing objects: 16% (3/18) Writing objects: 22% (4/18) Writing objects: 27% (5/18) Writing objects: 33% (6/18) Writing objects: 38% (7/18) Writing objects: 44% (8/18) Writing objects: 50% (9/18) Writing objects: 55% (10/18) Writing objects: 61% (11/18) Writing objects: 66% (12/18) Writing objects: 72% (13/18) Writing objects: 77% (14/18) Writing objects: 83% (15/18) Writing objects: 88% (16/18) Writing objects: 94% (17/18) Writing objects: 100% (18/18) Writing objects: 100% (18/18), 91.43 KiB | 1.63 MiB/s, done. -Total 18 (delta 8), reused 0 (delta 0) -remote: . Processing 1 references -remote: Processed 1 references in total -To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git - f683017..856d742 master -> master -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: 2021 De Rham/DeRhamComputation[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -OSError Traceback (most recent call last) -Input In [1], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:244, in load(filename, globals, attach) - 242 break - 243 else: ---> 244 raise IOError('did not find file %r to load or attach' % filename) - 246 ext = os.path.splitext(fpath)[1].lower() - 247 if ext == '.py': - -OSError: did not find file 'init.sage' to load or attach -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage/ -]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.curve() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [3], in () -----> 1 C.x.curve() - -TypeError: 'superelliptic' object is not callable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.curve()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.curve -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lbin[?7h[?12l[?25h[?25l[?7lbino[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: binomial - binomial  - binomial_coefficients - - - [?7h[?12l[?25h[?25l[?7l - binomial  - - [?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: binomial(4, 2) -[?7h[?12l[?25h[?2004l[?7h6 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(f).replace("x", "[x]")[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lrw_form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lon[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: superelliptic_drw_form(C.one, 0, 0) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [2], in () -----> 1 superelliptic_drw_form(C.one, Integer(0), Integer(0)) - -TypeError: superelliptic_drw_form.__init__() missing 1 required positional argument: 'h' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: superelliptic_drw_form(C.one, 0, 0) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [3], in () -----> 1 superelliptic_drw_form(C.one, Integer(0), Integer(0)) - -TypeError: superelliptic_drw_form.__init__() missing 1 required positional argument: 'h' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbinomial(4, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: superelliptic_drw_form(C.one, 0, 0) -[?7h[?12l[?25h[?2004l[?7h[1] d[x] + V(0) + dV([0]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx+1[?7h[?12l[?25h[?25l[?7lsage: x -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: x - x -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx - x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: x - x == 0 -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [9] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :26 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :83 - if result ="": - ^ -SyntaxError: invalid syntax. Maybe you meant '==' or ':=' instead of '='? - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lx - x == 0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: superelliptic_drw_form(C.one, 0, 0) -[?7h[?12l[?25h[?2004l[?7h) failed: AttributeError: 'sage.rings.integer.Integer' object has no attribute 'form'> -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*, 0)[?7h[?12l[?25h[?25l[?7lC, 0)[?7h[?12l[?25h[?25l[?7l., 0)[?7h[?12l[?25h[?25l[?7ld, 0)[?7h[?12l[?25h[?25l[?7lx, 0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lsage: superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) -[?7h[?12l[?25h[?2004l[?7h[1] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2+2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lasupereliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l supereliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l=supereliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l supereliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0, 0) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbinomial(4, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: b = a+b -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [14], in () -----> 1 b = a+b - -NameError: name 'b' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+b[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: b = a+a -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [15], in () -----> 1 b = a+a - -File :106, in __add__(self, other) - -File :27, in __add__(self, other) - -TypeError: superelliptic_witt.__init__() takes 3 positional arguments but 4 were given -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsuperelliptic_drwform(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0, 0) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.curve[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [19], in () -----> 1 a+a - -File :106, in __add__(self, other) - -File :95, in __rmul__(self, other) - -NameError: name 'f0' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la+[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0, 0) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*, 0)[?7h[?12l[?25h[?25l[?7lC, 0)[?7h[?12l[?25h[?25l[?7l., 0)[?7h[?12l[?25h[?25l[?7ld, 0)[?7h[?12l[?25h[?25l[?7lx, 0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0)[?7h[?12l[?25h[?25l[?7l*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7lsage: b = a+a -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [23], in () -----> 1 b = a+a - -File :106, in __add__(self, other) - -File :95, in __rmul__(self, other) - -NameError: name 'h0' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lsage: b = a+a -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [26], in () -----> 1 b = a+a - -File :107, in __add__(self, other) - -File :105, in __add__(self, other) - -File :38, in __add__(self, other) - -AttributeError: 'superelliptic_form' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lsage: b = a+a -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lsage: b -[?7h[?12l[?25h[?2004l[?7h[1] d[x]V(x dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = a+a[?7h[?12l[?25h[?25l[?7lsage: b = a+a -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lsage: b -[?7h[?12l[?25h[?2004l[?7h[1] d[x] + V(x dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = a+a[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: b = b+a -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = b+a[?7h[?12l[?25h[?25l[?7lsage: b -[?7h[?12l[?25h[?2004l[?7h[1] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = b+a[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb+a[?7h[?12l[?25h[?25l[?7lsage: b = b+a -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = b+a[?7h[?12l[?25h[?25l[?7lsage: b -[?7h[?12l[?25h[?2004l[?7h[1] d[x] + V(x dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[1] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[1] d[x] + V((-x^2) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[1] d[x] + V((-x^2) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h[1] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a+a -[?7h[?12l[?25h[?2004l[?7hV((x^2) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lhelp(second_patch)[?7h[?12l[?25h[?25l[?7l = yy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: h = x/x -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh = x/x[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: h == 1 -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrent(g)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(x) -[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx - x == 0[?7h[?12l[?25h[?25l[?7l+1[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: x+y -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [51], in () -----> 1 x+y - -NameError: name 'y' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: -C.x -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [53], in () -----> 1 -C.x - -TypeError: superelliptic_function.__neg__() missing 1 required positional argument: 'other' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l-C.x[?7h[?12l[?25h[?25l[?7lsage: -C.x -[?7h[?12l[?25h[?2004l[?7h2*x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.x[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: -C.dx -[?7h[?12l[?25h[?2004l[?7h(-1) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [1] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :26 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :43 - ????? - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h[1] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2+2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 2*a -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [4], in () -----> 1 Integer(2)*a - -File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() - 1962 return y - 1963 --> 1964 return coercion_model.bin_op(left, right, operator.mul) - 1965 - 1966 cpdef _mul_(self, right): - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() - 1240 mul_method = getattr(y, '__r%s__'%op_name, None) - 1241 if mul_method is not None: --> 1242 res = mul_method(x) - 1243 if res is not None and res is not NotImplemented: - 1244 return res - -File :108, in __rmul__(self, other) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 't' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.curve[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller() -[?7h[?12l[?25h[?2004l[?7h[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [7] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :26 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :75 - dy = [f(x)]'/2*y dx - ^ -SyntaxError: unterminated string literal (detected at line 75) - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lteichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h[1] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*a[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 2*a -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*a[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 2*a -[?7h[?12l[?25h[?2004l[?7h[2] d[x] + V((x^2) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3^4[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 3*a -[?7h[?12l[?25h[?2004l[?7hV((x^2) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 9*a -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.dx[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: -3*a -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [15], in () -----> 1 -Integer(3)*a - -File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() - 1962 return y - 1963 --> 1964 return coercion_model.bin_op(left, right, operator.mul) - 1965 - 1966 cpdef _mul_(self, right): - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() - 1240 mul_method = getattr(y, '__r%s__'%op_name, None) - 1241 if mul_method is not None: --> 1242 res = mul_method(x) - 1243 if res is not None and res is not NotImplemented: - 1244 return res - -File :127, in __rmul__(self, other) - -TypeError: bad operand type for unary -: 'superelliptic_drw_form' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-3*a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-3*a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*a[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-3)*a -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [16], in () -----> 1 (-Integer(3))*a - -File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() - 1962 return y - 1963 --> 1964 return coercion_model.bin_op(left, right, operator.mul) - 1965 - 1966 cpdef _mul_(self, right): - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() - 1240 mul_method = getattr(y, '__r%s__'%op_name, None) - 1241 if mul_method is not None: --> 1242 res = mul_method(x) - 1243 if res is not None and res is not NotImplemented: - 1244 return res - -File :127, in __rmul__(self, other) - -TypeError: bad operand type for unary -: 'superelliptic_drw_form' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-3*a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: -a -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [18], in () -----> 1 -a - -TypeError: superelliptic_drw_form.__neg__() missing 1 required positional argument: 'other' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-a[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l-a[?7h[?12l[?25h[?25l[?7lsage: -a -[?7h[?12l[?25h[?2004l[?7h[2] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^3 + 2*x - 1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: f = x^5 - x^4 + 2*x -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^5 - x^4 + 2*x[?7h[?12l[?25h[?25l[?7lsage: f -[?7h[?12l[?25h[?2004l[?7hx^5 + 2*x^4 + 2*x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(x)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(f) -[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lMf.monomials()[0][?7h[?12l[?25h[?25l[?7l f.monomials()[0][?7h[?12l[?25h[?25l[?7l=f.monomials()[0][?7h[?12l[?25h[?25l[?7l f.monomials()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = f.monomials()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = f.monomials()[0][?7h[?12l[?25h[?25l[?7lsage: M -[?7h[?12l[?25h[?2004l[?7hx^5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.determinant()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M. - M.abs M.all_roots_in_interval M.base_ring M.change_variable_name M.compose_trunc  - M.adams_operator M.any_root M.cartesian_product M.coefficients M.composed_op  - M.add_bigoh M.args M.category M.complex_roots M.constant_coefficient > - M.additive_order M.base_extend M.change_ring M.compose_power M.content_ideal  - [?7h[?12l[?25h[?25l[?7labs - M.abs  - - - - [?7h[?12l[?25h[?25l[?7lll_roots_in_interval - M.abs  M.all_roots_in_interval [?7h[?12l[?25h[?25l[?7lbase_ring - M.all_roots_in_interval  M.base_ring [?7h[?12l[?25h[?25l[?7lchange_variable_name - M.base_ring  M.change_variable_name [?7h[?12l[?25h[?25l[?7lompose_tunc - M.change_variable_name  M.compose_trunc [?7h[?12l[?25h[?25l[?7lycltomic_part - ll_roots_in_intervalbase_ring change_variable_nameompose_tunc ycltomic_part - ny_rot cartesian_productoefficients mposed_op degree  -<rgs categoryomplex_rootsnstant_cefficientdeomiator  - base_extend chang_rigompose_powerntentidealderivaive [?7h[?12l[?25h[?25l[?7ldit -base_ring change_variable_nameompose_tunc ycltomic_partdit  -cartesian_productoefficients mposed_op degree iff  -categoryomplex_rootsnstant_cefficientdeomiator iffereniate -chang_rigompose_powerntentidealderivaive iscrimnant[?7h[?12l[?25h[?25l[?7lspersion -change_variable_nameompose_tunc ycltomic_partdit spersion -oefficients mposed_op degree iff spersion_set -omplex_rootsnstant_cefficientdeomiator iffereniatevides  -ompose_powerntentidealderivaive iscrimnantump [?7h[?12l[?25h[?25l[?7lums -ompose_tunc ycltomic_partdit spersionums  -mposed_op degree iff spersion_seteuclidean_degree -nstant_cefficientdeomiator iffereniatevides exponnts -ntentidealderivaive iscrimnantump factor[?7h[?12l[?25h[?25l[?7leclidean_degree - M.dumps  - M.euclidean_degree [?7h[?12l[?25h[?25l[?7lxponents - - M.euclidean_degree  - M.exponents [?7h[?12l[?25h[?25l[?7lfactor - - - M.exponents  - M.factor [?7h[?12l[?25h[?25l[?7lexponents - - - M.exponents  - M.factor [?7h[?12l[?25h[?25l[?7l - - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.exponents() -[?7h[?12l[?25h[?2004l[?7h[5] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lM.exponents()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: M.exponents()[0] -[?7h[?12l[?25h[?2004l[?7h5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h[1] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = b+a[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(.teichmuler()[?7h[?12l[?25h[?25l[?7l().teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC).teichmuler()[?7h[?12l[?25h[?25l[?7l.).teichmuler()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l^).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).teichmuler()[?7h[?12l[?25h[?25l[?7l^).teichmuler()[?7h[?12l[?25h[?25l[?7l3).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7l+).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7l(().teichmuler()[?7h[?12l[?25h[?25l[?7lC).teichmuler()[?7h[?12l[?25h[?25l[?7l.).teichmuler()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l(()).teichmuler()[?7h[?12l[?25h[?25l[?7l^).teichmuler()[?7h[?12l[?25h[?25l[?7l2).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: auxilliar - auxilliaries/  - auxilliary_derivative - - - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lies/ - auxilliaries/  - - [?7h[?12l[?25h[?25l[?7ly_derivative - auxilliaries/  - auxilliary_derivative[?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [31], in () -----> 1 auxilliary_derivative(b) - -File :92, in auxilliary_derivative(P) - -TypeError: unsupported operand type(s) for -: 'superelliptic_witt' and 'superelliptic_witt' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [34], in () -----> 1 auxilliary_derivative(b) - -File :97, in auxilliary_derivative(P) - -NameError: name 'superelliptic_drw' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7llliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [38], in () -----> 1 auxilliary_derivative(b) - -File :97, in auxilliary_derivative(P) - -File :175, in __add__(self, other) - -TypeError: unsupported operand type(s) for +: 'PolynomialRing_field_with_category.element_class' and 'superelliptic_function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [41], in () -----> 1 auxilliary_derivative(b) - -File :97, in auxilliary_derivative(P) - -File :132, in __repr__(self) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class() - 354 dummy_error_message.cls = type(self) - 355 dummy_error_message.name = name ---> 356 raise AttributeError(dummy_error_message) - 357 cdef PyObject* attr = instance_getattr(cls, name) - 358 if attr is NULL: - -AttributeError: 'PolynomialRing_field_with_category.element_class' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) -[?7h[?12l[?25h[?2004l0 -[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l (C.x)^2).teichmuler()[?7h[?12l[?25h[?25l[?7l- (C.x)^2).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(2.teichmuler()[?7h[?12l[?25h[?25l[?7l.teichmuler()[?7h[?12l[?25h[?25l[?7l().teichmuler()[?7h[?12l[?25h[?25l[?7l(()).teichmuler()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 - (C.x)).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7llliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) -[?7h[?12l[?25h[?2004l0 -[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 - (C.x)).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 - (C.x)).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.teichmuller()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7llliary_derivative(b)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(C.x.teichmuller()) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(C.x.teichmuller()) -[?7h[?12l[?25h[?2004lx 1 -0 -[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(C.x.teichmuller()) -[?7h[?12l[?25h[?2004lx 1 -0 [1] d[x] -[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.teichmuller()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbC.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = C.x.function -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = C.x.function[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7lsage: b.monomials()\ -[?7h[?12l[?25h[?2004l[?7h[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.monomials()\[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.monomials() -[?7h[?12l[?25h[?2004l[?7h[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.monomials()[?7h[?12l[?25h[?25l[?7lsage: b -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.monomials()[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7l = C.x.function[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(C.x.teichmuller()) -[?7h[?12l[?25h[?2004l1 x -1 [1] d[x] -[?7h[1] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^).teichmuler()[?7h[?12l[?25h[?25l[?7l3).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7l-).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7lC).teichmuler()[?7h[?12l[?25h[?25l[?7l.).teichmuler()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((C.x^3 - C.x).teichmuller()) -[?7h[?12l[?25h[?2004l1 x^3 -3 V((x^8) dx) -2 x -1 [2] d[x] -[?7h[2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lC.x.teichmuller())[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((C.x^3 - C.x).teichmuller()) -[?7h[?12l[?25h[?2004l1 x^3 -2 x -[?7h[2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((C.x^3 - C.x).teichmuller()) -[?7h[?12l[?25h[?2004l[?7h[2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((C.x^3).teichmuller()) -[?7h[?12l[?25h[?2004l[?7hV((x^8) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) -[?7h[?12l[?25h[?2004l[?7h[2] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(()-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7lauxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: -auxilliary_derivative((C.x).teichmuller()) -[?7h[?12l[?25h[?2004l[?7h[2] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l-auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lauxiliary_derivative((-) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) -[?7h[?12l[?25h[?2004leq1 True -try -[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) -[?7h[?12l[?25h[?2004leq1 True -try -[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-3)*a[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (0*C.x).pth_root() -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(0*C.x).pth_root()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(0*C.x).pth_root()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) -[?7h[?12l[?25h[?2004leq1 True -0 -try -[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltry[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: try: -....: [?7h[?12l[?25h[?25l[?7lprint(b.cartier())[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrint(b.cartier())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b.cartier())[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print('a') -....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() - [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() -....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lexcept[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....: except: -....: [?7h[?12l[?25h[?25l[?7l....:  -....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lprint(b.cartier())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() -....: [?7h[?12l[?25h[?25l[?7lsage: try: -....:  print('a') -....: except: -....:  print('b') -....:  -[?7h[?12l[?25h[?2004la -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: try: -....:  print('a') -....: except: -....:  print('b')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) -  -  - [?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) -[?7h[?12l[?25h[?2004leq1 True ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [32], in () -----> 1 auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) - -File :115, in __eq__(self, other) - -AttributeError: 'superelliptic_function' object has no attribute 'pthroot' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.teichmuller()[?7h[?12l[?25h[?25l[?7ly*v*(v - C.y)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lchmuller[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller() -[?7h[?12l[?25h[?2004l[?7h[y] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l = supeelliptic_drw_form(Cone, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: a = C.dx - C.a_number C.basis_of_cohomology C.degrees_de_rham0 C.dx C.frobenius_matrix  - C.base_ring C.cartier_matrix C.degrees_de_rham1 C.exponent C.genus  - C.basis_de_rham_degrees C.characteristic C.degrees_holomorphic_differentials C.fct_field C.holomorphic_differentials_basis > - C.basis_holomorphic_differentials_degree C.de_rham_basis C.dr_frobenius_matrix C.final_type C.is_smooth  - [?7h[?12l[?25h[?25l[?7ly - - - -[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lchmuller[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = C.y.teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - - - - [?7h[?12l[?25h[?25l[?7la = C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l+a+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a -[?7h[?12l[?25h[?2004l[?7h) failed: NameError: name 'f1' is not defined> -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la+[?7h[?12l[?25h[?25l[?7l = C.y.teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = C.y.teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a -[?7h[?12l[?25h[?2004l[?7h[2*y] + V((x^3 + 2*x)*y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l11/3-4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7lsage: 1/2 in QQ -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7lsage: Integers(25)(2)^(-1) in ZZ -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.teichmuller()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lle[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller()*C.y.teichmuller() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [44], in () -----> 1 C.x.teichmuller()*C.y.teichmuller() - -TypeError: unsupported operand type(s) for *: 'superelliptic_witt' and 'superelliptic_witt' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.y.teichmuller() -[?7h[?12l[?25h[?2004l[?7h[2*y] + V((x^3 + 2*x)*y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 2*C.y.teichmuller() == -7*C.y.teichmuller() -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y.teichmuller() == -7*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler()[?7h[?12l[?25h[?25l[?7lx.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() -[?7h[?12l[?25h[?2004l[?7h[2*x] + V(x^3) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7ly() == -7*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler()[?7h[?12l[?25h[?25l[?7lx.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler() = -7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7lx.teichmuler() = -7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() == -7*C.x.teichmuller() -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller() == -7*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l -7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l+ -7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l()*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() + (-7)*C.x.teichmuller() -[?7h[?12l[?25h[?2004l[?7h[x] + V(x^3) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller() + (-7)*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() -[?7h[?12l[?25h[?2004l[?7h[2*x] + V(x^3) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9*a[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 9*C.x.teichmuller() -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l() + (-7)*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l()(-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l(), (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller(), (-7)*C.x.teichmuller() -[?7h[?12l[?25h[?2004l[?7h([2*x] + V(x^3), [2*x] + V(x^3)) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller(), (-7)*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l() (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l= (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l= (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() == (-7)*C.x.teichmuller() -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller() == (-7)*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() == (-7)*C.x.teichmuller() -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [56], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :203, in __add__(self, other) - -File :54, in __mul__(self, other) - -AttributeError: 'superelliptic_drw_form' object has no attribute 't' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldenominator(((C.y)^(-1)*C.dx).form) == y[?7h[?12l[?25h[?25l[?7limension_of_RHS = p*gY + (len(list_of_m) - 1)*(p-1) + sum(sum(i*alpha(i, m, p) for i in range(1, p)) for m in list_of_m)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7lsage: diffn(C.y.teichmuller)\ -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [60], in () -----> 1 diffn(C.y.teichmuller) - -NameError: name 'diffn' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn(C.y.teichmuller)\[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: diffn(C.y.teichmuller()) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [61], in () -----> 1 diffn(C.y.teichmuller()) - -NameError: name 'diffn' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn(C.y.teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [62], in () -----> 1 C.y.teichmuller().diffn() - -File :86, in diffn(self) - -File :122, in auxilliary_derivative(P) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 't' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.x^3 - C.x -[?7h[?12l[?25h[?2004l[?7hx^3 + 2*x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x^3 - C.x[?7h[?12l[?25h[?25l[?7ly.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7ldiffn(C.y.teichmuller())[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.x^3 - C.x[?7h[?12l[?25h[?25l[?7ly.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn() -[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx^3 - C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y)[?7h[?12l[?25h[?25l[?7l*C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la(C.x*C.y)[?7h[?12l[?25h[?25l[?7l (C.x*C.y)[?7h[?12l[?25h[?25l[?7l=(C.x*C.y)[?7h[?12l[?25h[?25l[?7l (C.x*C.y)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).function() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).function()[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7hx*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.lift()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonents[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.exponents() -[?7h[?12l[?25h[?2004l[?7h[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.exponents()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lx. = PolynomialRing(GF(4)[?7h[?12l[?25h[?25l[?7ly. = PlynomalRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7l. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lsage: Rxy. = PolynomialRing(GF(3), 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.exponents()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y.function()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR(2)[?7h[?12l[?25h[?25l[?7lxyz(1)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = Rxy(a) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = Rxy(a)[?7h[?12l[?25h[?25l[?7lRxy.<, y> = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7la.exponents()[?7h[?12l[?25h[?25l[?7lsage: a.exponents() -[?7h[?12l[?25h[?2004l[?7h[(1, 1)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.exponents()[?7h[?12l[?25h[?25l[?7l = Rxy(a)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC..teichmuller()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).function()[?7h[?12l[?25h[?25l[?7l).function()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().function()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7l.exponents([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [74], in () -----> 1 a.diffn() - -File :93, in diffn(self) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:6094, in sage.rings.polynomial.polynomial_element.Polynomial.monomial_coefficient() - 6092 """ - 6093 if not m.parent() is self._parent: --> 6094 raise TypeError("monomial must have same parent as self.") - 6095 - 6096 d = m.degree() - -TypeError: monomial must have same parent as self. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [77], in () -----> 1 a.diffn() - -File :94, in diffn(self) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:6094, in sage.rings.polynomial.polynomial_element.Polynomial.monomial_coefficient() - 6092 """ - 6093 if not m.parent() is self._parent: --> 6094 raise TypeError("monomial must have same parent as self.") - 6095 - 6096 d = m.degree() - -TypeError: monomial must have same parent as self. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [82], in () -----> 1 a.diffn() - -File :96, in diffn(self) - -NameError: name 'P' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [85], in () -----> 1 a.diffn() - -File :98, in diffn(self) - -IndexError: list index out of range -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [88], in () -----> 1 a.diffn() - -File :99, in diffn(self) - -File :79, in diffn(self) - -TypeError: superelliptic_form.__init__() takes 3 positional arguments but 4 were given -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller(); a.diffn() -[?7h[?12l[?25h[?2004l[?7h[y + 1] d[x] + V(((-x^8*y - x^5*y - x^5 + x^3*y + x^3 - x^2*y)/y) dx) + dV([x^7 + 2*x^5]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.x.function[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b = C.x.teichmuller().diffn() + C.y.teichmuller().diffn() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller(); a.diffn()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: a == b -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [93], in () -----> 1 a == b - -File :69, in __eq__(self, other) - -AttributeError: 'superelliptic_drw_form' object has no attribute 't' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la == b[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: a.diffn() == b -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.diffn() == b[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() -[?7h[?12l[?25h[?2004l[?7h[y + 1] d[x] + V(((-x^8*y - x^5*y - x^5 + x^3*y + x^3 - x^2*y)/y) dx) + dV([x^7 + 2*x^5]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = C.x.teichmuller().diffn() + C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: b -[?7h[?12l[?25h[?2004l[?7h[(x + 1)/x] d[x] + V(((-x^6 + x^4 + x^2 - x - 1)/x) dx) + dV([x^4 + 2*x^2]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.y).diffn() -[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7l.y).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.y).diffn() -[?7h[?12l[?25h[?2004l[?7h(1/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.).difn()[?7h[?12l[?25h[?25l[?7lt).difn()[?7h[?12l[?25h[?25l[?7le).difn()[?7h[?12l[?25h[?25l[?7li).difn()[?7h[?12l[?25h[?25l[?7lc).difn()[?7h[?12l[?25h[?25l[?7lh).difn()[?7h[?12l[?25h[?25l[?7lm).difn()[?7h[?12l[?25h[?25l[?7lu).difn()[?7h[?12l[?25h[?25l[?7ll).difn()[?7h[?12l[?25h[?25l[?7ll).difn()[?7h[?12l[?25h[?25l[?7le).difn()[?7h[?12l[?25h[?25l[?7lr).difn()[?7h[?12l[?25h[?25l[?7l(().difn()[?7h[?12l[?25h[?25l[?7l(()).difn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn() -[?7h[?12l[?25h[?2004l[?7h[1/x] d[x] + V(((-x^6 + x^4 - x^2 - 1)/x) dx) + dV([x^4 + 2*x^2]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn() -[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) -[?7h[1/x] d[x] + V(((-x^6 + x^4 - x^2 - 1)/x) dx) + dV([x^4 + 2*x^2]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn() -[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) -[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbe[?7h[?12l[?25h[?25l[?7lni[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() -[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'superelliptic_form' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [105], in () -----> 1 (C.y.teichmuller()).diffn().frobenius() - -File :238, in frobenius(self) - -File :7, in __init__(self, C, g) - -File :245, in reduction_form(C, g) - -File :216, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert ((x^3 - x)/y) dx/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() -[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'superelliptic_form' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [106], in () -----> 1 (C.y.teichmuller()).diffn().frobenius() - -File :238, in frobenius(self) - -File :7, in __init__(self, C, g) - -File :245, in reduction_form(C, g) - -File :216, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert ((x^3 - x)/y) dx/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() -[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) -[?7h((x^3 - x)/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn() -[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) -[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l C.y^2*C.y.difn()[?7h[?12l[?25h[?25l[?7l C.y^2*C.y.difn()[?7h[?12l[?25h[?25l[?7l()C.y^2*C.y.difn()[?7h[?12l[?25h[?25l[?7l(), C.y^2*C.y.difn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius(), C.y^2*C.y.diffn() -[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) -[?7h(((x^3 - x)/y) dx, ((x^3 - x)/y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius(), C.y^2*C.y.diffn()[?7h[?12l[?25h[?25l[?7l == C.y^2*Cy.diffn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn() -[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) -[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn() -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd .. -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status -On branch master -Your branch is up to date with 'origin/master'. - -Changes not staged for commit: - (use "git add ..." to update what will be committed) - (use "git restore ..." to discard changes in working directory) - modified: sage/.run.term-0.term - modified: sage/drafty/draft.sage - modified: sage/drafty/superelliptic_drw.sage - modified: sage/superelliptic/superelliptic_form_class.sage - modified: sage/superelliptic/superelliptic_function_class.sage - -Untracked files: - (use "git add ..." to include in what will be committed) - .crystalline_p2.ipynb.sage-jupyter2 - .deRhamComputation.ipynb.sage-jupyter2 - .elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2 - .git.x11-0.term - .superelliptic.ipynb.sage-jupyter2 - .superelliptic_alpha.ipynb.sage-jupyter2 - .superelliptic_arbitrary_field.ipynb.sage-jupyter2 - git.x11 - sage/as_covers/tests/cartier_test.sage - sage/drafty/as_cartier.sage - sage/drafty/better_trace.sage - sage/drafty/cartier_image_representation.sage - sage/drafty/draft4.sage - sage/drafty/draft5.sage - sage/drafty/draft6.sage - sage/drafty/draft7.sage - sage/drafty/lift_to_de_rham.sage - sage/drafty/pole_numbers.sage - sage/drafty/regular_on_U0.sage - sage/drafty/second_patch.sage - sage/superelliptic/frobenius_kernel.sage - sage/superelliptic/tests/ - superelliptic_arbitrary_field.ipynb - -no changes added to commit (use "git add" and/or "git commit -a") -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/drqaafty/second_patch.sage -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""r"o"z"n"i"c"z"k"o"w"a"n"i"e" "f"o"r"m" "d"r"w" "z"r"o"b"i"o"n"e" "("?")" -[master 22872e2] rozniczkowanie form drw zrobione (?) - 6 files changed, 1514 insertions(+), 117 deletions(-) - create mode 100644 sage/drafty/second_patch.sage - rewrite sage/drafty/superelliptic_drw.sage (68%) -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push -Username for 'https://git.wmi.amu.edu.pl': jgarnek -Password for 'https://jgarnek@git.wmi.amu.edu.pl': -Enumerating objects: 19, done. -Counting objects: 5% (1/19) Counting objects: 10% (2/19) Counting objects: 15% (3/19) Counting objects: 21% (4/19) Counting objects: 26% (5/19) Counting objects: 31% (6/19) Counting objects: 36% (7/19) Counting objects: 42% (8/19) Counting objects: 47% (9/19) Counting objects: 52% (10/19) Counting objects: 57% (11/19) Counting objects: 63% (12/19) Counting objects: 68% (13/19) Counting objects: 73% (14/19) Counting objects: 78% (15/19) Counting objects: 84% (16/19) Counting objects: 89% (17/19) Counting objects: 94% (18/19) Counting objects: 100% (19/19) Counting objects: 100% (19/19), done. -Delta compression using up to 4 threads -Compressing objects: 9% (1/11) Compressing objects: 18% (2/11) Compressing objects: 27% (3/11) Compressing objects: 36% (4/11) Compressing objects: 45% (5/11) Compressing objects: 54% (6/11) Compressing objects: 63% (7/11) Compressing objects: 72% (8/11) Compressing objects: 81% (9/11) Compressing objects: 90% (10/11) Compressing objects: 100% (11/11) Compressing objects: 100% (11/11), done. -Writing objects: 9% (1/11) Writing objects: 18% (2/11) Writing objects: 27% (3/11) Writing objects: 36% (4/11) Writing objects: 45% (5/11) Writing objects: 54% (6/11) Writing objects: 63% (7/11) Writing objects: 72% (8/11) Writing objects: 81% (9/11) Writing objects: 90% (10/11) Writing objects: 100% (11/11) Writing objects: 100% (11/11), 18.02 KiB | 271.00 KiB/s, done. -Total 11 (delta 6), reused 0 (delta 0) -remote: . Processing 1 references -remote: Processed 1 references in total -To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git - 856d742..22872e2 master -> master -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7ldx == C.dx[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: a = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() - a.coordinates a.frobenius a.omega8  - a.curve a.is_cocycle a.verschiebung - a.f a.omega0  - - [?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lx^3 - C.x[?7h[?12l[?25h[?25l[?7l.teichmuller()*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.verschiebung() -[?7h[?12l[?25h[?2004l[?7hV(x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lC.x.verschiebung()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldx.verschiebung()[?7h[?12l[?25h[?25l[?7lsage: C.dx.verschiebung() -[?7h[?12l[?25h[?2004l[?7h) failed: AttributeError: 'superelliptic_form' object has no attribute 'function'> -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ltichmuller()*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7lx.verschiebung()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7lsage: C.dx.verschiebung() -[?7h[?12l[?25h[?2004l[?7hV(1 dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [9] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :6 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :7 - for a in - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn(C.y.teichmuller())[?7h[?12l[?25h[?25l[?7lenominator(((C.y)^(-1*C.dx).form) == y[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: decomposition - decomposition  - decomposition_g0_g8  - decomposition_omega0_omega8 - - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - decomposition  - - - [?7h[?12l[?25h[?25l[?7l_g0_g8 - decomposition  - decomposition_g0_g8 [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(C.y/C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [11], in () -----> 1 decomposition_g0_g8(C.y/C.x) - -File :6, in decomposition_g0_g8(fct) - -File :101, in coordinates(self, basis, basis_holo, prec) - -AttributeError: 'superelliptic' object has no attribute 'basis_of_cohomology' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(C.y/C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [13], in () -----> 1 decomposition_g0_g8(C.y/C.x) - -File :8, in decomposition_g0_g8(fct) - -NameError: name 'enumeratate' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(C.y/C.x) -[?7h[?12l[?25h[?2004l[?7h(0, 0, 1/x*y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7liC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega) - li lie lift_form_to_drw line linear_relation list  - libgap lie_algebras lift_to_sl2z line2d linear_representation_polynomials list_plot  - libgiac lie_conformal_algebras lim line3d linear_transformation list_plot3d > - license lift limit linear_program lisp list_plot_loglog  - [?7h[?12l[?25h[?25l[?7lft_form_to_drw(omega) - - - -[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(xi) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [18], in () -----> 1 lift_form_to_drw(xi) - -File :29, in lift_form_to_drw(omega) - -File :10, in regular_form(omega) - -AttributeError: 'superelliptic_cech' object has no attribute 'form' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lam_witt_lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [19], in () -----> 1 de_rham_witt_lift(xi) - -File :270, in de_rham_witt_lift(cech_class) - -File :88, in diffn(self) - -TypeError: unsupported operand type(s) for -: 'superelliptic_drw_form' and 'superelliptic_drw_form' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(xi)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [21], in () -----> 1 de_rham_witt_lift(xi) - -File :269, in de_rham_witt_lift(cech_class) - -File :5, in regular_form(omega) - -AttributeError: 'NoneType' object has no attribute 'curve' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi -[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7llift_form_odrw(xi)[?7h[?12l[?25h[?25l[?7lx = C.derham_bass()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [25], in () -----> 1 de_rham_witt_lift(xi) - -File :275, in de_rham_witt_lift(cech_class) - -TypeError: unsupported operand type(s) for -: 'tuple' and 'tuple' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [28], in () -----> 1 de_rham_witt_lift(xi) - -File :276, in de_rham_witt_lift(cech_class) - -AttributeError: 'superelliptic_function' object has no attribute 'decomposition_g0_g8' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [31], in () -----> 1 de_rham_witt_lift(xi) - -File :278, in de_rham_witt_lift(cech_class) - -AttributeError: 'superelliptic_form' object has no attribute 'decomposition_omega0_omega8' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -[?7h<__main__.superelliptic_drw_cech object at 0x7f09ba3d4f40> -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0]) -) failed: TypeError: __repr__ returned non-string (type NoneType)> -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l -I-search:[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi).omega0 - [?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi).omega0 -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi).omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi).omega0.omega -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -[?7h((x^7 - x^3 - x)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(xi).omega0.omega -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() - a.cartier a.expansion_at_infty a.is_regular_on_Uinfty a.verschiebung  - a.coordinates a.form a.jth_component  - a.curve a.is_regular_on_U0 a.serre_duality_pairing  - - [?7h[?12l[?25h[?25l[?7lcartier - a.cartier  - - - [?7h[?12l[?25h[?25l[?7loordinates - a.cartier  - a.coordinates [?7h[?12l[?25h[?25l[?7lurve - - a.coordinates  - a.curve [?7h[?12l[?25h[?25l[?7lis_rgular_on_U0 - - - a.curve  a.is_regular_on_U0 [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7lsage: a.is_regular_on_U0 -[?7h[?12l[?25h[?2004l[?7h -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7la.is_regular_on_U0[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.is_regular_on_U0() -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h((x^7 - x^3 - x)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_g8(Cy/C.x)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga0_omega8[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(a) -[?7h[?12l[?25h[?2004l[?7h(((x^5 + x^3)/y) dx, ((-x)/(x^2*y - y)) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(a)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(xi.omega0) -[?7h[?12l[?25h[?2004l[?7h(0 dx, (1/y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(xi.omega0)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(a) -[?7h[?12l[?25h[?2004l[?7h(((x^5 + x^3)/y) dx, ((-x)/(x^2*y - y)) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(a)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(a)[1].expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t^2 + t^6 + O(t^12) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(a)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7lrham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -((-x^5 - x^3)/y) dx -[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) -[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -0 -[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -[1] -[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -[1] -[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y]) -[1] -[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.verschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y]) -[?7hV(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lude_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lxde_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1) -aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega0_omega8(a)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lg0_8(C.y/C.x)[?7h[?12l[?25h[?25l[?7l0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [73], in () -----> 1 decomposition_g0_g8(aux) - -File :6, in decomposition_g0_g8(fct) - -AttributeError: 'superelliptic_drw_form' object has no attribute 'coordinates' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux.h1) -[?7h[?12l[?25h[?2004l[?7h(0, 0, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.h1.coordinates() -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h1.coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: aux.h1 -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux -[?7h[?12l[?25h[?2004l[?7hV(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7l.h1[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: aux.h2 -[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)/x^3)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.h2.coordinates() -[?7h[?12l[?25h[?2004l[?7h[2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[];[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -(1/y) dx ((-1)/y) dx (0, 1) -aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y]) -[1] -[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]; de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l1]; de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -(x/y) dx ((-1)/(x*y)) dx None ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [81], in () -----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi) - -File :304, in de_rham_witt_lift(cech_class) - -TypeError: 'NoneType' object is not subscriptable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -(x/y) dx ((-1)/(x*y)) dx None -None ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [82], in () -----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi) - -File :305, in de_rham_witt_lift(cech_class) - -TypeError: 'NoneType' object is not subscriptable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -omega8_re None ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [83], in () -----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi) - -File :304, in de_rham_witt_lift(cech_class) - -TypeError: 'NoneType' object is not subscriptable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -omega8_re None ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [84], in () -----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi) - -File :304, in de_rham_witt_lift(cech_class) - -TypeError: 'NoneType' object is not subscriptable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -second_patch(omega0) ((-1)/(x*y)) dx ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [85], in () -----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi) - -File :304, in de_rham_witt_lift(cech_class) - -TypeError: 'NoneType' object is not subscriptable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1].omega8; second_patch(xi) -[?7h[?12l[?25h[?2004l0 -[?7h(x/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1].omega8; second_patch(xi)[?7h[?12l[?25h[?25l[?7l; d_rham_witt_lif(xi)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -second_patch(omega0) ((-1)/(x*y)) dx -g0, g8 ((-x^8 + x^6)/y) dx ((-1)/(x^2*y - y)) dx -[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(x^2*y - y)) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h1)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lrham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004lsecond_patch(omega0) ((-1)/(x*y)) dx -g0, g8 ((-x^8 + x^6)/y) dx ((-1)/(x^2*y - y)) dx -[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(x^2*y - y)) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l.omga8; second_pach(xi)[?7h[?12l[?25h[?25l[?7l; d_rham_witt_lif(xi)[?7h[?12l[?25h[?25l[?7l.omga8; second_pach(xi)[?7h[?12l[?25h[?25l[?7l; d_rham_witt_lif(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a+a -[?7h[?12l[?25h[?2004l[?7h(V((x^4/(x^2*y - y)) dx), V(((2*x^2 + 1)/x^2)*y), V((x^4/(x^2*y - y)) dx) + dV([((x^2 + 2)/x^2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7llod('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (a+a+a).reduce() -[?7h[?12l[?25h[?2004l[?7h(dV([y]), [0], dV([y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git sagegit pushcommit -m "rozniczkowanie form drw zrobione (?)"add -u -]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git add -usagegit pushcommit -m "rozniczkowanie form drw zrobione (?)"""""""""""""""""""""""""""""""""""""b"^?""""l"i"f"t" "c"o"""k"o"c"y"k"l"i" "d"o" "d"r"w" "z"r"o"b"i"o"n"y"z"" "z" "d"r"o"b"n"y"m"i" "b"l"e"d"a"m"i" -[master e1a000f] lift kocykli do drw zrobiony z drobnymi bledami - 5 files changed, 524 insertions(+), 5 deletions(-) -]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git commit -m "lift kocykli do drw zrobiony z drobnymi bledami" add -usagegit push -Username for 'https://git.wmi.amu.edu.pl': jgarnek -Password for 'https://jgarnek@git.wmi.amu.edu.pl': -Enumerating objects: 19, done. -Counting objects: 5% (1/19) Counting objects: 10% (2/19) Counting objects: 15% (3/19) Counting objects: 21% (4/19) Counting objects: 26% (5/19) Counting objects: 31% (6/19) Counting objects: 36% (7/19) Counting objects: 42% (8/19) Counting objects: 47% (9/19) Counting objects: 52% (10/19) Counting objects: 57% (11/19) Counting objects: 63% (12/19) Counting objects: 68% (13/19) Counting objects: 73% (14/19) Counting objects: 78% (15/19) Counting objects: 84% (16/19) Counting objects: 89% (17/19) Counting objects: 94% (18/19) Counting objects: 100% (19/19) Counting objects: 100% (19/19), done. -Delta compression using up to 4 threads -Compressing objects: 10% (1/10) Compressing objects: 20% (2/10) Compressing objects: 30% (3/10) Compressing objects: 40% (4/10) Compressing objects: 50% (5/10) Compressing objects: 60% (6/10) Compressing objects: 70% (7/10) Compressing objects: 80% (8/10) Compressing objects: 90% (9/10) Compressing objects: 100% (10/10) Compressing objects: 100% (10/10), done. -Writing objects: 10% (1/10) Writing objects: 20% (2/10) Writing objects: 30% (3/10) Writing objects: 40% (4/10) Writing objects: 50% (5/10) Writing objects: 60% (6/10) Writing objects: 70% (7/10) Writing objects: 80% (8/10) Writing objects: 90% (9/10) Writing objects: 100% (10/10) Writing objects: 100% (10/10), 8.09 KiB | 78.00 KiB/s, done. -Total 10 (delta 9), reused 0 (delta 0) -remote: . Processing 1 references -remote: Processed 1 references in total -To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git - 22872e2..e1a000f master -> master -]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a+a+a).reduce()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l0]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+a+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a+a -[?7h[?12l[?25h[?2004l[?7h(V((x/(x^2*y - y)) dx), [0], V((x/(x^2*y - y)) dx)) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l1]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx \, dy + 3 x^3 \, dy + dV((2x^4 + 2x^2 + 2) y)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx \, dy + 3 x^3 \, dy + dV(2x^4 + 2x^2 + 2) y)[?7h[?12l[?25h[?25l[?7l.x \, dy + 3 x^3 \, dy + dV(2x^4 + 2x^2 + 2) y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: C.x \, dy + 3 x^3 \, dy + dV((2x^4 + 2x^2 + 2) ) -[?7h[?12l[?25h[?2004l Input In [5] - C.x * BackslashOperator() * , dy + Integer(3) x**Integer(3) * BackslashOperator() * , dy + dV((2x**Integer(4) + 2x**Integer(2) + Integer(2)) ) - ^ -SyntaxError: invalid decimal literal - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(C.dx,superelliptic_form)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller() * C.y.teichmuller().diffn() + 3 * C.x^3.teichmuller() * C.y.tecihmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: xi1 = C.x.teichmuller() * C.y.teichmuller().diffn() + 3 * C.x^3.teichmuller() * C.y.tecihmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().diffn() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [6], in () -----> 1 xi1 = C.x.teichmuller() * C.y.teichmuller().diffn() + Integer(3) * C.x**Integer(3).teichmuller() * C.y.tecihmuller().diffn() + (Integer(2)*(C.x**Integer(4) + C.x**Integer(2) + C.one) * C.y).verschiebung().diffn() - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'teichmuller' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller() * C.y.teichmuller().diffn() + 3 * (C.x^3).teichmuller() * C.y.tecihmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller() * C.y.teichmuller().diffn() + 3 * (C.x^3).teichmuller() * C.y.tecihmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().diffn() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [7], in () -----> 1 C.x.teichmuller() * C.y.teichmuller().diffn() + Integer(3) * (C.x**Integer(3)).teichmuller() * C.y.tecihmuller().diffn() + (Integer(2)*(C.x**Integer(4) + C.x**Integer(2) + C.one) * C.y).verschiebung().diffn() - -AttributeError: 'superelliptic_function' object has no attribute 'tecihmuller' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lceil(2/3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller() * C.y.teichmuller().diffn() + 3 * (C.x^3).teichmuller() * C.y.teichmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: c = C.x.teichmuller() * C.y.teichmuller().diffn() + 3 * (C.x^3).teichmuller() * C.y.teichmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().diffn() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc = C.x.teichmuller() * C.y.teichmuller().diffn() + 3 * (C.x^3).teichmuller() * C.y.teichmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: c -[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((-x^6 + x^4)/y) dx) + dV([(1/(x^2 + 2))*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(x^2*y - y)) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx^10 + x^8 + x^6 - x^4[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - 1)[?7h[?12l[?25h[?25l[?7l2 - 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: quo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [11], in () -----> 1 quo_rem(x**Integer(10) + x**Integer(8) + x**Integer(6) - x**Integer(4), x**Integer(2) - Integer(1)) - -NameError: name 'quo_rem' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(), x^2 - 1)[?7h[?12l[?25h[?25l[?7l()., x^2 - 1)[?7h[?12l[?25h[?25l[?7lq, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu, x^2 - 1)[?7h[?12l[?25h[?25l[?7lo, x^2 - 1)[?7h[?12l[?25h[?25l[?7l_, x^2 - 1)[?7h[?12l[?25h[?25l[?7lr, x^2 - 1)[?7h[?12l[?25h[?25l[?7le, x^2 - 1)[?7h[?12l[?25h[?25l[?7lm, x^2 - 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2 - 1)[?7h[?12l[?25h[?25l[?7lx^2 - 1)[?7h[?12l[?25h[?25l[?7l(x^2 - 1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(x^10 + x^8 + x^6 - x^4).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l(x^10 + x^8 + x^6 - x^4).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l(x^10 + x^8 + x^6 - x^4).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l(x^10 + x^8 + x^6 - x^4).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l(x^10 + x^8 + x^6 - x^4).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l(x^10 + x^8 + x^6 - x^4).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l(x^10 + x^8 + x^6 - x^4).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^10 + x^8 + x^6 - x^4).quo_rem(x^2 - 1) -[?7h[?12l[?25h[?2004l[?7h(x^8 + 2*x^6 + 2*x^2 + 2, 2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: a = a.omega0 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = a.omega0[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: c -[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((-x^6 + x^4)/y) dx) + dV([(1/(x^2 + 2))*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = a.omega0[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l= b[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: a == c -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la == c[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.frobenius() -[?7h[?12l[?25h[?2004l[?7h((-x^8 - x^6 + x^4)/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: c.frobenius() -[?7h[?12l[?25h[?2004l[?7h((x^2 - 1)/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.frobenius()[?7h[?12l[?25h[?25l[?7l == c[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l a.omega0[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y).teichmuller(); a.diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = (C.y/C.x).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.y/C.x).teichmuller()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3a[?7h[?12l[?25h[?25l[?7l*a[?7h[?12l[?25h[?25l[?7lsage: 3*a -[?7h[?12l[?25h[?2004l[?7hV(((x^2 + 2)/x^2)*y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: (3*a).f -[?7h[?12l[?25h[?2004l[?7h((x^2 + 2)/x^2)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).f[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((3*a).f)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7ld((3*a).f)[?7h[?12l[?25h[?25l[?7le((3*a).f)[?7h[?12l[?25h[?25l[?7lc((3*a).f)[?7h[?12l[?25h[?25l[?7lo((3*a).f)[?7h[?12l[?25h[?25l[?7lm((3*a).f)[?7h[?12l[?25h[?25l[?7lp((3*a).f)[?7h[?12l[?25h[?25l[?7lo((3*a).f)[?7h[?12l[?25h[?25l[?7ls((3*a).f)[?7h[?12l[?25h[?25l[?7li((3*a).f)[?7h[?12l[?25h[?25l[?7lt((3*a).f)[?7h[?12l[?25h[?25l[?7li((3*a).f)[?7h[?12l[?25h[?25l[?7lo((3*a).f)[?7h[?12l[?25h[?25l[?7ln((3*a).f)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_g0_g8(aux.h1)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux.h1) - decomposition_g0_g8  - decomposition_omega0_omega8 - - - [?7h[?12l[?25h[?25l[?7lg0_g8(aux.h1) - -[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l3))[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7la))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8((3*a).f) -[?7h[?12l[?25h[?2004l[?7h(y, 2/x^2*y, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7la = (C.y/C.x).teichmuller()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperellipic_drw_fom(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi1 = C.x.teichmuller() * C.y.teichmuller().diffn() + 3 * C.x^3.teichmuller() * C.y.tecihmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung() . -....: diffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l0 - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lx, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi0 = superelliptic_drw_form(0*C.x, 0*C.dx, 0*C.x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - - [?7h[?12l[?25h[?25l[?7lxi0 = superelliptic_drw_form(0*C.x, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l1C.x.tichmuller() * C.y.teichmuller().diffn() + 3 * C.x^3.teichmuller() * C.y.tecihmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung() . -....: diffn()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls - [?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi1 = (C.y/C.x).teichmuller() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lxi1 = (C.y/C.x).teichmuller()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = C.de_rham_bass()[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(xi0, xi1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(xi0, xi1)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi -[?7h[?12l[?25h[?2004l[?7h(0, [1/x*y], [((x^2 + 1)/(x^4 + 2*x^2))*y] d[x] + V((x^4/(x^2*y - y)) dx) + dV([(2/(x^2 + 2))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: reduce(xi) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [10], in () -----> 1 reduce(xi) - -TypeError: reduce expected at least 2 arguments, got 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduce(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxreduce()[?7h[?12l[?25h[?25l[?7lireduce()[?7h[?12l[?25h[?25l[?7l.reduce()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.reduce() -[?7h[?12l[?25h[?2004l[?7h(0, [1/x*y], [((x^2 + 1)/(x^4 + 2*x^2))*y] d[x] + V((x^4/(x^2*y - y)) dx) + dV([(2/(x^2 + 2))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7lreduce(xi)[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(xi0, xi1)[?7h[?12l[?25h[?25l[?7l1 = (C.y/C.x).teichmuller)[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cechxi0, xi1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3xi1)[?7h[?12l[?25h[?25l[?7l*xi1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(xi0, 3*xi1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(xi0, 3*xi1)[?7h[?12l[?25h[?25l[?7l.redc()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce() -[?7h[?12l[?25h[?2004l[?7h(dV([2*y]), [0], dV([2*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7l = sprelliptic_drw_cech(xi0, 3*xi1)[?7h[?12l[?25h[?25l[?7l.redc()[?7h[?12l[?25h[?25l[?7lreduce(xi)[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(xi0, xi1)[?7h[?12l[?25h[?25l[?7l1 = (C.y/C.x).teichmuller)[?7h[?12l[?25h[?25l[?7l0superellipic_drw_fom(0*C.x, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8((3*a).f)[?7h[?12l[?25h[?25l[?7l(3*a).f[?7h[?12l[?25h[?25l[?7l3*a[?7h[?12l[?25h[?25l[?7la = (C.y/C.x).teichmuller()[?7h[?12l[?25h[?25l[?7lload'init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.y/C.x).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(x^2*y - y)) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 3*a -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [16], in () -----> 1 Integer(3)*a - -File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() - 1962 return y - 1963 --> 1964 return coercion_model.bin_op(left, right, operator.mul) - 1965 - 1966 cpdef _mul_(self, right): - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() - 1246 # We should really include the underlying error. - 1247 # This causes so much headache. --> 1248 raise bin_op_exception(op, x, y) - 1249 - 1250 cpdef canonical_coercion(self, x, y): - -TypeError: unsupported operand parent(s) for *: 'Integer Ring' and '' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+a+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a+a -[?7h[?12l[?25h[?2004l[?7h(V((x^4/(x^2*y - y)) dx), V(((2*x^2 + 1)/x^2)*y), V((x^4/(x^2*y - y)) dx) + dV([((x^2 + 2)/x^2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a+a+a)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().reduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: (a+a+a).omega0.omega -[?7h[?12l[?25h[?2004l[?7h(x^4/(x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a+a+a).omega0.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb(a+a+a).omega0.omega[?7h[?12l[?25h[?25l[?7l (a+a+a).omega0.omega[?7h[?12l[?25h[?25l[?7l=(a+a+a).omega0.omega[?7h[?12l[?25h[?25l[?7l (a+a+a).omega0.omega[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = (a+a+a).omega0.omega -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = (a+a+a).omega0.omega[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 3*a -[?7h[?12l[?25h[?2004l[?7h(V((x^4/(x^2*y - y)) dx), V(((2*x^2 + 1)/x^2)*y), V((x^4/(x^2*y - y)) dx) + dV([((x^2 + 2)/x^2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 9*a -[?7h[?12l[?25h[?2004l[?7h(0, [0], 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -omega0_regular (0, x) -omega8_regular (0, 2/x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l0]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -omega0_regular (0, 1) -omega8_regular (0, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -omega0_regular (0, 1) -omega8_regular (0, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l1]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -omega0_regular (0, x) -omega8_regular (0, 2/x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi -[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: 3*xi -[?7h[?12l[?25h[?2004l[?7h(0 dx, 0, 0 dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*xi[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 3*a -[?7h[?12l[?25h[?2004l[?7h(V((x^4/(x^2*y - y)) dx), V(((2*x^2 + 1)/x^2)*y), V((x^4/(x^2*y - y)) dx) + dV([((x^2 + 2)/x^2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().f[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (3*a).reduce() -[?7h[?12l[?25h[?2004l[?7h(dV([y]), [0], dV([y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).reduce()[?7h[?12l[?25h[?25l[?7l3*a[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7l3*xi[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l(3*a).reduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(x^2*y - y)) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.frobenius()[?7h[?12l[?25h[?25l[?7lsage: a.frobenius() - a.curve a.omega8 - a.f a.reduce - a.omega0  - - [?7h[?12l[?25h[?25l[?7lcurve - a.curve  - - - [?7h[?12l[?25h[?25l[?7lf - a.curve  - a.f [?7h[?12l[?25h[?25l[?7lomega0 - - a.f  - a.omega0[?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7lsage: a.omega0 -[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3a.omega0[?7h[?12l[?25h[?25l[?7l*a.omega0[?7h[?12l[?25h[?25l[?7lsage: 3*a.omega0 -[?7h[?12l[?25h[?2004l[?7hV((x^4/(x^2*y - y)) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -omega0_regular (0, x) -omega8_regular (0, 2/x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).reduce()[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().reduce()[?7h[?12l[?25h[?25l[?7lsage: (3*a).reduce() -[?7h[?12l[?25h[?2004l[?7h(V((x^4/(x^2*y - y)) dx) + dV([y]), [0], V((x^4/(x^2*y - y)) dx) + dV([y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a.omega0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega0[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/ +[?7h[?12l[?25h[?25l[?7ld +[?7h[?12l[?25h[?25l[?7li +[?7h[?12l[?25h[?25l[?7lf +[?7h[?12l[?25h[?25l[?7lf +[?7h[?12l[?25h[?25l[?7ln +[?7h[?12l[?25h[?25l[?7l( +[?7h[?12l[?25h[?25l[?7l() +[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuler().difn() +[?7h[?12l[?25h[?25l[?7lC.y.teichmuler().difn() +[?7h[?12l[?25h[?25l[?7l(C.y.teichmuler().difn() +[?7h[?12l[?25h[?25l[?7lC.y.teichmuler().difn() +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7l().difn() +[?7h[?12l[?25h[?25l[?7lv().difn() +[?7h[?12l[?25h[?25l[?7le().difn() +[?7h[?12l[?25h[?25l[?7lr().difn() +[?7h[?12l[?25h[?25l[?7ls().difn() +[?7h[?12l[?25h[?25l[?7lc().difn() +[?7h[?12l[?25h[?25l[?7lh().difn() +[?7h[?12l[?25h[?25l[?7li().difn() +[?7h[?12l[?25h[?25l[?7le().difn() +[?7h[?12l[?25h[?25l[?7lb().difn() +[?7h[?12l[?25h[?25l[?7lu().difn() +[?7h[?12l[?25h[?25l[?7ln().difn() +[?7h[?12l[?25h[?25l[?7lg().difn() +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: 3*a.omega0 == C.y.verschiebung().diffn() + mult - mult_by_p multinomial_coefficients multiplicative_order  - multi_graphics multiple  - multinomial multiples  - - [?7h[?12l[?25h[?25l[?7l_by_p - mult_by_p  - - - [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 3*a.omega0 == C.y.verschiebung().diffn() + mult_by_p(C.x*C.y.diffn()) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [12], in () -----> 1 Integer(3)*a.omega0 == C.y.verschiebung().diffn() + mult_by_p(C.x*C.y.diffn()) - -File :247, in mult_by_p(omega) - -TypeError: superelliptic_drw_form.__init__() takes 4 positional arguments but 5 were given -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -omega0_regular (0, x) -omega8_regular (0, 2/x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l3*.omega0 == C.y.verschiebung().diffn() + mult_by_p(C.x*C.y.diffn())[?7h[?12l[?25h[?25l[?7lsage: 3*a.omega0 == C.y.verschiebung().diffn() + mult_by_p(C.x*C.y.diffn()) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [14], in () -----> 1 Integer(3)*a.omega0 == C.y.verschiebung().diffn() + mult_by_p(C.x*C.y.diffn()) - -File :246, in mult_by_p(omega) - -TypeError: superelliptic_form.__init__() missing 1 required positional argument: 'g' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a.omega0 == C.y.verschiebung().diffn() + mult_by_p(C.x*C.y.diffn())[?7h[?12l[?25h[?25l[?7llod('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -omega0_regular (0, x) -omega8_regular (0, 2/x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l3*.omega0 == C.y.verschiebung().diffn() + mult_by_p(C.x*C.y.diffn())[?7h[?12l[?25h[?25l[?7lsage: 3*a.omega0 == C.y.verschiebung().diffn() + mult_by_p(C.x*C.y.diffn()) -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a.omega0 == C.y.verschiebung().diffn() + mult_by_p(C.x*C.y.diffn())[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la.omega0 == C.y.verschiebung().diffn() + mult_by_p(C.x*C.y.diffn())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l()mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l( mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l() mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l( mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l- mult_by_p(C.x*C.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 3*a.omega0 - mult_by_p(C.x*C.y.diffn()) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a.omega0 - mult_by_p(C.x*C.y.diffn())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).reduce()[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l).reduce()[?7h[?12l[?25h[?25l[?7lsage: (3*a).reduce() -[?7h[?12l[?25h[?2004l[?7h(V((x^4/(x^2*y - y)) dx) + dV([y]), [0], V((x^4/(x^2*y - y)) dx) + dV([y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi -[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a.omega0 - mult_by_p(C.x*C.y.diffn())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(x^2*y - y)) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd .. -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -ucd ..sagegit pushcommit -m "lift kocykli do drw zrobiony z drobnymi bledami"""""""""""""""""""" "c"h"y"b"a" "o"k" -[master 8719e64] lift kocykli do drw zrobiony chyba ok - 2 files changed, 305 insertions(+), 3 deletions(-) -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push -Username for 'https://git.wmi.amu.edu.pl': jgarnek -Password for 'https://jgarnek@git.wmi.amu.edu.pl': -Enumerating objects: 11, done. -Counting objects: 9% (1/11) Counting objects: 18% (2/11) Counting objects: 27% (3/11) Counting objects: 36% (4/11) Counting objects: 45% (5/11) Counting objects: 54% (6/11) Counting objects: 63% (7/11) Counting objects: 72% (8/11) Counting objects: 81% (9/11) Counting objects: 90% (10/11) Counting objects: 100% (11/11) Counting objects: 100% (11/11), done. -Delta compression using up to 4 threads -Compressing objects: 16% (1/6) Compressing objects: 33% (2/6) Compressing objects: 50% (3/6) Compressing objects: 66% (4/6) Compressing objects: 83% (5/6) Compressing objects: 100% (6/6) Compressing objects: 100% (6/6), done. -Writing objects: 16% (1/6) Writing objects: 33% (2/6) Writing objects: 50% (3/6) Writing objects: 66% (4/6) Writing objects: 83% (5/6) Writing objects: 100% (6/6) Writing objects: 100% (6/6), 8.38 KiB | 158.00 KiB/s, done. -Total 6 (delta 5), reused 0 (delta 0) -remote: . Processing 1 references -remote: Processed 1 references in total -To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git - e1a000f..8719e64 master -> master -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [1] in  - load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; a = de_rham_witt_lift(xi) - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :26 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :322 - coord_lifted = - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.reduce()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinted() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [3], in () -----> 1 xi.coordinted() - -AttributeError: 'superelliptic_cech' object has no attribute 'coordinted' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinted()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7la()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7ls()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [4], in () -----> 1 xi.coordinates() - -File :75, in coordinates(self) - -File :113, in degree_of_rational_fctn(f, F) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in PolynomialRing(base_ring, *args, **kwds) - 52 r""" - 53 Return the globally unique univariate or multivariate polynomial - 54 ring with given properties and variable name or names. - (...) - 551  TypeError: unable to convert 'x' to an integer - 552 """ - 553 if not ring.is_Ring(base_ring): ---> 554 raise TypeError("base_ring {!r} must be a ring".format(base_ring)) - 556 n = -1 # Unknown number of variables - 557 names = None # Unknown variable names - -TypeError: base_ring 3 must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi -[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi -[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi[0].coordinates() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [7], in () -----> 1 xi[Integer(0)].coordinates() - -TypeError: 'superelliptic_cech' object is not subscriptable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[0].coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[0.cordinates()[?7h[?12l[?25h[?25l[?7l.cordinates()[?7h[?12l[?25h[?25l[?7l.cordinates()[?7h[?12l[?25h[?25l[?7l.cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lted()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l0]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[0].coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi -[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[0].coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: xi.omega0 -[?7h[?12l[?25h[?2004l[?7h(1/y) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.omega0.coordinates() -[?7h[?12l[?25h[?2004l[?7h[1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega0.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates() -[?7h[?12l[?25h[?2004l[?7h(1, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lor a in range(25):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: for xi in C.de - C.de_rham_basis C.degrees_de_rham1  - C.degrees_de_rham0 C.degrees_holomorphic_differentials - - - [?7h[?12l[?25h[?25l[?7l_rham_basis - C.de_rham_basis  - - [?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l -....: [?7h[?12l[?25h[?25l[?7lprint('b')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l() -....: [?7h[?12l[?25h[?25l[?7lsage: for xi in C.de_rham_basis(): -....:  print(xi.coordinates()) -....:  -[?7h[?12l[?25h[?2004l(1, 0) ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [13], in () - 1 for xi in C.de_rham_basis(): -----> 2 print(xi.coordinates()) - -File :75, in coordinates(self) - -File :113, in degree_of_rational_fctn(f, F) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in PolynomialRing(base_ring, *args, **kwds) - 52 r""" - 53 Return the globally unique univariate or multivariate polynomial - 54 ring with given properties and variable name or names. - (...) - 551  TypeError: unable to convert 'x' to an integer - 552 """ - 553 if not ring.is_Ring(base_ring): ---> 554 raise TypeError("base_ring {!r} must be a ring".format(base_ring)) - 556 n = -1 # Unknown number of variables - 557 names = None # Unknown variable names - -TypeError: base_ring 3 must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l];[?7h[?12l[?25h[?25l[?7l1];[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[] a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi) -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7loordinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates() -[?7h[?12l[?25h[?2004lf, F 2/x 3 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [17], in () -----> 1 xi.coordinates() - -File :75, in coordinates(self) - -File :114, in degree_of_rational_fctn(f, F) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in PolynomialRing(base_ring, *args, **kwds) - 52 r""" - 53 Return the globally unique univariate or multivariate polynomial - 54 ring with given properties and variable name or names. - (...) - 551  TypeError: unable to convert 'x' to an integer - 552 """ - 553 if not ring.is_Ring(base_ring): ---> 554 raise TypeError("base_ring {!r} must be a ring".format(base_ring)) - 556 n = -1 # Unknown number of variables - 557 names = None # Unknown variable names - -TypeError: base_ring 3 must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1];[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l];[?7h[?12l[?25h[?25l[?7l0];[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: xi. -[?7h[?12l[?25h[?2004l Input In [19] - xi. - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lordinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates() -[?7h[?12l[?25h[?2004lf, F 1 Finite Field of size 3 -[?7h(1, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller() * C.y.teichmuller().diffn() + 3 * (C.x^3).teichmuller() * C.y.tecihmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().dif f -....: n()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology() - [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le_ring[?7h[?12l[?25h[?25l[?7l_ring[?7h[?12l[?25h[?25l[?7lsage: C.base_ring -[?7h[?12l[?25h[?2004l[?7hFinite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.base_ring[?7h[?12l[?25h[?25l[?7lxi.coordates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7l()xi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7l(xi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l];[?7h[?12l[?25h[?25l[?7l1];[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[1];xi.coordinates() -[?7h[?12l[?25h[?2004lf, F 2/x 3 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [22], in () -----> 1 xi = C.de_rham_basis()[Integer(1)];xi.coordinates() - -File :75, in coordinates(self) - -File :114, in degree_of_rational_fctn(f, F) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in PolynomialRing(base_ring, *args, **kwds) - 52 r""" - 53 Return the globally unique univariate or multivariate polynomial - 54 ring with given properties and variable name or names. - (...) - 551  TypeError: unable to convert 'x' to an integer - 552 """ - 553 if not ring.is_Ring(base_ring): ---> 554 raise TypeError("base_ring {!r} must be a ring".format(base_ring)) - 556 n = -1 # Unknown number of variables - 557 names = None # Unknown variable names - -TypeError: base_ring 3 must be a ring -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l];[?7h[?12l[?25h[?25l[?7l1];[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates() -[?7h[?12l[?25h[?2004l0 -f, F 2/x Finite Field of size 3 -[?7h(0, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates() -[?7h[?12l[?25h[?2004l0 -[?7h(0, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[1];xi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coorinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfxi.cordinates()[?7h[?12l[?25h[?25l[?7loxi.cordinates()[?7h[?12l[?25h[?25l[?7lrxi.cordinates()[?7h[?12l[?25h[?25l[?7lfor xi.cordinates()[?7h[?12l[?25h[?25l[?7laxi.cordinates()[?7h[?12l[?25h[?25l[?7l xi.cordinates()[?7h[?12l[?25h[?25l[?7lixi.cordinates()[?7h[?12l[?25h[?25l[?7lnxi.cordinates()[?7h[?12l[?25h[?25l[?7lin xi.cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for a in xi.coordinates(): -....: [?7h[?12l[?25h[?25l[?7lprint(xi.coordinates())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(type(a)) -....: [?7h[?12l[?25h[?25l[?7lsage: for a in xi.coordinates(): -....:  print(type(a)) -....:  -[?7h[?12l[?25h[?2004l - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in xi.coordinates(): -....:  print(type(a))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ltyp(a))[?7h[?12l[?25h[?25l[?7l(a))[?7h[?12l[?25h[?25l[?7l(a))[?7h[?12l[?25h[?25l[?7l(a))[?7h[?12l[?25h[?25l[?7ll(a))[?7h[?12l[?25h[?25l[?7li(a))[?7h[?12l[?25h[?25l[?7lt(a))[?7h[?12l[?25h[?25l[?7l(a))[?7h[?12l[?25h[?25l[?7lf(a))[?7h[?12l[?25h[?25l[?7lt(a))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(lift(a)) -....: [?7h[?12l[?25h[?25l[?7lsage: for a in xi.coordinates(): -....:  print(lift(a)) -....:  -[?7h[?12l[?25h[?2004l0 -1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ losage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.base_ring[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.base_ring[?7h[?12l[?25h[?25l[?7lcrtier_matrix()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lystalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l[?7h[([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y])), - ([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(x^2*y - y)) dx) + dV([(2*x^4 + 2*x^2 + 2)*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aaa = C.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7llen[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: len(aaa) -[?7h[?12l[?25h[?2004l[?7h2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8((3*a).f)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ldef[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: def chang(a): -....: [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l....:  a = a+1 -....: [?7h[?12l[?25h[?25l[?7lsage: def chang(a): -....:  a = a+1 -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc.frobenius()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = (a+a+a).omega0.omega[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: b = 3 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc.frobenius()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: chang(b) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = 3[?7h[?12l[?25h[?25l[?7lsage: b -[?7h[?12l[?25h[?2004l[?7h3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(aaa)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [10] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :26 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :323 - if basis = _sage_const_0 : - ^ -SyntaxError: invalid syntax. Maybe you meant '==' or ':=' instead of '='? - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lux.h2.coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [12], in () -----> 1 autom(C.x) - -File :359, in autom(self) - -NameError: name 'y' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x) -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7lsage: autom(C.y) -[?7h[?12l[?25h[?2004l[?7hy -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.y)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(C.dx) -[?7h[?12l[?25h[?2004l[?7h1 dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx)[?7h[?12l[?25h[?25l[?7l.C.dx)[?7h[?12l[?25h[?25l[?7lxC.dx)[?7h[?12l[?25h[?25l[?7l*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(C.x*C.dx) -[?7h[?12l[?25h[?2004l[?7h(x - 1) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x*C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).reduce()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lD)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.dx)[?7h[?12l[?25h[?25l[?7lC.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).function() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [18], in () -----> 1 (C.x*C.dx).function() - -AttributeError: 'superelliptic_form' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).function()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).function -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [19], in () -----> 1 (C.x*C.dx).function - -AttributeError: 'superelliptic_form' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).form -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.teichmuller() * C.y.teichmuller().diffn() + 3 * (C.x^3).teichmuller() * C.y.tecihmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: C.x.function -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x*C.dx)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(C.x) -[?7h[?12l[?25h[?2004l[?7hx - 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x) -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x) -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l(x)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x) -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x) -[?7h[?12l[?25h[?2004l[?7hx + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).form[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).form -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).form[?7h[?12l[?25h[?25l[?7lautom(C.)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).form[?7h[?12l[?25h[?25l[?7lunction[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lautom(C.*C.dx)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x*C.dx) -[?7h[?12l[?25h[?2004l[?7h(x + 1) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x*C.dx)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x*C.dx) -[?7h[?12l[?25h[?2004l[?7h(x + 1) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = 3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x.teichmuller().diffn() + C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lystalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b = C.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [32], in () -----> 1 b[Integer(0)].coordinates() - -File :321, in coordinates(self, basis) - -AttributeError: 'function' object has no attribute 'coordinates' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: b = C.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [35], in () -----> 1 b[Integer(0)].coordinates() - -File :321, in coordinates(self, basis) - -AttributeError: 'function' object has no attribute 'coordinates' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: b = C.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[0].coordinates()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[0].coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates(basis = b) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [38], in () -----> 1 b[Integer(0)].coordinates(basis = b) - -File :321, in coordinates(self, basis) - -File :318, in r(self) - -File :5, in __init__(self, C, omega, fct) - -File :50, in __sub__(self, other) - -AttributeError: 'superelliptic_form' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].coordinates(basis = b)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [39], in () -----> 1 b[Integer(0)].coordinates() - -File :321, in coordinates(self, basis) - -File :318, in r(self) - -File :5, in __init__(self, C, omega, fct) - -File :50, in __sub__(self, other) - -AttributeError: 'superelliptic_form' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].coordinates()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[0].r() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [40], in () -----> 1 b[Integer(0)].r() - -File :318, in r(self) - -File :5, in __init__(self, C, omega, fct) - -File :50, in __sub__(self, other) - -AttributeError: 'superelliptic_form' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].r()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].r()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lbasis = b)[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: b = C.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].r()[?7h[?12l[?25h[?25l[?7lsage: b[0].r() -[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].r()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].r()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates(basis = b) -[?7h[?12l[?25h[?2004l(1, 0) -[?7h(0, [0], 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].coordinates(basis = b)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lab[0].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7lub[0].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7ltb[0].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7lob[0].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7lmb[0].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7l(b[0].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l([]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).coordinates(basis = b) -[?7h[?12l[?25h[?2004l(1, 0) -[?7h(V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduce(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).coordinates(basis = b)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrautom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7leautom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7lsautom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7l autom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7l=autom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7l autom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7lsage: res = autom(b[0]).coordinates(basis = b) -[?7h[?12l[?25h[?2004l(1, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lres = autom(b[0]).coordinates(basis = b)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: res1 = res.f.f -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lres1 = res.f.f[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: res1 -[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lres1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lroot[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: res1.pth_root() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [49], in () -----> 1 res1.pth_root() - -File :144, in pth_root(self) - -ValueError: Function is not a p-th power. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lres1.pth_root()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.pth_root()[?7h[?12l[?25h[?25l[?7l1.pth_root()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()|[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: res.reduce() -[?7h[?12l[?25h[?2004l[?7h(V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).coordinates(basis = b)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[0]).coordinates(basis = b)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: autom(b[0]) == 4*b[0] + 6*b[1] -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]) == 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(). = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7lr = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7le = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7ld = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7lu = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7lc = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7le = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7l( = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7l() = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).reduce() == (4*b[0] + 6*b[1]).reduce() -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).reduce() == (4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l (4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l (4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l()(4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l(), (4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).reduce(), (4*b[0] + 6*b[1]).reduce() -[?7h[?12l[?25h[?2004l[?7h(([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 + x^6 - x^4 + x^3 - 1)/(x^2*y - x*y)) dx) + dV([((2*x^3 + 2*x + 1)/(x^2 + 2*x))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 + x^6 - x^4 + x^3 - 1)/(x^2*y - x*y)) dx) + dV([((2*x^3 + x + 2)/(x^2 + 2*x))*y])), - ([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^4 - x^3)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x^2 + 2*x + 1)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^4 - x^3)/(x^2*y - y)) dx) + dV([((2*x^4 + 2*x^3 + x^2 + x + 1)/(x^3 + 2*x))*y]))) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l = sperelliptic(x^4 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^4 + x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4 + x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + x, 2)[?7h[?12l[?25h[?25l[?7l^ + x, 2)[?7h[?12l[?25h[?25l[?7l3 + x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x, 2)[?7h[?12l[?25h[?25l[?7l- x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x + 1, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(f)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltch(C)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C) -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1 = patch(C) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7llline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [57], in () -----> 1 C1.crystalline_cohomology_basis() - -File :354, in crystalline_cohomology_basis(self) - -File :348, in de_rham_witt_lift(cech_class) - -File :50, in decomposition_omega0_omega8(omega, prec) - -NameError: name 'Error' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7l.crysalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C1.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [58], in () -----> 1 C1.crystalline_cohomology_basis() - -File :354, in crystalline_cohomology_basis(self) - -File :348, in de_rham_witt_lift(cech_class) - -File :50, in decomposition_omega0_omega8(omega, prec) - -NameError: name 'Error' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7lsage: C1 = patch(C) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.crysalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C1.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l[?7h[([(2/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(2/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y])), - ([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(x^2*y - y)) dx) + dV([(x^4 + x^2 + 1)*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1 -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x + 1, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7lsage: C1 = patch(C) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C1.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [65], in () -----> 1 C1.crystalline_cohomology_basis() - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :50, in decomposition_omega0_omega8(omega, prec) - -ValueError: Something went wrong.((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx((x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.x.function[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.residue() -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.dx.residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7l.C.dx.residue()[?7h[?12l[?25h[?25l[?7lxC.dx.residue()[?7h[?12l[?25h[?25l[?7l()C.dx.residue()[?7h[?12l[?25h[?25l[?7l()^C.dx.residue()[?7h[?12l[?25h[?25l[?7l(C.dx.residue()[?7h[?12l[?25h[?25l[?7l-C.dx.residue()[?7h[?12l[?25h[?25l[?7l0C.dx.residue()[?7h[?12l[?25h[?25l[?7l1C.dx.residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7l-C.dx.residue()[?7h[?12l[?25h[?25l[?7l1C.dx.residue()[?7h[?12l[?25h[?25l[?7l()C.dx.residue()[?7h[?12l[?25h[?25l[?7l()*C.dx.residue()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx.residue()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().residue()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-1)*C.dx).residue() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x + 1, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7lsage: C1 = patch(C) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.crysalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C1.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [72], in () -----> 1 C1.crystalline_cohomology_basis() - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :32, in decomposition_omega0_omega8(omega, prec) - -ValueError: Non zero residue! -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = supereliptic(x^3 - x + 1, 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l. = PolynmialRng(GF(4))[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx>[?7h[?12l[?25h[?25l[?7l = PolynomialRing(GF(4))[?7h[?12l[?25h[?25l[?7l = PolynomialRing(GF(4))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(2)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = supereliptic(x^3 - x + 1, 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l(, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x, 1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.y)^(-1)])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7las_cover(C, [(C.y)^(-1)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7lC])[?7h[?12l[?25h[?25l[?7l.])[?7h[?12l[?25h[?25l[?7lx])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l)])[?7h[?12l[?25h[?25l[?7l^])[?7h[?12l[?25h[?25l[?7l3])[?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l(])[?7h[?12l[?25h[?25l[?7lC])[?7h[?12l[?25h[?25l[?7l.])[?7h[?12l[?25h[?25l[?7lx])[?7h[?12l[?25h[?25l[?7l)])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x)^3, (C.x)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x)^3, (C.x)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [6], in () -----> 1 AS.de_rham_basis() - -File :389, in de_rham_basis(self, threshold) - -File :342, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :342, in (.0) - -File :109, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :109, in (.0) - -File :102, in residue(self, place) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:618, in sage.rings.laurent_series_ring_element.LaurentSeries.residue() - 616 Integer Ring - 617 """ ---> 618 return self[-1] - 619 - 620 def exponents(self): - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() - 542 return type(self)(self._parent, f, self.__n) - 543 ---> 544 return self.__u[i - self.__n] - 545 - 546 def __iter__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() - 451 return self.base_ring().zero() - 452 else: ---> 453 raise IndexError("coefficient not known") - 454 return self.__f[n] - 455 - -IndexError: coefficient not known -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis(prec=100) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [7], in () -----> 1 AS.de_rham_basis(prec=Integer(100)) - -TypeError: as_cover.de_rham_basis() got an unexpected keyword argument 'prec' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis(prec=100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.x)^3, (C.x)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x)^3, (C.x)], prec = 50) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x)^3, (C.x)], prec = 50)[?7h[?12l[?25h[?25l[?7l.de_rham_basis(prec=100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), - ( (z1) * dx, 0 ), - ( (x) * dx, z0/x ), - ( (x*z1) * dx, z0*z1/x )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.x)^3, (C.x)], prec = 50)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l ], prec = 50)[?7h[?12l[?25h[?25l[?7l+], prec = 50)[?7h[?12l[?25h[?25l[?7l ], prec = 50)[?7h[?12l[?25h[?25l[?7l(], prec = 50)[?7h[?12l[?25h[?25l[?7lC], prec = 50)[?7h[?12l[?25h[?25l[?7l.], prec = 50)[?7h[?12l[?25h[?25l[?7lx], prec = 50)[?7h[?12l[?25h[?25l[?7l)], prec = 50)[?7h[?12l[?25h[?25l[?7l^], prec = 50)[?7h[?12l[?25h[?25l[?7l5], prec = 50)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x)^3, (C.x) + (C.x)^5], prec = 50) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x)^3, (C.x) + (C.x)^5], prec = 50)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), - ( (x*z0 + z1) * dx, 0 ), - ( (z0) * dx, 0 ), - ( (x) * dx, 0 ), - ( (x^2) * dx, 0 ), - ( (x^3) * dx, z1/x ), - ( (0) * dx, z0/x ), - ( (x^3*z0 + x*z1) * dx, z0*z1/x ), - ( (x^2*z0 + x*z0) * dx, z0*z1/x^2 ), - ( (x*z0) * dx, z0*z1/x^3 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices - group_action_matrices group_action_matrices_log  - group_action_matrices_dR group_action_matrices_old  - group_action_matrices_holo  - - [?7h[?12l[?25h[?25l[?7l - group_action_matrices  - - - [?7h[?12l[?25h[?25l[?7l_dR - group_action_matrices  - group_action_matrices_dR [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices_dR(AS) -[?7h[?12l[?25h[?2004l[?7h[ -[1 0 1 0 0 0 0 0 0 0] [1 1 0 0 0 0 0 0 0 0] -[0 1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0] -[0 0 1 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0] -[0 1 0 1 0 0 0 0 1 1] [0 0 0 1 0 0 0 1 0 0] -[0 0 0 0 1 0 0 0 1 0] [0 0 0 0 1 0 0 0 0 0] -[0 0 0 0 0 1 0 1 0 0] [0 0 0 0 0 1 0 0 0 0] -[0 0 0 0 0 0 1 0 1 0] [0 0 0 0 0 0 1 1 0 0] -[0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 1 0 0] -[0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 1 0] -[0 0 0 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 1] -] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l,group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lBgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l=group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 3[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: magma - magma  - magma_free - magmathis  - - [?7h[?12l[?25h[?25l[?7l - magma  - - - [?7h[?12l[?25h[?25l[?7l_free - magma  - magma_free[?7h[?12l[?25h[?25l[?7lthis - - magma_free - magmathis [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) -[?7h[?12l[?25h[?2004l[?7h[ -RModule of dimension 2 over GF(3), -RModule of dimension 2 over GF(3), -RModule of dimension 3 over GF(3), -RModule of dimension 3 over GF(3) -] -{ -[1 0] -[0 1], -[1 0] -[1 1] -} -{ -[1 0] -[0 1], -[1 0] -[2 1] -} -{ -[1 0 1] -[0 1 0] -[0 0 1], -[1 1 0] -[0 1 0] -[0 0 1] -} -{ -[1 0 2] -[0 1 1] -[0 0 1], -[1 0 0] -[0 1 1] -[0 0 1] -} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^3 -z1^2 - z1 = x^5 + x - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: AS.nb_of_pts_at_infty -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lgroup_actionmarices_dR(AS)[?7h[?12l[?25h[?25l[?7lAS.derham_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.x)^3, (C.x) + (C.x)^5], prec = 50)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l7], prec = 50)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x)^3, (C.x) + (C.x)^7], prec = 50) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x)^3, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lgroup_actionmarices_dR(AS)[?7h[?12l[?25h[?25l[?7lAS.derham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), - ( (x^2*z0 + z1) * dx, 0 ), - ( (z0) * dx, 0 ), - ( (x) * dx, 0 ), - ( (x*z0) * dx, 0 ), - ( (x^2) * dx, 0 ), - ( (x^3) * dx, 0 ), - ( (x^5) * dx, z1/x ), - ( (0) * dx, z0/x ), - ( (x^5*z0 + x*z1) * dx, z0*z1/x ), - ( (x^4) * dx, z1/x^2 ), - ( (x^4*z0 + x^2*z0) * dx, z0*z1/x^2 ), - ( (x^3*z0) * dx, z0*z1/x^3 ), - ( (x^2*z0) * dx, z0*z1/x^4 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.x)^3, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l , (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l+, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l , (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l(, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7lC, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l., (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7lx, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l(), (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l()^, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l5, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x)^3 + (C.x)^5, (C.x) + (C.x)^7], prec = 50) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x)^3 + (C.x)^5, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), - ( (z1) * dx, 0 ), - ( (z0) * dx, 0 ), - ( (x) * dx, 0 ), - ( (x^2*z0 + x*z1) * dx, 0 ), - ( (x*z0) * dx, 0 ), - ( (x^2) * dx, 0 ), - ( (x^3) * dx, 0 ), - ( (x^5) * dx, z1/x ), - ( (0) * dx, z0/x ), - ( (x^5*z0 + x^4 + x^3*z1 + x^2*z0) * dx, z0*z1/x ), - ( (x^4) * dx, z1/x^2 ), - ( (x^2 + 1) * dx, z0/x^2 ), - ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), - ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), - ( (x^2*z0) * dx, z0*z1/x^4 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.residue()[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.z[0]/C.x[?7h[?12l[?25h[?25l[?7lA.z[0]/C.x[?7h[?12l[?25h[?25l[?7lS.z[0]/C.x[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7lA.x[?7h[?12l[?25h[?25l[?7lS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.z[0]/AS.x -[?7h[?12l[?25h[?2004l[?7hz0/x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]/AS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]/AS.x).pth_root() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [22], in () -----> 1 (AS.z[Integer(0)]/AS.x).pth_root() - -AttributeError: 'as_function' object has no attribute 'pth_root' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.x).pth_root()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]/AS.x).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + t^2 + t^3 + t^7 + t^8 + t^10 + t^11 + t^14 + t^19 + t^21 + t^22 + t^23 + t^26 + t^28 + t^29 + t^31 + t^32 + t^34 + t^35 + t^36 + t^37 + t^39 + t^40 + t^42 + t^43 + O(t^44) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ldexpansion_at_infty()[?7h[?12l[?25h[?25l[?7liexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lnexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l(expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]/AS.x).diffn().expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + t^10 + t^18 + t^20 + t^22 + t^28 + t^30 + O(t^33) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.x).diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]/AS.x[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^5 + x^3 -z1^2 - z1 = x^7 + x - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.x).diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]/(AS.x)^4).diffn() -[?7h[?12l[?25h[?2004l[?7h((x^6*z0 + x^4*z1 + x^2*z1 + z0)/x^4) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [1], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -AttributeError: 'superelliptic' object has no attribute 'crystalline_cohomology' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [2], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :32, in decomposition_omega0_omega8(omega, prec) - -ValueError: Non zero residue! -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.residue()[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [4] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :6 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :33 - if sum(omega.residue(place = i) i in range(delta)) != _sage_const_0 : - ^ -SyntaxError: invalid syntax. Perhaps you forgot a comma? - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsum[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: sum(omega.residue(place = i) for i in range(2)) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [5], in () -----> 1 sum(omega.residue(place = i) for i in range(Integer(2))) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -Input In [5], in (.0) -----> 1 sum(omega.residue(place = i) for i in range(Integer(2))) - -NameError: name 'omega' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsum(omega.residue(place = i) for i in range(2))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7lC.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7ld.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7lx.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7lsage: sum(C.dx.residue(place = i) for i in range(2)) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [7] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :6 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :33 - if sum(omega.residue(place = i) i in range(delta)) != _sage_const_0 : - ^ -SyntaxError: invalid syntax. Perhaps you forgot a comma? - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [8], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :54, in decomposition_omega0_omega8(omega, prec) - -ValueError: Something went wrong.((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx((x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [9], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :54, in decomposition_omega0_omega8(omega, prec) - -ValueError: Something went wrong for ((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx. Result would be ((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx and ((x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^15 - x^14 + x^13 + x^12 + x^1 + x^10 - x^8)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + 1)[?7h[?12l[?25h[?25l[?7l + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + x^2 + 1)[?7h[?12l[?25h[?25l[?7l + x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1) -[?7h[?12l[?25h[?2004l[?7h(x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^3 + 2*x + 1, x^5 + x^4 + 2*x^2 + x + 2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in xi.coordinates():[?7h[?12l[?25h[?25l[?7lfffff.coordinates()[?7h[?12l[?25h[?25l[?7l = ((C.y)^3/(C.x)^2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^5 + x^4 + 2*x^2 + x + 2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^5 + x^4 + 2*x^2 + x + 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lx^6 + x^5 + x^4 - x^3 + x^2 + 1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (x^5 + x^4 + 2*x^2 + x + 2)/(x^6 + x^5 + x^4 - x^3 + x^2 + 1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = (x^5 + x^4 + 2*x^2 + x + 2)/(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= (x^5 + x^4 + 2*x^2 + x + 2)/(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff = superelliptic_function(C, ff) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = superelliptic_function(C, ff)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: ff/C.y -[?7h[?12l[?25h[?2004l[?7h((x^5 + x^4 + 2*x^2 + x + 2)/(x^9 + x^8 + 2*x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff/C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf/C.y[?7h[?12l[?25h[?25l[?7lf/C.y[?7h[?12l[?25h[?25l[?7l f/C.y[?7h[?12l[?25h[?25l[?7l=f/C.y[?7h[?12l[?25h[?25l[?7l f/C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = ff/C.y -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ff/C.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^5 + t^9 + 2*t^11 + 2*t^13 + t^21 + 2*t^23 + O(t^25) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty(place = 0) -[?7h[?12l[?25h[?2004l[?7ht^5 + t^9 + 2*t^11 + 2*t^13 + t^21 + 2*t^23 + O(t^25) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty(place = 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty(place = 1) -[?7h[?12l[?25h[?2004l[?7ht^5 + t^9 + 2*t^11 + 2*t^13 + t^21 + 2*t^23 + O(t^25) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = ff/C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: ff = ff*C.dx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ff*C.dx[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty(place = 1) -[?7h[?12l[?25h[?2004l[?7ht^2 + t^8 + t^10 + O(t^12) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty(place = 0) -[?7h[?12l[?25h[?2004l[?7ht^2 + t^8 + t^10 + O(t^12) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'superelliptic_function' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [21], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :51, in decomposition_omega0_omega8(omega, prec) - -File :216, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert ((x^14 + 2*x^13 + x^12 + x^11 + x^10 + x^9 + 2*x^7)/(x^9 + 2*x^6 + 1))*y/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [22], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :60, in decomposition_omega0_omega8(omega, prec) - -ValueError: Something went wrong for (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx. Result would be ((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx and ((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l().quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7lsage: (x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1) -[?7h[?12l[?25h[?2004l[?7h(x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^3 + 2*x + 1, x^5 + x^4 + 2*x^2 + x + 2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty(place = 0)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = ff*C.dx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = ff/C.y[?7h[?12l[?25h[?25l[?7l/C.y[?7h[?12l[?25h[?25l[?7l = superelliptic_function(C, ff)[?7h[?12l[?25h[?25l[?7l/C.y[?7h[?12l[?25h[?25l[?7l = ff/C.y[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lplace = 0)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = ff*C.dx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [1], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :60, in decomposition_omega0_omega8(omega, prec) - -ValueError: Something went wrong for (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx. Result would be ((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx and ((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7ldx.residue()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.holomorphic_differentials_basis()[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = gg^8*gg.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: om = C.dx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l.C.dx[?7h[?12l[?25h[?25l[?7lyC.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l()^C.dx[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l-C.dx[?7h[?12l[?25h[?25l[?7l1C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l()*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = (C.y)^(-1)*C.dx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: om.is_regular_on_U - om.is_regular_on_U0  - om.is_regular_on_Uinfty - - - [?7h[?12l[?25h[?25l[?7l - -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - om.cartier om.expansion_at_infty om.is_regular_on_Uinfty om.serre_duality_pairing - om.coordinates om.form om.jth_component om.verschiebung  - om.curve om.is_regular_on_U0 om.residue [?7h[?12l[?25h[?25l[?7lcartier - om.cartier  - - - [?7h[?12l[?25h[?25l[?7loordinates - om.cartier  - om.coordinates [?7h[?12l[?25h[?25l[?7lfrm - - om.coordinates  om.form [?7h[?12l[?25h[?25l[?7ljth_component - - om.form  om.jth_component [?7h[?12l[?25h[?25l[?7lvershiebung - - om.jth_component  om.verschiebung [?7h[?12l[?25h[?25l[?7ljth_omponent - - om.jth_component  om.verschiebung [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.jth_component() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [5], in () -----> 1 om.jth_component() - -TypeError: superelliptic_form.jth_component() missing 1 required positional argument: 'j' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.jth_component()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: om.jth_component(1) -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.jth_component(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = (C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l.C.dx[?7h[?12l[?25h[?25l[?7lxC.dx[?7h[?12l[?25h[?25l[?7l*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = (C.y)^(-1)*C.x*C.dx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y)^(-1)*C.x*C.dx[?7h[?12l[?25h[?25l[?7l.jth_component(1)[?7h[?12l[?25h[?25l[?7lsage: om.jth_component(1) -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7ldx.residue()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lvrschiebung()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.valuation() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [9], in () -----> 1 C.dx.valuation() - -AttributeError: 'superelliptic_form' object has no attribute 'valuation' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [10], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :81, in decomposition_omega0_omega8(omega, prec) - -File :105, in jth_component(self, j) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [11], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :81, in decomposition_omega0_omega8(omega, prec) - -File :105, in jth_component(self, j) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [12], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :81, in decomposition_omega0_omega8(omega, prec) - -File :105, in jth_component(self, j) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lself, j (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx 0 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [13], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :81, in decomposition_omega0_omega8(omega, prec) - -File :106, in jth_component(self, j) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lself, j (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx 0 -g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))/y_inv ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [14], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :81, in decomposition_omega0_omega8(omega, prec) - -File :107, in jth_component(self, j) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lself, j (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx 0 -g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))/y_inv ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [15], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :81, in decomposition_omega0_omega8(omega, prec) - -File :107, in jth_component(self, j) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() - 786 return self._call_with_args(x, args, kwds) - 787 ---> 788 cpdef Element _call_(self, x): - 789 """ - 790 Call method with a single argument, not implemented in the base class. - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) - 1249 return num - 1250 if check and not den.is_unit(): - 1251 # This should probably be a ValueError. - 1252 # However, too much existing code is expecting this to throw a - 1253 # TypeError, so we decided to keep it for the time being. --> 1254 raise TypeError("fraction must have unit denominator") - 1255 return num * den.inverse_of_unit() - -TypeError: fraction must have unit denominator -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lself, j (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx 0 ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [16], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :81, in decomposition_omega0_omega8(omega, prec) - -File :105, in jth_component(self, j) - -File :140, in coff(f, d) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement_1poly_field' object has no attribute 'coefficients' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lself, j (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx 0 -component 0 ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [17], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :83, in decomposition_omega0_omega8(omega, prec) - -NameError: name 'quo_rem' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lcomponent 0 -q, r 0 0 -component 0 -q, r 0 0 -component 0 -q, r 0 0 -component 0 -q, r 0 0 -[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7lC.x*C.d).form[?7h[?12l[?25h[?25l[?7l.x*C.dx).form[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).jth_component(1) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).jth_component(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).jth_component(0) -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7lC*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l.*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7ly*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x/C.y*C.dx).jth_component(0) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x/C.y*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: (C.x/C.y*C.dx).jth_component(1) -[?7h[?12l[?25h[?2004l[?7hx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -component 0 -q, r 0 0 -component 0 -q, r 0 0 -((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx -component 0 -q, r 0 0 -component 0 -q, r 0 0 -[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -component, j 0 0 -q, r 0 0 -component, j 0 1 -q, r 0 0 -((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx -component, j 0 0 -q, r 0 0 -component, j 0 1 -q, r 0 0 -[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x/C.y*C.dx).jth_component(1)[?7h[?12l[?25h[?25l[?7l(C.x)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().residue()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-1)*C.dx).jth_component(1) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y -g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3 -component, j 0 0 -q, r 0 0 -g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y -g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3 -component, j 0 1 -q, r 0 0 -g 0 -g2 0 -((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx -g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y -g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3 -component, j 0 0 -q, r 0 0 -g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y -g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3 -component, j 0 1 -q, r 0 0 -g 0 -g2 0 -[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7lx. = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l3))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(3)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Fx = FractionField(Rx) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFx = FractionField(Rx)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: FxRy. = PolynomialRing(Fx) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ggg = FxRy(C.y/C.x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'superelliptic_function' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [30], in () -----> 1 ggg = FxRy(C.y/C.x) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:469, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds) - 467 elif isinstance(x, sage.rings.power_series_ring_element.PowerSeries): - 468 x = x.truncate() ---> 469 return C(self, x, check, is_gen, construct=construct, **kwds) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element_generic.py:1083, in Polynomial_generic_dense_field.__init__(self, parent, x, check, is_gen, construct) - 1082 def __init__(self, parent, x=None, check=True, is_gen = False, construct=False): --> 1083 Polynomial_generic_dense.__init__(self, parent, x, check, is_gen) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:11222, in sage.rings.polynomial.polynomial_element.Polynomial_generic_dense.__init__() - 11220 # x = [] # zero polynomial - 11221 if check: -> 11222 self.__coeffs = [R(z, **kwds) for z in x] - 11223 self.__normalize() - 11224 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert 1/x*y/1 to an element of Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lggg = FxRy(C.y/C.x)[?7h[?12l[?25h[?25l[?7lFxRy. = PolynomialRing(Fx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxRy. = PolynomialRing(Fx)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: FxRy -[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxRy[?7h[?12l[?25h[?25l[?7lggg = FxRy(C.y/C.x)[?7h[?12l[?25h[?25l[?7lFxRy. = PolynomialRing(Fx)[?7h[?12l[?25h[?25l[?7lggg = FxRy(C.y/C.x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: ggg = FxRy(y/x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lggg = FxRy(y/x)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7licients[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ggg.coefficient(y) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [33], in () -----> 1 ggg.coefficient(y) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class() - 354 dummy_error_message.cls = type(self) - 355 dummy_error_message.name = name ---> 356 raise AttributeError(dummy_error_message) - 357 cdef PyObject* attr = instance_getattr(cls, name) - 358 if attr is NULL: - -AttributeError: 'PolynomialRing_field_with_category.element_class' object has no attribute 'coefficient' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lggg.coefficient(y)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lmcoeficient(y)[?7h[?12l[?25h[?25l[?7locoeficient(y)[?7h[?12l[?25h[?25l[?7lncoeficient(y)[?7h[?12l[?25h[?25l[?7locoeficient(y)[?7h[?12l[?25h[?25l[?7lmcoeficient(y)[?7h[?12l[?25h[?25l[?7licoeficient(y)[?7h[?12l[?25h[?25l[?7lacoeficient(y)[?7h[?12l[?25h[?25l[?7llcoeficient(y)[?7h[?12l[?25h[?25l[?7l_coeficient(y)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ggg.monomial_coefficient(y) -[?7h[?12l[?25h[?2004l[?7h1/x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y -g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3 -component, j 0 0 -q, r 0 0 -g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y -g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3 -component, j 0 1 -q, r 0 0 -g 0 -g2 0 -((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx -g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y -g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3 -component, j 0 0 -q, r 0 0 -g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y -g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3 -component, j 0 1 -q, r 0 0 -g 0 -g2 0 -[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lggg.monomial_coefficient(y)[?7h[?12l[?25h[?25l[?7lceffcient(y)[?7h[?12l[?25h[?25l[?7l = FxRy(y/x)[?7h[?12l[?25h[?25l[?7lFxRy[?7h[?12l[?25h[?25l[?7lggg = FxRy(y/x)[?7h[?12l[?25h[?25l[?7lFxRy[?7h[?12l[?25h[?25l[?7lggg = FxRy(C.y/C.x)[?7h[?12l[?25h[?25l[?7lFxRy. = PolynomialRing(Fx)[?7h[?12l[?25h[?25l[?7l = FractionField(Rx)[?7h[?12l[?25h[?25l[?7lR. = Polynomialing(GF(3))[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).jth_component(1)[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-1)*C.dx).jth_component(1) -[?7h[?12l[?25h[?2004lg 1/x -g2 1/x*y^2 -[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).jth_component(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-1)*C.dx).jth_component(0) -[?7h[?12l[?25h[?2004lg 1/x -g2 1/x*y^2 -[?7h1/x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y -g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3 -g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y -g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3 -component, j 0 0 0 -q, r 0 0 -g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y -g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3 -g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y -g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3 -component, j 0 1 0 -q, r 0 0 -g 0 -g2 0 -((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx -g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y -g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3 -g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y -g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3 -component, j 0 0 0 -q, r 0 0 -g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y -g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3 -g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y -g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3 -component, j 0 1 0 -q, r 0 0 -g 0 -g2 0 -[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lres.reduce()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lduc(xi)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: reduce(C, 1/y) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [39], in () -----> 1 reduce(C, Integer(1)/y) - -TypeError: reduce() arg 2 must support iteration -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduce(C, 1/y)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C, 1/y)[?7h[?12l[?25h[?25l[?7lt(C, 1/y)[?7h[?12l[?25h[?25l[?7li(C, 1/y)[?7h[?12l[?25h[?25l[?7lo(C, 1/y)[?7h[?12l[?25h[?25l[?7ln(C, 1/y)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: reduction(C, 1/y) -[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + 2*x + 1))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -component, j 0 0 0 -q, r 0 0 -component, j (x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^2) 1 (x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^2) -q, r x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^3 + 2*x + 1 2*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x + 1 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1008 # now try calling the base ring's __call__ methods --> 1009 element = self.base_ring()(element) - 1010 _p = p_NSet(sa2si(element,_ring), _ring) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1651 if nmod_poly_degree(x._denom) != 0: --> 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: - -ValueError: not integral - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [41], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :9, in  - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :87, in decomposition_omega0_omega8(omega, prec) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1013, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1011 return new_MP(self,_p) - 1012 except (TypeError, ValueError): --> 1013 raise TypeError("Could not find a mapping of the passed element to this ring.") - 1014 - 1015 def _repr_(self): - -TypeError: Could not find a mapping of the passed element to this ring. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -component, j 0 0 0 -q, r 0 0 -component, j (x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^2) 1 (x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^2) -q, r x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^3 + 2*x + 1 2*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x + 1 -((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx -component, j 0 0 0 -q, r 0 0 -component, j (x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x) 1 (x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x) -q, r x^15 + x^14 + x^9 + 2*x^7 + 2*x^4 + 2*x^2 + x + 1 2*x^6 + 2*x^5 + 2*x^4 + x^3 + x^2 + 1 -[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx -[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.valuation()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lf((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lf((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7lC)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7lo)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7ln)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7le)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff -[?7h[?12l[?25h[?2004l[?7h((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef chang(a):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_g8((3*a).f)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8((3*a).f)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega0_omega8(a)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(a)[1].expansion_at_infty() - decomposition_omega0_omega8  - decomposition_omega0_omega82 - dec…omega0_omega8_old  - - [?7h[?12l[?25h[?25l[?7l( - - -[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff) -[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -[?7h(((x^9 + x^8 - x^7 - x^6 - x^3 - x + 1)/y) dx, - ((x^9 + x^8 - x^7 - x^6 - x^3 - x + 1)/y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lldecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7ledecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7lndecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: len(decomposition_omega0_omega8(fff)) -[?7h[?12l[?25h[?2004l(((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^11 + x^10 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2))*y) dx -[?7h2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7lsage: len(decomposition_omega0_omega8(fff)) -[?7h[?12l[?25h[?2004l(((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^11 + x^10 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2))*y) dx -[?7h2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llendecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff) -[?7h[?12l[?25h[?2004l(((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^11 + x^10 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2))*y) dx -[?7h(((x^9 + x^8 - x^7 - x^6 - x^3 - x + 1)/y) dx, - ((x^9 + x^8 - x^7 - x^6 - x^3 - x + 1)/y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7load('init.age')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx -((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx -[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7lfff[?7h[?12l[?25h[?25l[?7l = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lfff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: fff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff) -[?7h[?12l[?25h[?2004l[?7h(((x^9 + x^8 - x^7 - x^6 - x^3 - x + 1)/y) dx, - ((x^7 + x^6 + x^5 - x^4 - x^3 + x - 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff)[0] - ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y ) -....: )[?7h[?12l[?25h[?25l[?7l(() -[?7h[?12l[?25h[?25l[?7l( - [?7h[?12l[?25h[?25l[?7l 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-  decomposition decomposition_omega0_omega82  - decomposition_g0_g8 decomposition_omega0_omega8_old - decomposition_omega0_omega8  - - [?7h[?12l[?25h[?25l[?7l - decomposition  - - - [?7h[?12l[?25h[?25l[?7l_g0_g8 - decomposition  - decomposition_g0_g8 [?7h[?12l[?25h[?25l[?7lomea0_omega8 - - decomposition_g0_g8  - decomposition_omega0_omega8 [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1] == fff -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - [?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1] == fff[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l f[?7h[?12l[?25h[?25l[?7l f[?7h[?12l[?25h[?25l[?7l[]f[?7h[?12l[?25h[?25l[?7l[], f[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1], fff -[?7h[?12l[?25h[?2004l[?7h(((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + x^7 + x^6 - x^5 - x^4 + x^2 - x + 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx, - (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^11 + x^10 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2))*y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1], fff[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]), 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f.form)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: reduction(C, (decomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1]).form- fff.form) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduction(C, (decomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1]).form- fff.form)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[1]).form- fff.form)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[]decomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[decomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()decomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l(decomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecompositon_omega0_omega8(ff)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff)[1].expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + t^10 + O(t^12) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.dx.valuation()[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l[?7h[([(1/(x^3 + 2*x + 1))*y] d[x] + V(((x^11 - x^9 + x^8 - x^7 + x^6 + x^5 - x^3 - x + 1)/(x^6*y + x^4*y - x^3*y + x^2*y + x*y + y)) dx) + dV([((2*x^7 + x^6 + 2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + x^4 + 2*x^3 + x^2 + x + 1))*y]), V(1/x*y), [(1/(x^3 + 2*x + 1))*y] d[x] + V(((x^11 - x^9 + x^8 - x^7 + x^6 + x^5 - x^3 - x + 1)/(x^6*y + x^4*y - x^3*y + x^2*y + x*y + y)) dx) + dV([((2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x + 2)/(x^7 + x^5 + 2*x^4 + x^3 + x^2 + x))*y])), - ([(x/(x^3 + 2*x + 1))*y] d[x] + V(((x^14 - x^9 - x^8 + x^5 + x^4 + x^3 + x^2 - x)/(x^6*y + x^4*y - x^3*y + x^2*y + x*y + y)) dx) + dV([((2*x^10 + x^9 + x^8 + x^7 + x^6 + 2*x^5 + x^4)/(x^6 + x^4 + 2*x^3 + x^2 + x + 1))*y]), [2/x*y] + V(2/x*y), [((2*x + 2)/(x^5 + 2*x^3 + x^2))*y] d[x] + V(((x^15 - x^10 + x^9 + x^6 + x^5 - x^4 + x^3 - x + 1)/(x^7*y + x^5*y - x^4*y + x^3*y + x^2*y + x*y)) dx) + dV([((2*x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^6 + x^4 + 1)/(x^8 + x^6 + 2*x^5 + x^4 + x^3 + x^2))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7ltC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lcC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lhC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l(C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: patch(C).crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l[?7h[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), - ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lsage: C1 = patch(C) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lp_rank()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: C.polynomial -[?7h[?12l[?25h[?2004l[?7hx^3 + 2*x + 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.polynomial[?7h[?12l[?25h[?25l[?7l1 = patch(C)[?7h[?12l[?25h[?25l[?7l.crysalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: C1.polynomial -[?7h[?12l[?25h[?2004l[?7hx^4 + 2*x^3 + x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: Rx -[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lC1.polynomial[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgC1.polynomial[?7h[?12l[?25h[?25l[?7l C1.polynomial[?7h[?12l[?25h[?25l[?7l=C1.polynomial[?7h[?12l[?25h[?25l[?7l C1.polynomial[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = C1.polynomial -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C1.polynomial[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = g(x^3 - x) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = g(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: g -[?7h[?12l[?25h[?2004l[?7hx^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.polynomial[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C2 = superelliptic(g, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2 = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C2 -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C2.genus() -[?7h[?12l[?25h[?2004l[?7h5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.genus()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C2.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [13], in () -----> 1 C2.crystalline_cohomology_basis() - -File :355, in crystalline_cohomology_basis(self) - -File :349, in de_rham_witt_lift(cech_class) - -File :69, in decomposition_omega0_omega8(omega, prec) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :69, in (.0) - -File :143, in residue(self, place, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() - 542 return type(self)(self._parent, f, self.__n) - 543 ---> 544 return self.__u[i - self.__n] - 545 - 546 def __iter__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() - 451 return self.base_ring().zero() - 452 else: ---> 453 raise IndexError("coefficient not known") - 454 return self.__f[n] - 455 - -IndexError: coefficient not known -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l(); xi = C.de_rham_basis()[1];xi.coordinates()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC2 = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lne_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); C2 = superelliptic(g, 2); C2.crystalline_cohomology_basis(prec = 100) -[?7h[?12l[?25h[?2004l[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] ---------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [14], in () -----> 1 load('init.sage'); C2 = superelliptic(g, Integer(2)); C2.crystalline_cohomology_basis(prec = Integer(100)) - -File :355, in crystalline_cohomology_basis(self, prec) - -File :347, in de_rham_witt_lift(cech_class, prec) - -File :6, in decomposition_g0_g8(fct) - -File :107, in coordinates(self, basis, basis_holo, prec) - -File :77, in serre_duality_pairing(self, fct, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() - 542 return type(self)(self._parent, f, self.__n) - 543 ---> 544 return self.__u[i - self.__n] - 545 - 546 def __iter__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() - 451 return self.base_ring().zero() - 452 else: ---> 453 raise IndexError("coefficient not known") - 454 return self.__f[n] - 455 - -IndexError: coefficient not known -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); C2 = superelliptic(g, 2); C2.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage'); C2 = superelliptic(g, 2); C2.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l^[[A    [([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l= superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7lsage: C2 = superelliptic(g, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2 = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C2 -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lam_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C2.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), - ((x/y) dx, 0, (x/y) dx), - ((x^2/y) dx, 0, (x^2/y) dx), - ((x^3/y) dx, 0, (x^3/y) dx), - ((x^4/y) dx, 0, (x^4/y) dx), - (((x^10 + x^8 - x^7 - x^4 - x^2 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx), - (((-x^9 + x^6 + x^3 + 1)/y) dx, 2/x^2*y, 0 dx), - (((-x^6 + 1)/y) dx, 2/x^3*y, (1/(x^3*y)) dx), - (((x^7 + x^5 - x^4 - x)/y) dx, 2/x^4*y, ((x^3 + x^2 - 1)/(x^4*y)) dx), - (((-x^6 + x^3 + 1)/y) dx, 2/x^5*y, ((-1)/(x^3*y)) dx)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.de_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC2.de_rham_basis()[2][?7h[?12l[?25h[?25l[?7l C2.de_rham_basis()[2][?7h[?12l[?25h[?25l[?7l=C2.de_rham_basis()[2][?7h[?12l[?25h[?25l[?7l C2.de_rham_basis()[2][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a = C2.de_rham_basis()[2] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_form_to_drw(xi)[?7h[?12l[?25h[?25l[?7lft_form_to_drw(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(a) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [20], in () -----> 1 lift_form_to_drw(a) - -File :29, in lift_form_to_drw(omega) - -File :10, in regular_form(omega) - -AttributeError: 'superelliptic_cech' object has no attribute 'form' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(xi)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(a) -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C2.de_rham_basis()[2][?7h[?12l[?25h[?25l[?7ldic_expansion(gg, x^3 - x)[?7h[?12l[?25h[?25l[?7lic_expansion(gg, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [22], in () -----> 1 adic_expansion(g, x**Integer(3) - x) - -NameError: name 'adic_expansion' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(a)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage') -[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx -t^-40 + O(t^-30) -[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x) -[?7h[?12l[?25h[?2004l[?7h[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage'[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7llift_form_odrw(a)[?7h[?12l[?25h[?25l[?7la = C2.derham_basis()[2][?7h[?12l[?25h[?25l[?7lC2.de_rham_bsis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: Rx -[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage'[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7llift_form_odrw(a)[?7h[?12l[?25h[?25l[?7la = C2.derham_basis()[2][?7h[?12l[?25h[?25l[?7lC2.de_rham_bsis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(); C2 = superelliptic(g, 2); C2.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7lC2.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = g(x^3 - x)[?7h[?12l[?25h[?25l[?7lC1.polynomial[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lC1.polynomial[?7h[?12l[?25h[?25l[?7l.polynomial[?7h[?12l[?25h[?25l[?7l1 = patch(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1 = patch(C)[?7h[?12l[?25h[?25l[?7l.polynomial[?7h[?12l[?25h[?25l[?7l1.polynomial[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lg = C1.polynomial[?7h[?12l[?25h[?25l[?7lg(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2 = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage'); C2 = superelliptic(g, 2); C2.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC2 = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7la = C2.de_rhm_basis()[2][?7h[?12l[?25h[?25l[?7llift_formto_drw(a)[?7h[?12l[?25h[?25l[?7lde_rham_witlift(a)[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage'[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.de_rham_basis()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C2 -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = g(x^3 - x)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC1.polynomial[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: g = C2.polynomial -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x) -[?7h[?12l[?25h[?2004l[?7h[1, 2, 0, 1, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lg = C2.olynmial[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage'[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7llift_form_odrw(a)[?7h[?12l[?25h[?25l[?7lde_rham_witlift(a)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(a)[?7h[?12l[?25h[?25l[?7l1de_rham_wit_lift(a)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(a)[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(a)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(a)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a1 = de_rham_witt_lift(a) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C).crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: p*a1 -[?7h[?12l[?25h[?2004l[?7h(V((x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx), [0], V((x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx)) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd .. -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status -On branch master -Your branch is up to date with 'origin/master'. - -Changes not staged for commit: - (use "git add ..." to update what will be committed) - (use "git restore ..." to discard changes in working directory) - modified: sage/.run.term-0.term - modified: sage/drafty/draft.sage - modified: sage/drafty/superelliptic_drw.sage - modified: sage/superelliptic/decomposition_into_g0_g8.sage - modified: sage/superelliptic/superelliptic_cech_class.sage - modified: sage/superelliptic/superelliptic_form_class.sage - -Untracked files: - (use "git add ..." to include in what will be committed) - .crystalline_p2.ipynb.sage-jupyter2 - .deRhamComputation.ipynb.sage-jupyter2 - .elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2 - .git.x11-0.term - .superelliptic.ipynb.sage-jupyter2 - .superelliptic_alpha.ipynb.sage-jupyter2 - .superelliptic_arbitrary_field.ipynb.sage-jupyter2 - git.x11 - sage/as_covers/tests/cartier_test.sage - sage/drafty/as_cartier.sage - sage/drafty/better_trace.sage - sage/drafty/cartier_image_representation.sage - sage/drafty/draft4.sage - sage/drafty/draft5.sage - sage/drafty/draft6.sage - sage/drafty/draft7.sage - sage/drafty/lift_to_de_rham.sage - sage/drafty/pole_numbers.sage - sage/drafty/regular_on_U0.sage - sage/superelliptic/frobenius_kernel.sage - sage/superelliptic/tests/ - superelliptic_arbitrary_field.ipynb - -no changes added to commit (use "git add" and/or "git commit -a") -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""p"o"p"r"a"w"i"o"n"e" """y" "r"o"z"k"l"a"d" "n"a" "o"m"e"g"a"0" "-" "o"m"e"g"a"8" -[master 7e8546b] poprawiony rozklad na omega0 - omega8 - 6 files changed, 2553 insertions(+), 29 deletions(-) -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push -Username for 'https://git.wmi.amu.edu.pl': jgarnek -Password for 'https://jgarnek@git.wmi.amu.edu.pl': -Enumerating objects: 21, done. -Counting objects: 4% (1/21) Counting objects: 9% (2/21) Counting objects: 14% (3/21) Counting objects: 19% (4/21) Counting objects: 23% (5/21) Counting objects: 28% (6/21) Counting objects: 33% (7/21) Counting objects: 38% (8/21) Counting objects: 42% (9/21) Counting objects: 47% (10/21) Counting objects: 52% (11/21) Counting objects: 57% (12/21) Counting objects: 61% (13/21) Counting objects: 66% (14/21) Counting objects: 71% (15/21) Counting objects: 76% (16/21) Counting objects: 80% (17/21) Counting objects: 85% (18/21) Counting objects: 90% (19/21) Counting objects: 95% (20/21) Counting objects: 100% (21/21) Counting objects: 100% (21/21), done. -Delta compression using up to 4 threads -Compressing objects: 9% (1/11) Compressing objects: 18% (2/11) Compressing objects: 27% (3/11) Compressing objects: 36% (4/11) Compressing objects: 45% (5/11) Compressing objects: 54% (6/11) Compressing objects: 63% (7/11) Compressing objects: 72% (8/11) Compressing objects: 81% (9/11) Compressing objects: 90% (10/11) Compressing objects: 100% (11/11) Compressing objects: 100% (11/11), done. -Writing objects: 9% (1/11) Writing objects: 18% (2/11) Writing objects: 27% (3/11) Writing objects: 36% (4/11) Writing objects: 45% (5/11) Writing objects: 54% (6/11) Writing objects: 63% (7/11) Writing objects: 72% (8/11) Writing objects: 81% (9/11) Writing objects: 90% (10/11) Writing objects: 100% (11/11) Writing objects: 100% (11/11), 27.84 KiB | 293.00 KiB/s, done. -Total 11 (delta 9), reused 0 (delta 0) -remote: . Processing 1 references -remote: Processed 1 references in total -To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git - 8719e64..7e8546b master -> master -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') - in initial_seed install_scripts integer_floor integrate invariant_theory inverse_jacobi_cs inverse_jacobi_nc inverse_jacobi_sd  - infinity input installed_packages integral interacts inverse_jacobi inverse_jacobi_dc inverse_jacobi_nd inverse_jacobi_sn  - infix_operator install_dict int integral_closure interfaces inverse_jacobi_cd inverse_jacobi_dn inverse_jacobi_ns inverse_laplace  - init.sage install_doc integer_ceil integral_numerical interval inverse_jacobi_cn inverse_jacobi_ds inverse_jacobi_sc inverse_mod  - [?7h[?12l[?25h[?25l[?7l(it.sage') - - - -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [1], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :13, in  - -File :18, in convert_super_into_AS(C) - -ValueError: This is not a polynomial of x^p - x! -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[Finite Field of size 3] ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [2], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :13, in  - -File :19, in convert_super_into_AS(C) - -ValueError: This is not a polynomial of x^p - x! -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [4], in () -----> 1 AS - -NameError: name 'AS' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [5], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :36, in convert_super_fct_into_AS(fct) - -File :4, in adic_expansion(g, h) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.fraction_field_FpT.FpTElement' object has no attribute 'degree' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x ---------------------------------------------------------------------------- -NotImplementedError Traceback (most recent call last) -Input In [6], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :36, in convert_super_fct_into_AS(fct) - -File :4, in adic_expansion(g, h) - -File /ext/sage/9.7/src/sage/structure/element.pyx:4100, in sage.structure.element.EuclideanDomainElement.degree() - 4098 - 4099 def degree(self): --> 4100 raise NotImplementedError - 4101 - 4102 def leading_coefficient(self): - -NotImplementedError: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x -component.numerator(), component.denominator() x^4 + 2*x 1 -adic_expansion(component.numerator(), x^p - x) [x^2 - x, x] -component.numerator(), component.denominator() 0 1 ---------------------------------------------------------------------------- -NotImplementedError Traceback (most recent call last) -Input In [7], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :37, in convert_super_fct_into_AS(fct) - -File :4, in adic_expansion(g, h) - -File /ext/sage/9.7/src/sage/structure/element.pyx:4100, in sage.structure.element.EuclideanDomainElement.degree() - 4098 - 4099 def degree(self): --> 4100 raise NotImplementedError - 4101 - 4102 def leading_coefficient(self): - -NotImplementedError: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x -component.numerator(), component.denominator() x^4 + 2*x 1 -adic_expansion(component.numerator(), x^p - x) [x^2 - x, x] -component.numerator(), component.denominator() 0 1 -adic_expansion(component.numerator(), x^p - x) [0] ---------------------------------------------------------------------------- -NotImplementedError Traceback (most recent call last) -Input In [8], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :41, in convert_super_fct_into_AS(fct) - -File :6, in adic_expansion(g, h) - -File /ext/sage/9.7/src/sage/structure/element.pyx:4100, in sage.structure.element.EuclideanDomainElement.degree() - 4098 - 4099 def degree(self): --> 4100 raise NotImplementedError - 4101 - 4102 def leading_coefficient(self): - -NotImplementedError: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x -component.numerator(), component.denominator() x^4 + 2*x 1 -adic_expansion(component.numerator(), x^p - x) [x^2 + 2*x, x] -adic_expansion(Rx(component.denominator()), x^p - x) [1] -component.numerator(), component.denominator() 0 1 -adic_expansion(component.numerator(), x^p - x) [0] -adic_expansion(Rx(component.denominator()), x^p - x) [1] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [9], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -File :48, in convert_super_fct_into_AS(fct) - -TypeError: 'sage.rings.integer.Integer' object is not callable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x -component.numerator(), component.denominator() x^4 + 2*x 1 -adic_expansion(component.numerator(), x^p - x) [x^2 + 2*x, x] -adic_expansion(Rx(component.denominator()), x^p - x) [1] -component.numerator(), component.denominator() 0 1 -adic_expansion(component.numerator(), x^p - x) [0] -adic_expansion(Rx(component.denominator()), x^p - x) [1] -x*z0 + z0^2 - z0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x -component.numerator(), component.denominator() x^4 + 2*x^2 1 -adic_expansion(component.numerator(), x^p - x) [0, x] -adic_expansion(Rx(component.denominator()), x^p - x) [1] -component.numerator(), component.denominator() 0 1 -adic_expansion(component.numerator(), x^p - x) [0] -adic_expansion(Rx(component.denominator()), x^p - x) [1] -x*z0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x -x*z0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lchang(b)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: con - %conda conjugate continue contour_plot converted  - cones constructions continued_fraction convert_super_fct_into_AS convolution  - %config continuant continued_fraction_list convert_super_into_AS conway_polynomial  - - [?7h[?12l[?25h[?25l[?7l%conda - %conda  - - - [?7h[?12l[?25h[?25l[?7lconjugate - %conda  conjugate [?7h[?12l[?25h[?25l[?7lcontinue - conjugate  continue [?7h[?12l[?25h[?25l[?7lcontour_plot - continue  contour_plot [?7h[?12l[?25h[?25l[?7lverted - contour_plot  converted [?7h[?12l[?25h[?25l[?7lolution - converted  - convolution [?7h[?12l[?25h[?25l[?7lert_super_fct_into_AS - - convert_super_fct_into_AS convolution [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.dx[?7h[?12l[?25h[?25l[?7l2C2.dx[?7h[?12l[?25h[?25l[?7l.C2.dx[?7h[?12l[?25h[?25l[?7lyC2.dx[?7h[?12l[?25h[?25l[?7l*C2.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.dx[?7h[?12l[?25h[?25l[?7l2C2.dx[?7h[?12l[?25h[?25l[?7l.C2.dx[?7h[?12l[?25h[?25l[?7lxC2.dx[?7h[?12l[?25h[?25l[?7l^C2.dx[?7h[?12l[?25h[?25l[?7l2C2.dx[?7h[?12l[?25h[?25l[?7l*C2.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(C2.y*C2.x^2*C2.dx) -[?7h[?12l[?25h[?2004l[?7h(y*z0^2) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x -x*z0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C2 -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lorain xi.coordinates():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B = C2.crystalline_cohomology_basis() -[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 379 try: ---> 380 z = integer_ring.Z(value) - 381 except (TypeError, ValueError): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_() - 286 cdef Map m ---> 287 cdef Element e = method(C) - 288 if e is None: - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:832, in sage.rings.fraction_field_element.FractionFieldElement._conversion() - 831 self.reduce() ---> 832 num = R(self.__numerator) - 833 inv_den = R(self.__denominator).inverse_of_unit() - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - -File /ext/sage/9.7/src/sage/categories/map.pyx:1677, in sage.categories.map.FormalCompositeMap._call_() - 1676 --> 1677 cpdef Element _call_(self, x): - 1678 """ - -File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() - 1691 for f in self.__list: --> 1692 x = f._call_(x) - 1693 return x - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1619 --> 1620 cpdef Element _call_(self, _x): - 1621 """ - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() - 1651 if nmod_poly_degree(x._denom) != 0: --> 1652 raise ValueError("not integral") - 1653 if nmod_poly_degree(x._numer) > 0: - -ValueError: not integral - -During handling of the above exception, another exception occurred: - -KeyboardInterrupt Traceback (most recent call last) -Input In [16], in () -----> 1 B = C2.crystalline_cohomology_basis() - -File :356, in crystalline_cohomology_basis(self, prec) - -File :340, in de_rham_witt_lift(cech_class, prec) - -File :65, in __mul__(self, other) - -File :23, in __sub__(self, other) - -File :7, in __init__(self, C, g) - -File :259, in reduction_form(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) - 636 ring_one = self.ring().one() - 637 try: ---> 638 return self._element_class(self, x, ring_one, coerce=coerce) - 639 except (TypeError, ValueError): - 640 pass - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() - 112 FieldElement.__init__(self, parent) - 113 if coerce: ---> 114 self.__numerator = parent.ring()(numerator) - 115 self.__denominator = parent.ring()(denominator) - 116 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1007 try: - 1008 # now try calling the base ring's __call__ methods --> 1009 element = self.base_ring()(element) - 1010 _p = p_NSet(sa2si(element,_ring), _ring) - 1011 return new_MP(self,_p) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) - 1143 """ - 1144 TESTS:: - 1145 - (...) - 1182  True - 1183 """ - 1184 try: --> 1185 return integer_mod.IntegerMod(self, x) - 1186 except (NotImplementedError, PariError): - 1187 raise TypeError("error coercing to finite field") - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() - 199 return a - 200 t = modulus.element_class() ---> 201 return t(parent, value) - 202 - 203 - -File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:388, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() - 386 value = py_scalar_to_element(value) - 387 if isinstance(value, Element) and value.parent().is_exact(): ---> 388 value = sage.rings.rational_field.QQ(value) - 389 z = value % self.__modulus.sageInteger - 390 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 536 """ - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - 540 def __reduce__(self): - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 624 - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - 628 elif isinstance(x, tuple) and len(x) == 2: - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_() - 782 1/2 - 783 """ ---> 784 return self._conversion(QQ) - 785 - 786 def _conversion(self, R): - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:832, in sage.rings.fraction_field_element.FractionFieldElement._conversion() - 830 else: - 831 self.reduce() ---> 832 num = R(self.__numerator) - 833 inv_den = R(self.__denominator).inverse_of_unit() - 834 return num * inv_den - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 536 """ - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - 540 def __reduce__(self): - -File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() - 624 - 625 elif hasattr(x, "_rational_"): ---> 626 set_from_Rational(self, x._rational_()) - 627 - 628 elif isinstance(x, tuple) and len(x) == 2: - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1446, in sage.rings.polynomial.polynomial_element.Polynomial._rational_() - 1444 TypeError: not a constant polynomial - 1445 """ --> 1446 return self._scalar_conversion(sage.rings.rational.Rational) - 1447 - 1448 def _symbolic_(self, R): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion() - 1389 if self.degree() > 0: - 1390 raise TypeError("cannot convert nonconstant polynomial") --> 1391 return R(self.get_coeff_c(0)) - 1392 - 1393 _real_double_ = _scalar_conversion - -File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() - 536 """ - 537 if x is not None: ---> 538 self.__set_value(x, base) - 539 - 540 def __reduce__(self): - -File /ext/sage/9.7/src/sage/rings/rational.pyx:691, in sage.rings.rational.Rational.__set_value() - 689 - 690 else: ---> 691 raise TypeError("unable to convert {!r} to a rational".format(x)) - 692 - 693 cdef void set_from_mpq(Rational self, mpq_t value): - -File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() - 192 except AttributeError: - 193 return super().__repr__() ---> 194 result = reprfunc() - 195 if isinstance(result, str): - 196 return result - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:340, in sage.rings.fraction_field_FpT.FpTElement._repr_() - 338 return repr(self.numer()) - 339 else: ---> 340 numer_s = repr(self.numer()) - 341 denom_s = repr(self.denom()) - 342 if '-' in numer_s or '+' in numer_s: - -File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() - 192 except AttributeError: - 193 return super().__repr__() ---> 194 result = reprfunc() - 195 if isinstance(result, str): - 196 return result - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_() - 2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3 - 2689 """ --> 2690 return self._repr() - 2691 - 2692 def _latex_(self, name=None): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2662, in sage.rings.polynomial.polynomial_element.Polynomial._repr() - 2660 x = "(%s)"%x - 2661 if n > 1: --> 2662 var = "*%s^%s"%(name,n) - 2663 elif n==1: - 2664 var = "*%s"%name - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C2.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C2.crystalline_cohomology_basis(prec = 100) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [17], in () -----> 1 B = C2.crystalline_cohomology_basis(prec = Integer(100)) - -File :356, in crystalline_cohomology_basis(self, prec) - -File :347, in de_rham_witt_lift(cech_class, prec) - -File :6, in decomposition_g0_g8(fct, prec) - -File :107, in coordinates(self, basis, basis_holo, prec) - -File :77, in serre_duality_pairing(self, fct, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() - 542 return type(self)(self._parent, f, self.__n) - 543 ---> 544 return self.__u[i - self.__n] - 545 - 546 def __iter__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() - 451 return self.base_ring().zero() - 452 else: ---> 453 raise IndexError("coefficient not known") - 454 return self.__f[n] - 455 - -IndexError: coefficient not known -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C2.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: A = C2.de - C2.de_rham_basis C2.degrees_de_rham1  - C2.degrees_de_rham0 C2.degrees_holomorphic_differentials - - - [?7h[?12l[?25h[?25l[?7l_rham_basis - C2.de_rham_basis  - - [?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A = C2.de_rham_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - - [?7h[?12l[?25h[?25l[?7lA = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: A -[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), - ((x/y) dx, 0, (x/y) dx), - ((x^2/y) dx, 0, (x^2/y) dx), - ((x^3/y) dx, 0, (x^3/y) dx), - ((x^4/y) dx, 0, (x^4/y) dx), - (((x^10 + x^8 - x^7 - x^4 - x^2 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx), - (((-x^9 + x^6 + x^3 + 1)/y) dx, 2/x^2*y, 0 dx), - (((-x^6 + 1)/y) dx, 2/x^3*y, (1/(x^3*y)) dx), - (((x^7 + x^5 - x^4 - x)/y) dx, 2/x^4*y, ((x^3 + x^2 - 1)/(x^4*y)) dx), - (((-x^6 + x^3 + 1)/y) dx, 2/x^5*y, ((-1)/(x^3*y)) dx)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laA[2][?7h[?12l[?25h[?25l[?7l A[2][?7h[?12l[?25h[?25l[?7l=A[2][?7h[?12l[?25h[?25l[?7l A[2][?7h[?12l[?25h[?25l[?7ldA[2][?7h[?12l[?25h[?25l[?7lA[2][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(A[2])[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(A[2])[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(A[2])[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(A[2])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(A[2]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(C2.y*C2.x^2*C2.dx)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrt_super_fct_into_AS(C2.y*C2.x^2*C2.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a) -[?7h[?12l[?25h[?2004l[?7h((y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), - ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, - (x^15*y*z0^2 + x^15*y*z0 + x^14*y*z0^2 - x^15*y - x^13*y*z0^2 - x^13*y*z0 + x^12*y*z0^2 + x^13*y + x^11*y*z0^2 + x^12*y + x^11*y*z0 + x^10*y*z0^2 + x^10*y*z0 - x^9*y*z0^2 + x^10*y - x^9*y*z0 - x^9*y - x^8*y*z0 + x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^6*y + x^4*y - x^2*y*z0^2 + x^3*y + x^2*y*z0 - x*y*z0^2 - x*y - y*z0)/(x^7*z0 - x^6*z0^2 + x^6*z0 - x^5*z0^2 + x^6 + x^5*z0 - x^4*z0^2 + x^5 - x^4*z0 + x^3*z0^2 + x^4 + x^3*z0 - x^2*z0^2 - x^3 + x^2 + x*z0 - z0^2 + 1)), - (0, (-x*y*z0 - y)/(x*z0^2 + x + z0)), - (y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), - ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, - (x^17*y*z0 + x^16*y*z0^2 + x^17*y - x^15*y*z0 - x^14*y*z0^2 - x^13*y*z0^2 + x^13*y*z0 - x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^12*y - x^11*y*z0 + x^10*y*z0^2 + x^11*y - x^9*y*z0^2 - x^9*y*z0 + x^9*y + x^8*y*z0 - x^7*y*z0^2 + x^8*y - x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^5*y*z0^2 + x^5*y*z0 + x^4*y*z0^2 - x^4*y*z0 - x^3*y*z0^2 - x^4*y + x^2*y*z0^2 + x^3*y - x^2*y*z0 + y*z0^2 + y)/(x^9 + x^8*z0 + x^8 + x^7*z0 + x^7 + x^6*z0 - x^6 - x^5*z0 + x^5 + x^4*z0 + x^3 + x^2*z0))) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.omega0[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lduce[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.reduce() -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.reduce()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.r() -[?7h[?12l[?25h[?2004l[?7h((x^2/y) dx, 0, (x^2/y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x -x*z0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.r()[?7h[?12l[?25h[?25l[?7leduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(A[2]) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [27], in () -----> 1 a = de_rham_witt_lift(A[Integer(2)]) - -File :341, in de_rham_witt_lift(cech_class, prec) - -File :5, in regular_form(omega) - -AttributeError: 'NoneType' object has no attribute 'curve' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.r()[?7h[?12l[?25h[?25l[?7leduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: A = C2.de_rham_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lade_rham_witt_lft(A[2])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(A[2]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(a) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [30], in () -----> 1 de_rham_witt_lift(a) - -File :339, in de_rham_witt_lift(cech_class, prec) - -File :10, in regular_form(omega) - -AttributeError: 'superelliptic_drw_form' object has no attribute 'form' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrt_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a) -[?7h[?12l[?25h[?2004l[?7h((y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), - ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, - (x^15*y*z0^2 + x^15*y*z0 + x^14*y*z0^2 - x^15*y - x^13*y*z0^2 - x^13*y*z0 + x^12*y*z0^2 + x^13*y + x^11*y*z0^2 + x^12*y + x^11*y*z0 + x^10*y*z0^2 + x^10*y*z0 - x^9*y*z0^2 + x^10*y - x^9*y*z0 - x^9*y - x^8*y*z0 + x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^6*y + x^4*y - x^2*y*z0^2 + x^3*y + x^2*y*z0 - x*y*z0^2 - x*y - y*z0)/(x^7*z0 - x^6*z0^2 + x^6*z0 - x^5*z0^2 + x^6 + x^5*z0 - x^4*z0^2 + x^5 - x^4*z0 + x^3*z0^2 + x^4 + x^3*z0 - x^2*z0^2 - x^3 + x^2 + x*z0 - z0^2 + 1)), - (0, (-x*y*z0 - y)/(x*z0^2 + x + z0)), - (y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), - ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, - (x^17*y*z0 + x^16*y*z0^2 + x^17*y - x^15*y*z0 - x^14*y*z0^2 - x^13*y*z0^2 + x^13*y*z0 - x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^12*y - x^11*y*z0 + x^10*y*z0^2 + x^11*y - x^9*y*z0^2 - x^9*y*z0 + x^9*y + x^8*y*z0 - x^7*y*z0^2 + x^8*y - x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^5*y*z0^2 + x^5*y*z0 + x^4*y*z0^2 - x^4*y*z0 - x^3*y*z0^2 - x^4*y + x^2*y*z0^2 + x^3*y - x^2*y*z0 + y*z0^2 + y)/(x^9 + x^8*z0 + x^8 + x^7*z0 + x^7 + x^6*z0 - x^6 - x^5*z0 + x^5 + x^4*z0 + x^3 + x^2*z0))) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.r() -[?7h[?12l[?25h[?2004l[?7h((x^2/y) dx, 0, (x^2/y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.r()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: a.omega0.h1 -[?7h[?12l[?25h[?2004l[?7h(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.h1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: a.omega0.h1 == a.r().omega0 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [35], in () -----> 1 a.omega0.h1 == a.r().omega0 - -File :18, in __eq__(self, other) - -AttributeError: 'superelliptic_form' object has no attribute 'function' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsa.omega0.form[?7h[?12l[?25h[?25l[?7lua.omega0.form[?7h[?12l[?25h[?25l[?7lpa.omega0.form[?7h[?12l[?25h[?25l[?7lea.omega0.form[?7h[?12l[?25h[?25l[?7lra.omega0.form[?7h[?12l[?25h[?25l[?7lea.omega0.form[?7h[?12l[?25h[?25l[?7lla.omega0.form[?7h[?12l[?25h[?25l[?7lla.omega0.form[?7h[?12l[?25h[?25l[?7lia.omega0.form[?7h[?12l[?25h[?25l[?7lta.omega0.form[?7h[?12l[?25h[?25l[?7lpa.omega0.form[?7h[?12l[?25h[?25l[?7la.omega0.form[?7h[?12l[?25h[?25l[?7la.omega0.form[?7h[?12l[?25h[?25l[?7lpa.omega0.form[?7h[?12l[?25h[?25l[?7lta.omega0.form[?7h[?12l[?25h[?25l[?7lia.omega0.form[?7h[?12l[?25h[?25l[?7lca.omega0.form[?7h[?12l[?25h[?25l[?7l_a.omega0.form[?7h[?12l[?25h[?25l[?7lfa.omega0.form[?7h[?12l[?25h[?25l[?7lua.omega0.form[?7h[?12l[?25h[?25l[?7lna.omega0.form[?7h[?12l[?25h[?25l[?7lca.omega0.form[?7h[?12l[?25h[?25l[?7lta.omega0.form[?7h[?12l[?25h[?25l[?7lia.omega0.form[?7h[?12l[?25h[?25l[?7loa.omega0.form[?7h[?12l[?25h[?25l[?7lna.omega0.form[?7h[?12l[?25h[?25l[?7l(a.omega0.form[?7h[?12l[?25h[?25l[?7lCa.omega0.form[?7h[?12l[?25h[?25l[?7l2a.omega0.form[?7h[?12l[?25h[?25l[?7l,a.omega0.form[?7h[?12l[?25h[?25l[?7l a.omega0.form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: superelliptic_function(C2, a.omega0.form) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [36], in () -----> 1 superelliptic_function(C2, a.omega0.form) - -AttributeError: 'superelliptic_drw_form' object has no attribute 'form' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C2, a.omega0.form)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lfor)[?7h[?12l[?25h[?25l[?7lfo)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: superelliptic_function(C2, a.omega0.h1) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) - 705 try: ---> 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) - 682 def resolve_fractions(x, y): ---> 683 xn = x.numerator() - 684 xd = x.denominator() - -AttributeError: 'superelliptic_function' object has no attribute 'numerator' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [37], in () -----> 1 superelliptic_function(C2, a.omega0.h1) - -File :14, in __init__(self, C, g) - -File :216, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 159 print(type(C), C) - 160 print(type(C._element_constructor), C._element_constructor) ---> 161 raise - 162 - 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) - 706 x, y = resolve_fractions(x0, y0) - 707 except (AttributeError, TypeError): ---> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( - 709 x0, y0, self)) - 710 try: - 711 return self._element_class(self, x, y, coerce=coerce) - -TypeError: cannot convert (x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C2, a.omega0.h1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: superelliptic_function(C2, a.omega0.h1.function) -[?7h[?12l[?25h[?2004l[?7h(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: C2.polynomial -[?7h[?12l[?25h[?2004l[?7hx^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: - z^3 - z = x -x*z0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C2, a.omega0.h1.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lform)[?7h[?12l[?25h[?25l[?7la.omega0.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lAC2.de_rham_bass()[?7h[?12l[?25h[?25l[?7lade_rham_witt_lft(A[2])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.r()[?7h[?12l[?25h[?25l[?7leduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: A = C2.de_rham_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C2, a.omega0.h1.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lform)[?7h[?12l[?25h[?25l[?7la.omega0.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(A[2]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lAC2.de_rham_bass()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C2, a.omega0.h1.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lform)[?7h[?12l[?25h[?25l[?7la.omega0.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a) -[?7h[?12l[?25h[?2004l[?7h((y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), - ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, - (x^15*y*z0^2 + x^15*y*z0 + x^14*y*z0^2 - x^15*y - x^13*y*z0^2 - x^13*y*z0 + x^12*y*z0^2 + x^13*y + x^11*y*z0^2 + x^12*y + x^11*y*z0 + x^10*y*z0^2 + x^10*y*z0 - x^9*y*z0^2 + x^10*y - x^9*y*z0 - x^9*y - x^8*y*z0 + x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^6*y + x^4*y - x^2*y*z0^2 + x^3*y + x^2*y*z0 - x*y*z0^2 - x*y - y*z0)/(x^7*z0 - x^6*z0^2 + x^6*z0 - x^5*z0^2 + x^6 + x^5*z0 - x^4*z0^2 + x^5 - x^4*z0 + x^3*z0^2 + x^4 + x^3*z0 - x^2*z0^2 - x^3 + x^2 + x*z0 - z0^2 + 1)), - (0, (-x*y*z0 - y)/(x*z0^2 + x + z0)), - (y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), - ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, - (x^17*y*z0 + x^16*y*z0^2 + x^17*y - x^15*y*z0 - x^14*y*z0^2 - x^13*y*z0^2 + x^13*y*z0 - x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^12*y - x^11*y*z0 + x^10*y*z0^2 + x^11*y - x^9*y*z0^2 - x^9*y*z0 + x^9*y + x^8*y*z0 - x^7*y*z0^2 + x^8*y - x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^5*y*z0^2 + x^5*y*z0 + x^4*y*z0^2 - x^4*y*z0 - x^3*y*z0^2 - x^4*y + x^2*y*z0^2 + x^3*y - x^2*y*z0 + y*z0^2 + y)/(x^9 + x^8*z0 + x^8 + x^7*z0 + x^7 + x^6*z0 - x^6 - x^5*z0 + x^5 + x^4*z0 + x^3 + x^2*z0))) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.omega0.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: a.omega0 -[?7h[?12l[?25h[?2004l[?7h[(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7l.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: a.omega0.h1 -[?7h[?12l[?25h[?2004l[?7h(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.h1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lra.omega0[?7h[?12l[?25h[?25l[?7lea.omega0[?7h[?12l[?25h[?25l[?7lda.omega0[?7h[?12l[?25h[?25l[?7lua.omega0[?7h[?12l[?25h[?25l[?7lca.omega0[?7h[?12l[?25h[?25l[?7lea.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lra.omega0[?7h[?12l[?25h[?25l[?7lea.omega0[?7h[?12l[?25h[?25l[?7lda.omega0[?7h[?12l[?25h[?25l[?7lua.omega0[?7h[?12l[?25h[?25l[?7lca.omega0[?7h[?12l[?25h[?25l[?7lta.omega0[?7h[?12l[?25h[?25l[?7lia.omega0[?7h[?12l[?25h[?25l[?7loa.omega0[?7h[?12l[?25h[?25l[?7lna.omega0[?7h[?12l[?25h[?25l[?7lCa.omega0[?7h[?12l[?25h[?25l[?7l2a.omega0[?7h[?12l[?25h[?25l[?7l,a.omega0[?7h[?12l[?25h[?25l[?7l a.omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C2, a.omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lya.omega0.h1)[?7h[?12l[?25h[?25l[?7l^a.omega0.h1)[?7h[?12l[?25h[?25l[?7l2a.omega0.h1)[?7h[?12l[?25h[?25l[?7l*a.omega0.h1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: reduction(C2, y^2*a.omega0.h1)/y^2 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [47], in () -----> 1 reduction(C2, y**Integer(2)*a.omega0.h1)/y**Integer(2) - -NameError: name 'y' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,> = Poi[?7h[?12l[?25h[?25l[?7l > = Poi[?7h[?12l[?25h[?25l[?7ly> = Poi[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7llRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lsage: Rxy. = PolynomialRing(GF(3), 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lreduction(C2, y^2*a.omega0.h1)/y^2[?7h[?12l[?25h[?25l[?7lsage: reduction(C2, y^2*a.omega0.h1)/y^2 -[?7h[?12l[?25h[?2004l[?7hx^2/y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a) -[?7h[?12l[?25h[?2004l[?7h((y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), - ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, - (x^15*y*z0^2 + x^15*y*z0 + x^14*y*z0^2 - x^15*y - x^13*y*z0^2 - x^13*y*z0 + x^12*y*z0^2 + x^13*y + x^11*y*z0^2 + x^12*y + x^11*y*z0 + x^10*y*z0^2 + x^10*y*z0 - x^9*y*z0^2 + x^10*y - x^9*y*z0 - x^9*y - x^8*y*z0 + x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^6*y + x^4*y - x^2*y*z0^2 + x^3*y + x^2*y*z0 - x*y*z0^2 - x*y - y*z0)/(x^7*z0 - x^6*z0^2 + x^6*z0 - x^5*z0^2 + x^6 + x^5*z0 - x^4*z0^2 + x^5 - x^4*z0 + x^3*z0^2 + x^4 + x^3*z0 - x^2*z0^2 - x^3 + x^2 + x*z0 - z0^2 + 1)), - (0, (-x*y*z0 - y)/(x*z0^2 + x + z0)), - (y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), - ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, - (x^17*y*z0 + x^16*y*z0^2 + x^17*y - x^15*y*z0 - x^14*y*z0^2 - x^13*y*z0^2 + x^13*y*z0 - x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^12*y - x^11*y*z0 + x^10*y*z0^2 + x^11*y - x^9*y*z0^2 - x^9*y*z0 + x^9*y + x^8*y*z0 - x^7*y*z0^2 + x^8*y - x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^5*y*z0^2 + x^5*y*z0 + x^4*y*z0^2 - x^4*y*z0 - x^3*y*z0^2 - x^4*y + x^2*y*z0^2 + x^3*y - x^2*y*z0 + y*z0^2 + y)/(x^9 + x^8*z0 + x^8 + x^7*z0 + x^7 + x^6*z0 - x^6 - x^5*z0 + x^5 + x^4*z0 + x^3 + x^2*z0))) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a).omega0 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [51], in () -----> 1 convert_super_fct_into_AS(a).omega0 - -AttributeError: 'tuple' object has no attribute 'omega0' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a).omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.h1[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: a[1] -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [53], in () -----> 1 a[Integer(1)] - -TypeError: 'superelliptic_drw_cech' object is not subscriptable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a).omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a)[1] -[?7h[?12l[?25h[?2004l[?7h(0, (-x*y*z0 - y)/(x*z0^2 + x + z0)) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a)[0] -[?7h[?12l[?25h[?2004l[?7h(y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), - ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, - (x^15*y*z0^2 + x^15*y*z0 + x^14*y*z0^2 - x^15*y - x^13*y*z0^2 - x^13*y*z0 + x^12*y*z0^2 + x^13*y + x^11*y*z0^2 + x^12*y + x^11*y*z0 + x^10*y*z0^2 + x^10*y*z0 - x^9*y*z0^2 + x^10*y - x^9*y*z0 - x^9*y - x^8*y*z0 + x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^6*y + x^4*y - x^2*y*z0^2 + x^3*y + x^2*y*z0 - x*y*z0^2 - x*y - y*z0)/(x^7*z0 - x^6*z0^2 + x^6*z0 - x^5*z0^2 + x^6 + x^5*z0 - x^4*z0^2 + x^5 - x^4*z0 + x^3*z0^2 + x^4 + x^3*z0 - x^2*z0^2 - x^3 + x^2 + x*z0 - z0^2 + 1)) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[0][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a)[0][1] -[?7h[?12l[?25h[?2004l[?7h((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a.omega0 - mult_by_p(C.x*C.y.diffn())[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 3*a -[?7h[?12l[?25h[?2004l[?7h(V((x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx), [0], V((x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx)) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l3*a).reduce()[?7h[?12l[?25h[?25l[?7l3.[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*a).reduce()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: (3*a).omega0 -[?7h[?12l[?25h[?2004l[?7hV((x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: (3*a).omega0.omega -[?7h[?12l[?25h[?2004l[?7h(x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).omega0.omega[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (3*a).omega0.omega.reduce2() -[?7h[?12l[?25h[?2004l[?7h(x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).omega0.omega.reduce2()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: C2.polynomial -[?7h[?12l[?25h[?2004l[?7hx^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[1][?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.omega0.h1[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmega0.h1[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lga0.h1[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: a.omega0 -[?7h[?12l[?25h[?2004l[?7h[(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7l.h1[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: a.omega0.frobenius -[?7h[?12l[?25h[?2004l[?7h -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.frobenius[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.omega0.frobenius() -[?7h[?12l[?25h[?2004l[?7h((x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7)/(x^9*y - x^6*y - x^4*y - x^3*y - x^2*y + y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).omega0.omega.reduce2()[?7h[?12l[?25h[?25l[?7lx^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lsage: (x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(x^9*y - x^6*y - x^4*y - x^3*y - x^2*y + y -....: [?7h[?12l[?25h[?25l[?7l( -)[?7h[?12l[?25h[?25l[?7lsage: (x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(x^9*y - x^6*y - x^4*y - x^3*y - x^2*y + y -....: ) -[?7h[?12l[?25h[?2004l[?7h(0, - x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(x^9*y - x^6*y - x^4*y - x^3*y - x^2*y + y -....: )[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l( -)[?7h[?12l[?25h[?25l[?7l ( -)[?7h[?12l[?25h[?25l[?7l) -[?7h[?12l[?25h[?25l[?7l 1 -)[?7h[?12l[?25h[?25l[?7l( -)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + 1 ) -[?7h[?12l[?25h[?25l[?7l + 1)  - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^2 + 1)[?7h[?12l[?25h[?25l[?7l - x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^4 - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l - x^4 - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^6 - x^4 - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l - x^6 - x^4 - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(x^9 - x^6 - x^4 - x^3 - x^2 + 1) -[?7h[?12l[?25h[?2004l[?7h(x^36 - x^34 - x^33 - x^32 - x^30 - x^29 - x^28 - x^27 + x^26 - x^25 - x^24 - x^22 - x^18 + x^17 - x^15 + x^14 + x^13 + x^12 - x^11 - x^10 + x^7 - x^6 + x^2 + x, - -x^7 - x^6 - x^5 - x^4 + x^3 - x^2 - x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(x^9 - x^6 - x^4 - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(C2.polynomial) -[?7h[?12l[?25h[?2004l[?7h(x^33 - x^30 - x^29 - x^28 + x^27 + x^26 + x^23 - x^22 - x^20 - x^19 - x^18 - x^17 - x^16 + x^15 + x^13 - x^12 - x^11 - x^8 - x^7 - x^6 - x^5 + x^3 + x, - -x^11 + x^10 + x^8 + x^7 - x^5 - x^4 + x^2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^3 + x^32 + x^30 + x^28 + x^26 + x^2 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^1 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^3 + x^32 + x^30 + x^28 + x^26 + x^2 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^1 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^3 + x^32 + x^30 + x^28 + x^26 + x^2 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^1 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7)).quo_rem(C2.polynomial) -[?7h[?12l[?25h[?2004l[?7h(x^34 - x^31 - x^30 - x^29 + x^28 + x^27 + x^24 - x^23 - x^21 - x^20 - x^19 - x^18 - x^17 + x^16 + x^14 - x^13 - x^12 - x^9 - x^8 - x^7 - x^6 + x^4 + x^2 - 1, - x^11 - x^10 + x^8 + x^6 - x^5 + x^4 - x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: C2.polynomial -[?7h[?12l[?25h[?2004l[?7hx^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7)).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^3 + x^32 + x^30 + x^28 + x^26 + x^2 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^1 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l2*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^3 + x^32 + x^30 + x^28 + x^26 + x^2 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^1 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^2*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7)).quo_rem(C2.polynomial) -[?7h[?12l[?25h[?2004l[?7h(x^35 - x^32 - x^31 - x^30 + x^29 + x^28 + x^25 - x^24 - x^22 - x^21 - x^20 - x^19 - x^18 + x^17 + x^15 - x^14 - x^13 - x^10 - x^9 - x^8 - x^7 + x^5 + x^3 - x + 1, - -x^11 + x^10 - x^9 + x^7 + x^5 - x^4 + x^3 - x^2 + x) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.frobenius()[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.omega0.frobenius()[?7h[?12l[?25h[?25l[?7lfrobenius()[?7h[?12l[?25h[?25l[?7lsage: a.f -[?7h[?12l[?25h[?2004l[?7hV(((2*x^4 + x^2 + 2)/x^5)*y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[0][1][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lvert_super_fct_into_AS(a)[0][1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a.f) -[?7h[?12l[?25h[?2004l[?7h(0, (-x*y*z0 - y)/(x*z0^2 + x + z0)) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1 -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.polynomial[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7llline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: A -[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), - ((x/y) dx, 0, (x/y) dx), - ((x^2/y) dx, 0, (x^2/y) dx), - ((x^3/y) dx, 0, (x^3/y) dx), - ((x^4/y) dx, 0, (x^4/y) dx), - (((x^10 + x^8 - x^7 - x^4 - x^2 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx), - (((-x^9 + x^6 + x^3 + 1)/y) dx, 2/x^2*y, 0 dx), - (((-x^6 + 1)/y) dx, 2/x^3*y, (1/(x^3*y)) dx), - (((x^7 + x^5 - x^4 - x)/y) dx, 2/x^4*y, ((x^3 + x^2 - 1)/(x^4*y)) dx), - (((-x^6 + x^3 + 1)/y) dx, 2/x^5*y, ((-1)/(x^3*y)) dx)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.polynomial[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: C1.de - C1.de_rham_basis C1.degrees_de_rham1  - C1.degrees_de_rham0 C1.degrees_holomorphic_differentials - - - [?7h[?12l[?25h[?25l[?7l_rham_basis - C1.de_rham_basis  - - [?7h[?12l[?25h[?25l[?7l - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), (((-x^2 - x)/y) dx, 2/x*y, (1/(x*y)) dx)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7leC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l_C1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lrC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lhC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7laC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lmC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l_C1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lwC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7liC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7ltC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7ltC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l_C1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7llC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7liC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lfC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7ltC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l)C1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l(C1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(C1.de_rham_basis()[0]) -[?7h[?12l[?25h[?2004l[?7h([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCde_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l1de_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lde_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lrde_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lwde_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C1drw = de_rham_witt_lift(C1.de_rham_basis()[0]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1drw = de_rham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldrw.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: C1drw.f -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1drw.f[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lpolynoial[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.p_rank() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [82], in () -----> 1 C1.p_rank() - -File :176, in p_rank(self) - -File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1889, in HyperellipticCurve_finite_field.p_rank(self) - 1855 r""" - 1856 INPUT: - 1857 - (...) - 1880  0 - 1881 """ - 1882 #We use caching here since Hasse Witt is needed to compute p_rank. So if the Hasse Witt - 1883 #is already computed it is stored in list A. If it was not cached (i.e. A is empty), we simply - 1884 #compute it. If it is cached then we need to make sure that we have the correct one. So check - (...) - 1887 # However, it seems a waste of time to manually analyse the cache - 1888 # -- See Trac Ticket #11115 --> 1889 N, E = self._Hasse_Witt_cached() - 1890 if E != self: - 1891 self._Hasse_Witt_cached.clear_cache() - -File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__() - 2297 if self.cache is None: - 2298 f = self.f --> 2299 self.cache = f(self._instance) - 2300 return self.cache - 2301 - -File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1727, in HyperellipticCurve_finite_field._Hasse_Witt_cached(self) - 1647 r""" - 1648 This is where Hasse_Witt is actually computed. - 1649 - (...) - 1712  0 - 1713 """ - 1714 # If Cartier Matrix is already cached for this curve, use that or evaluate it to get M, - 1715 #Coeffs, genus, Fq=base field of self, p=char(Fq). This is so we have one less matrix to - 1716 #compute. - (...) - 1725 #that don't accept arguments. Anyway, the easiest is to call - 1726 #the cached method and simply see whether the data belong to self. --> 1727 M, Coeffs, g, Fq, p, E = self._Cartier_matrix_cached() - 1728 if E != self: - 1729 self._Cartier_matrix_cached.clear_cache() - -File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__() - 2297 if self.cache is None: - 2298 f = self.f --> 2299 self.cache = f(self._instance) - 2300 return self.cache - 2301 - -File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1523, in HyperellipticCurve_finite_field._Cartier_matrix_cached(self) - 1521 #this implementation is for odd degree only, even degree will be handled later. - 1522 if d%2 == 0: --> 1523 raise ValueError("In this implementation the degree of f must be odd") - 1524 #Compute resultant to make sure no repeated roots - 1525 df=f.derivative() - -ValueError: In this implementation the degree of f must be odd -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.p_rank()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.p_rank()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1drw.f[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lde_ham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lC1dw = de_rham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lw.f[?7h[?12l[?25h[?25l[?7lsage: C1drw -[?7h[?12l[?25h[?2004l[?7h([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.f[?7h[?12l[?25h[?25l[?7lsage: a -[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.f[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: a.f -[?7h[?12l[?25h[?2004l[?7hV(((2*x^4 + x^2 + 2)/x^5)*y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [1], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :6, in  - -NameError: name 'C' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lIncrease precision. -Increase precision. ---------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [2], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :389, in de_rham_basis(self, threshold) - -File :342, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :342, in (.0) - -File :109, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :109, in (.0) - -File :102, in residue(self, place) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:618, in sage.rings.laurent_series_ring_element.LaurentSeries.residue() - 616 Integer Ring - 617 """ ---> 618 return self[-1] - 619 - 620 def exponents(self): - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() - 542 return type(self)(self._parent, f, self.__n) - 543 ---> 544 return self.__u[i - self.__n] - 545 - 546 def __iter__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() - 451 return self.base_ring().zero() - 452 else: ---> 453 raise IndexError("coefficient not known") - 454 return self.__f[n] - 455 - -IndexError: coefficient not known -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^3 -z1^2 - z1 = x^5 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[0]/AS.x[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x)/expansion_at_infty() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [5], in () -----> 1 (AS.z[Integer(1)]/AS.x)/expansion_at_infty() - -NameError: name 'expansion_at_infty' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x)/expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-3 + t^-2 + t + t^2 + t^3 + t^4 + t^6 + t^7 + t^8 + t^9 + t^12 + t^13 + t^14 + t^15 + t^16 + t^17 + t^19 + t^21 + t^22 + t^24 + t^26 + t^27 + t^28 + t^29 + t^30 + t^35 + t^36 + t^41 + t^43 + t^44 + t^47 + t^49 + t^50 + t^51 + t^55 + t^57 + t^58 + t^59 + t^63 + t^64 + t^65 + t^66 + t^67 + t^70 + t^73 + t^76 + t^77 + t^79 + t^83 + t^86 + t^88 + t^89 + t^91 + O(t^94) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l^).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x^2).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-2 + t + t^2 + t^4 + t^5 + t^8 + t^9 + t^12 + t^13 + t^14 + t^16 + t^17 + t^19 + t^20 + t^22 + t^24 + t^25 + t^26 + t^27 + t^29 + t^30 + t^32 + t^33 + t^36 + t^38 + t^40 + t^41 + t^45 + t^47 + t^54 + t^56 + t^57 + t^58 + t^61 + t^65 + t^68 + t^70 + t^75 + t^76 + t^77 + t^81 + t^82 + t^86 + t^89 + t^91 + t^94 + t^96 + t^97 + O(t^98) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x^3).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^2 + t^5 + t^6 + t^9 + t^10 + t^11 + t^12 + t^15 + t^16 + t^20 + t^21 + t^25 + t^26 + t^27 + t^28 + t^29 + t^30 + t^31 + t^32 + t^34 + t^37 + t^39 + t^41 + t^43 + t^44 + t^46 + t^47 + t^49 + t^50 + t^53 + t^54 + t^56 + t^58 + t^59 + t^61 + t^63 + t^64 + t^67 + t^72 + t^75 + t^76 + t^78 + t^79 + t^80 + t^82 + t^83 + t^87 + t^88 + t^89 + t^93 + t^94 + t^99 + t^100 + t^101 + O(t^102) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^3 -z1^2 - z1 = x^5 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]/AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l0]/AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]/AS.x).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-2 + t^2 + t^5 + t^8 + t^9 + t^10 + t^16 + t^17 + t^19 + t^20 + t^22 + t^24 + t^29 + t^30 + t^33 + t^36 + t^37 + t^38 + t^41 + t^43 + t^44 + t^45 + t^46 + t^47 + t^51 + t^52 + t^53 + t^57 + t^58 + t^60 + t^61 + t^64 + t^65 + t^67 + t^72 + t^75 + t^79 + t^89 + t^90 + t^92 + t^94 + t^95 + t^96 + t^97 + O(t^98) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l(AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l^).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]/(AS.x)^2).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + t^8 + t^9 + t^10 + t^12 + t^13 + t^16 + t^17 + t^18 + t^22 + t^24 + t^25 + t^26 + t^27 + t^29 + t^32 + t^38 + t^40 + t^41 + t^43 + t^44 + t^45 + t^52 + t^54 + t^58 + t^60 + t^62 + t^66 + t^69 + t^70 + t^73 + t^77 + t^80 + t^81 + t^83 + t^84 + t^86 + t^90 + t^91 + t^92 + t^94 + t^96 + t^101 + O(t^102) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[0]/AS.x[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^3 -z1^2 - z1 = x^5 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim() -[?7h[?12l[?25h[?2004l[?7h13 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x^3*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^7) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^7*z0 + x*z1) * dx, z0*z1/x ), ( (x^6) * dx, z1/x^2 ), ( (x^6*z0 + z1) * dx, z0*z1/x^2 ), ( (x^5) * dx, z1/x^3 ), ( (x^5*z0) * dx, z0*z1/x^3 ), ( (x^4*z0) * dx, z0*z1/x^4 ), ( (x^3*z0) * dx, z0*z1/x^5 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x^5*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^4*z0) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^11) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^11*z0 + x*z1) * dx, z0*z1/x ), ( (x^10) * dx, z1/x^2 ), ( (x^10*z0 + z1) * dx, z0*z1/x^2 ), ( (x^9) * dx, z1/x^3 ), ( (x^9*z0) * dx, z0*z1/x^3 ), ( (x^8) * dx, z1/x^4 ), ( (x^8*z0) * dx, z0*z1/x^4 ), ( (x^7) * dx, z1/x^5 ), ( (x^7*z0) * dx, z0*z1/x^5 ), ( (x^6*z0) * dx, z0*z1/x^6 ), ( (x^5*z0) * dx, z0*z1/x^7 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^2) * dx, z0/x^2 ), ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), ( (x^2*z0 + z1) * dx, z0*z1/x^4 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^5 -z1^2 - z1 = x^7 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^5*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^4*z0) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^11) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ), ( (x^10) * dx, z1/x^2 ), ( (x^2) * dx, z0/x^2 ), ( (x^10*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x^9) * dx, z1/x^3 ), ( (x^9*z0 + x^5*z0) * dx, z0*z1/x^3 ), ( (x^8) * dx, z1/x^4 ), ( (x^8*z0 + z1) * dx, z0*z1/x^4 ), ( (x^7) * dx, z1/x^5 ), ( (x^7*z0) * dx, z0*z1/x^5 ), ( (x^6*z0) * dx, z0*z1/x^6 ), ( (x^5*z0) * dx, z0*z1/x^7 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le_ring[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS. - AS.a_number AS.cartier_matrix AS.dx AS.fct_field AS.height  - AS.at_most_poles AS.characteristic AS.dx_series AS.functions AS.holomorphic_differentials_basis  - AS.at_most_poles_forms AS.cohomology_of_structure_sheaf_basis AS.exponent_of_different AS.genus AS.ith_ramification_gp > - AS.base_ring AS.de_rham_basis AS.exponent_of_different_prim AS.group AS.jumps  - [?7h[?12l[?25h[?25l[?7la_number - AS.a_number  - - - - [?7h[?12l[?25h[?25l[?7lcartier_matrix - AS.a_number  AS.cartier_matrix [?7h[?12l[?25h[?25l[?7ldx - AS.cartier_matrix  AS.dx [?7h[?12l[?25h[?25l[?7lcartier_matrix - AS.cartier_matrix  AS.dx [?7h[?12l[?25h[?25l[?7lharacteristc - AS.cartier_matrix  - AS.characteristic [?7h[?12l[?25h[?25l[?7lohomology_of_structure_sheaf_basis - - AS.characteristic  - AS.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l - - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis() -[?7h[?12l[?25h[?2004l[?7h[z1/x, - z0/x, - z0*z1/x, - z1/x^2, - z0/x^2, - z0*z1/x^2, - z1/x^3, - z0*z1/x^3, - z1/x^4, - z0*z1/x^4, - z1/x^5, - z0*z1/x^5, - z0*z1/x^6, - z0*z1/x^7] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^5 -z1^2 - z1 = x^13 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^6*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^4*z0) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^5*z0) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^7) * dx, 0 ), ( (x^13) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^13*z0 + x^8 + x^3*z1) * dx, z0*z1/x ), ( (x^12) * dx, z1/x^2 ), ( (x^2) * dx, z0/x^2 ), ( (x^12*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x^11) * dx, z1/x^3 ), ( (x^11*z0 + x^6*z0) * dx, z0*z1/x^3 ), ( (x^10) * dx, z1/x^4 ), ( (x^10*z0 + z1) * dx, z0*z1/x^4 ), ( (x^9) * dx, z1/x^5 ), ( (x^9*z0) * dx, z0*z1/x^5 ), ( (x^8) * dx, z1/x^6 ), ( (x^8*z0) * dx, z0*z1/x^6 ), ( (x^7*z0) * dx, z0*z1/x^7 ), ( (x^6*z0) * dx, z0*z1/x^8 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis() -[?7h[?12l[?25h[?2004l[?7h[z1/x, - z0/x, - z0*z1/x, - z1/x^2, - z0/x^2, - z0*z1/x^2, - z1/x^3, - z0*z1/x^3, - z1/x^4, - z0*z1/x^4, - z1/x^5, - z0*z1/x^5, - z1/x^6, - z0*z1/x^6, - z0*z1/x^7, - z0*z1/x^8] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [25], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :316, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :145, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [26], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :316, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :145, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [27], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :316, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :145, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^7 -z1^2 - z1 = x^11 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^3 -z1^2 - z1 = x^11 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^3 -z1^2 - z1 = x^11 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z1/x^5, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^3 -z1^2 - z1 = x^13 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/2 in QQ[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: 13 -1 + 1 -[?7h[?12l[?25h[?2004l[?7h13 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lnu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h13 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z1/x^5, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h14 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l13 -1 + 1[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^7 -z1^2 - z1 = x^11 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lnus()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h13 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7, z0*z1/x^8] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^7 -z1^2 - z1 = x^13 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h15 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [45], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :316, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :145, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h17 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [47], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :316, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :145, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z0/x^4, z0*z1/x^4, z0/x^5, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7, z0*z1/x^8, z0*z1/x^9] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z1/x^5, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7, z0*z1/x^8] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h15 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l\[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0*z1/x, z0*z1/x^2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in z2 of size 2^2 with the equations: -z0^2 - z0 = x^3 -z1^2 - z1 = z2*x^3 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ s - age -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0*z1/x, z0*z1/x^2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0*z1/x^2, z0*z1/x^3] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z0*z1/x^4, z0*z1/x^5] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z1/x^5, z0*z1/x^5, z1/x^6, z0*z1/x^6, z0*z1/x^7, z0*z1/x^8, z0*z1/x^9] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z0/x^3, z0*z1/x^3, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] -False -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] -z0/x^4 False -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] -z1/x^4 False -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] -z1/x^4 False -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].coordinates(basis = b)[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lti[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: bbb[0].function -[?7h[?12l[?25h[?2004l[?7hz1/x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].function.exponents() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [7], in () -----> 1 bbb[Integer(0)].function.exponents() - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement' object has no attribute 'exponents' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function.exponents()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldb[0].function.exponents()[?7h[?12l[?25h[?25l[?7leb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lnb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lob[0].function.exponents()[?7h[?12l[?25h[?25l[?7lmb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lib[0].function.exponents()[?7h[?12l[?25h[?25l[?7lnb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lab[0].function.exponents()[?7h[?12l[?25h[?25l[?7ltb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lob[0].function.exponents()[?7h[?12l[?25h[?25l[?7lrb[0].function.exponents()[?7h[?12l[?25h[?25l[?7l(b[0].function.exponents()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lbbb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lbbb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lb[0].function.exponents()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldexponents()[?7h[?12l[?25h[?25l[?7lexponents()[?7h[?12l[?25h[?25l[?7lnexponents()[?7h[?12l[?25h[?25l[?7loexponents()[?7h[?12l[?25h[?25l[?7lmexponents()[?7h[?12l[?25h[?25l[?7liexponents()[?7h[?12l[?25h[?25l[?7lnexponents()[?7h[?12l[?25h[?25l[?7laexponents()[?7h[?12l[?25h[?25l[?7ltexponents()[?7h[?12l[?25h[?25l[?7loexponents()[?7h[?12l[?25h[?25l[?7lrexponents()[?7h[?12l[?25h[?25l[?7l(exponents()[?7h[?12l[?25h[?25l[?7l()exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l exponents()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].function.denominator(). exponents() -[?7h[?12l[?25h[?2004l[?7h[(1, 0, 0, 0)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function.denominator(). exponents()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexponents()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: bbb[0].function.denominator().exponents() -[?7h[?12l[?25h[?2004l[?7h[(1, 0, 0, 0)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function.denominator().exponents()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7ln().exponents()[?7h[?12l[?25h[?25l[?7lu().exponents()[?7h[?12l[?25h[?25l[?7lm().exponents()[?7h[?12l[?25h[?25l[?7le().exponents()[?7h[?12l[?25h[?25l[?7lr().exponents()[?7h[?12l[?25h[?25l[?7la().exponents()[?7h[?12l[?25h[?25l[?7lt().exponents()[?7h[?12l[?25h[?25l[?7lo().exponents()[?7h[?12l[?25h[?25l[?7lr().exponents()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].function.numerator().exponents() -[?7h[?12l[?25h[?2004l[?7h[(0, 0, 0, 1)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function.numerator().exponents()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [11] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :28 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :14 - if a.function.numerator().exponents()[_sage_const_3 :] = (_sage_const_1 , _sage_const_1 ): - ^ -SyntaxError: cannot assign to subscript here. Maybe you meant '==' instead of '='? - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lsage: lo -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [12], in () -----> 1 lo - -NameError: name 'lo' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[] -[] -[] -[] -[] -[] -[] -[] -[] -[] -[] -[] -[] -[] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[(0, 0, 0, 1)] -[(0, 0, 1, 0)] -[(0, 0, 1, 1)] -[(0, 0, 0, 1)] -[(0, 0, 1, 0)] -[(0, 0, 1, 1)] -[(0, 0, 0, 1)] -[(0, 0, 1, 0)] -[(0, 0, 1, 1)] -[(0, 0, 0, 1)] -[(0, 0, 1, 1)] -[(0, 0, 1, 1)] -[(0, 0, 1, 1)] -[(0, 0, 1, 1)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [18], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :14, in  - -TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got list) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [19], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :14, in  - -TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [20], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :14, in  - -TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [21] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :28 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :14 - print(a.function.numerator().exponents())[_sage_const_0 ][_sage_const_2 :]) - ^ -SyntaxError: unmatched ')' - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(0, 1) ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [22], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [23], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :14, in  - -TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [24], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :14, in  - -TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lz1/x (0, 0, 0, 1) ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [25], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lz1/x [0, 0, 0, 1] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [26], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :15, in  - -TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [27], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :20, in  - -IndexError: list index out of range -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [28], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :20, in  - -IndexError: list index out of range -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[0, 1] -[1, 0] -[1, 1] -z0*z1/x -[0, 1] -[1, 0] -[1, 1] -z0*z1/x^2 -[0, 1] -[1, 0] -[1, 1] -z0*z1/x^3 -[0, 1] -[1, 1] -z0*z1/x^4 -[1, 1] -z0*z1/x^5 -[1, 1] -z0*z1/x^6 -[1, 1] -z0*z1/x^7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [30], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :27, in  - -TypeError: 'int' object is not iterable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: z0z1 -[?7h[?12l[?25h[?2004l[?7h[] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[0, 0, 0, 1] [1, 0, 0, 0] ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [32], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -TypeError: 'int' object is not iterable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l7 3 4 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 11 9 -7 3 4 -4 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 11 5 -6 4 2 -2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 11 5 -6 4 2 -8 ? 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 11 3 -6 4 1 -8 ? 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 11 1 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [38], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :30, in  - -ValueError: max() arg is an empty sequence -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lz0z1[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 11 1 -5 5 0 -8 ? 0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 11 1 -5 5 0 -8 ? 0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l2.sage')[?7h[?12l[?25h[?25l[?7lg.sage')[?7h[?12l[?25h[?25l[?7lp.sage')[?7h[?12l[?25h[?25l[?7lc.sage')[?7h[?12l[?25h[?25l[?7lo.sage')[?7h[?12l[?25h[?25l[?7lv.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [2], in () -----> 1 load('drafty/2gpcovers.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :36, in __init__(self, C, list_of_fcts, prec) - -File :135, in expansion_at_infty(self, place, prec) - -TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [3], in () -----> 1 load('drafty/2gpcovers.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :36, in __init__(self, C, list_of_fcts, prec) - -File :135, in expansion_at_infty(self, place, prec) - -TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1drw[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^3 = x^3 + 1 over Finite Field of size 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.polynomial[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^11 -z1^2 - z1 = x - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [7], in () -----> 1 load('drafty/2gpcovers.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :36, in __init__(self, C, list_of_fcts, prec) - -File :135, in expansion_at_infty(self, place, prec) - -TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx.function[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9C.x)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x)^2[?7h[?12l[?25h[?25l[?7l(C.x)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x)^2 -[?7h[?12l[?25h[?2004l[?7hx^2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [9], in () -----> 1 load('drafty/2gpcovers.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :36, in __init__(self, C, list_of_fcts, prec) - -File :135, in expansion_at_infty(self, place, prec) - -TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [10], in () -----> 1 load('drafty/2gpcovers.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :7, in  - -File :36, in __init__(self, C, list_of_fcts, prec) - -File :135, in expansion_at_infty(self, place, prec) - -TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^3 = x^3 + 1 over Finite Field in a of size 2^2 with the equation: - z^2 - z = x^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: AS.a - AS.a_number  - AS.at_most_poles  - AS.at_most_poles_forms - - [?7h[?12l[?25h[?25l[?7l_number - AS.a_number  - - - [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.a_number() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [13], in () -----> 1 AS.a_number() - -File :313, in a_number(self) - -File :154, in cartier_matrix(self, prec) - -File :140, in holomorphic_differentials_basis(self, threshold) - -File :140, in (.0) - -TypeError: as_form.expansion_at_infty() got an unexpected keyword argument 'place' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.a_number()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la_number()[?7h[?12l[?25h[?25l[?7lsage: AS.a_number() -[?7h[?12l[?25h[?2004l[?7h3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.a_number()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.a_number()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: ASP1. - ASP1.a_number ASP1.cartier_matrix ASP1.dx  - ASP1.at_most_poles ASP1.characteristic ASP1.dx_series  - ASP1.at_most_poles_forms ASP1.cohomology_of_structure_sheaf_basis ASP1.exponent_of_different > - ASP1.base_ring ASP1.de_rham_basis ASP1.exponent_of_different_prim  - [?7h[?12l[?25h[?25l[?7la - - - -[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ASP1.a_number() -[?7h[?12l[?25h[?2004l[?7h3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - [?7h[?12l[?25h[?25l[?7lASP1.a_number()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^3 = x^5 + 1 over Finite Field in a of size 2^2 with the equation: - z^2 - z = x^3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.a_number()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_number()[?7h[?12l[?25h[?25l[?7lsage: AS.a_number() -[?7h[?12l[?25h[?2004l[?7h4 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x^3 + x over Finite Field in a of size 2^2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x^3 + x over Finite Field in a of size 2^2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.a_number()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lnb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: AS.nb_of_pts_at_infty -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lof_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: AS3.nb_of_pts_at_infty -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C . -....: y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: f -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [31], in () -----> 1 f - -NameError: name 'f' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = x^5 - x^4 + 2*x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3+2*x-1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: f = x^3 - x -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^3 - x[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.derivative()(1) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()(1)[?7h[?12l[?25h[?25l[?7l = x^3 - x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f = (x+1)/(x-1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = (x+1)/(x-1)[?7h[?12l[?25h[?25l[?7l.derivative()(1)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.poles() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [35], in () -----> 1 f.poles() - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement_1poly_field' object has no attribute 'poles' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.poles()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lderivative()(1)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.denominator().roots() -[?7h[?12l[?25h[?2004l[?7h[] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.denominator().roots()[?7h[?12l[?25h[?25l[?7lsage: f -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [38] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :29 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :12 - def expansion(fct, (x0, y0)): - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l. = PolynmialRng(GF(3))[?7h[?12l[?25h[?25l[?7l = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(3)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^, 2)[?7h[?12l[?25h[?25l[?7l3, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + x, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lRx. = PoynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l5))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(5)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexcept:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: expan - expand  - expansion - - - [?7h[?12l[?25h[?25l[?7l - -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lx. = PolynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(5)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - - [?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth -[?7h[?12l[?25h[?2004l[?7h -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lC.is_smooth[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^2[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le((C.x)^(-1))[?7h[?12l[?25h[?25l[?7lp((C.x)^(-1))[?7h[?12l[?25h[?25l[?7la((C.x)^(-1))[?7h[?12l[?25h[?25l[?7ln((C.x)^(-1))[?7h[?12l[?25h[?25l[?7l((C.x)^(-1))[?7h[?12l[?25h[?25l[?7l((C.x)^(-1))[?7h[?12l[?25h[?25l[?7l((C.x)^(-1))[?7h[?12l[?25h[?25l[?7lx((C.x)^(-1))[?7h[?12l[?25h[?25l[?7lp((C.x)^(-1))[?7h[?12l[?25h[?25l[?7la((C.x)^(-1))[?7h[?12l[?25h[?25l[?7ln((C.x)^(-1))[?7h[?12l[?25h[?25l[?7ls((C.x)^(-1))[?7h[?12l[?25h[?25l[?7li((C.x)^(-1))[?7h[?12l[?25h[?25l[?7lo((C.x)^(-1))[?7h[?12l[?25h[?25l[?7ln((C.x)^(-1))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: expansion((C.x)^(-1), 0, 1) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -UnboundLocalError Traceback (most recent call last) -Input In [6], in () -----> 1 expansion((C.x)**(-Integer(1)), Integer(0), Integer(1)) - -File :22, in expansion(fct, x0, y0) - -UnboundLocalError: local variable 't' referenced before assignment -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lexpansion((C.x)^(-1), 0, 1)[?7h[?12l[?25h[?25l[?7lC.is_moth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lRx. = PoynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(5)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lexpansion((C.x)^(-1), 0, 1)[?7h[?12l[?25h[?25l[?7lC.is_moth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lRx. = PoynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lexpansion((C.x)^(-1), 0, 1)[?7h[?12l[?25h[?25l[?7lsage: expansion((C.x)^(-1), 0, 1) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [10], in () -----> 1 expansion((C.x)**(-Integer(1)), Integer(0), Integer(1)) - -File :23, in expansion(fct, x0, y0, prec) - -NameError: name 'y' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [12], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :29, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :32, in  - -File :25, in expansion(fct, x0, y0, prec) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:428, in sage.rings.polynomial.polynomial_element.Polynomial.subs() - 426 g = self._parent.gen() - 427 if g in x[0]: ---> 428 return self(x[0][g]) - 429 elif len(x[0]) > 0: - 430 raise TypeError("keys do not match self's parent") - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:870, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() - 868 # This can save lots of coercions when the common parent is the - 869 # polynomial's base ring (e.g., for evaluations at integers). ---> 870 cst, aa = coercion_model.canonical_coercion(cst, a) - 871 # Use fast multiplication actions like matrix × scalar. - 872 # If there is no action, replace a by an element of the - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1393, in sage.structure.coerce.CoercionModel.canonical_coercion() - 1391 self._record_exception() - 1392 --> 1393 raise TypeError("no common canonical parent for objects with parents: '%s' and '%s'"%(xp, yp)) - 1394 - 1395 - -TypeError: no common canonical parent for objects with parents: 'Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5' and 'Laurent Series Ring in t over Finite Field of size 5' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [13], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :29, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :32, in  - -File :25, in expansion(fct, x0, y0, prec) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:428, in sage.rings.polynomial.polynomial_element.Polynomial.subs() - 426 g = self._parent.gen() - 427 if g in x[0]: ---> 428 return self(x[0][g]) - 429 elif len(x[0]) > 0: - 430 raise TypeError("keys do not match self's parent") - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:870, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() - 868 # This can save lots of coercions when the common parent is the - 869 # polynomial's base ring (e.g., for evaluations at integers). ---> 870 cst, aa = coercion_model.canonical_coercion(cst, a) - 871 # Use fast multiplication actions like matrix × scalar. - 872 # If there is no action, replace a by an element of the - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1393, in sage.structure.coerce.CoercionModel.canonical_coercion() - 1391 self._record_exception() - 1392 --> 1393 raise TypeError("no common canonical parent for objects with parents: '%s' and '%s'"%(xp, yp)) - 1394 - 1395 - -TypeError: no common canonical parent for objects with parents: 'Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5' and 'Laurent Series Ring in t over Finite Field of size 5' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -t^-1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -3*t^-3 + 2 + 2*t^3 + 4*t^6 + 3*t^12 + 4*t^15 + 4*t^18 + 3*t^21 + 4*t^27 + 2*t^30 + 2*t^33 + 4*t^36 + O(t^47) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -1 + 4*t + 2*t^2 + 3*t^3 + 4*t^4 + t^5 + 3*t^6 + 2*t^7 + t^8 + 4*t^9 + O(t^10) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l'1 1 -1 + 4*t^2 + 2*t^3 + 2*t^4 + t^5 + 3*t^7 + 2*t^8 + 4*t^9 + t^10 + t^12 + 4*t^14 + 2*t^15 + 2*t^16 + t^17 + 3*t^19 + 2*t^20 + 4*t^21 + t^22 + t^24 + 4*t^26 + 2*t^27 + 2*t^28 + t^29 + 3*t^31 + 2*t^32 + 4*t^33 + t^34 + t^36 + 4*t^38 + 2*t^39 + 2*t^40 + t^41 + 3*t^43 + 2*t^44 + 4*t^45 + t^46 + t^48 + O(t^50) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -t^2 + 4*t^4 + 4*t^6 + 4*t^8 + 4*t^10 + 4*t^12 + 4*t^14 + 4*t^16 + 4*t^18 + 4*t^20 + 4*t^22 + 4*t^24 + 4*t^26 + 4*t^28 + 4*t^30 + 4*t^32 + 4*t^34 + 4*t^36 + 4*t^38 + 4*t^40 + 4*t^42 + 4*t^44 + 4*t^46 + 4*t^48 + 4*t^50 + 4*t^52 + 4*t^54 + 4*t^56 + 4*t^58 + 4*t^60 + 4*t^62 + 4*t^64 + 4*t^66 + 4*t^68 + 4*t^70 + 4*t^72 + 4*t^74 + 4*t^76 + 4*t^78 + 4*t^80 + 4*t^82 + 4*t^84 + 4*t^86 + 4*t^88 + 4*t^90 + 4*t^92 + 4*t^94 + 4*t^96 + 4*t^98 + 4*t^100 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -x_series t + 4*t^2 + 4*t^3 + 4*t^4 + 4*t^5 + 4*t^6 + 4*t^7 + 4*t^8 + 4*t^9 + 4*t^10 + 4*t^11 + 4*t^12 + 4*t^13 + 4*t^14 + 4*t^15 + 4*t^16 + 4*t^17 + 4*t^18 + 4*t^19 + 4*t^20 + 4*t^21 + 4*t^22 + 4*t^23 + 4*t^24 + 4*t^25 + 4*t^26 + 4*t^27 + 4*t^28 + 4*t^29 + 4*t^30 + 4*t^31 + 4*t^32 + 4*t^33 + 4*t^34 + 4*t^35 + 4*t^36 + 4*t^37 + 4*t^38 + 4*t^39 + 4*t^40 + 4*t^41 + 4*t^42 + 4*t^43 + 4*t^44 + 4*t^45 + 4*t^46 + 4*t^47 + 4*t^48 + 4*t^49 + 4*t^50 -t^2 + 4*t^4 + 4*t^6 + 4*t^8 + 4*t^10 + 4*t^12 + 4*t^14 + 4*t^16 + 4*t^18 + 4*t^20 + 4*t^22 + 4*t^24 + 4*t^26 + 4*t^28 + 4*t^30 + 4*t^32 + 4*t^34 + 4*t^36 + 4*t^38 + 4*t^40 + 4*t^42 + 4*t^44 + 4*t^46 + 4*t^48 + 4*t^50 + 4*t^52 + 4*t^54 + 4*t^56 + 4*t^58 + 4*t^60 + 4*t^62 + 4*t^64 + 4*t^66 + 4*t^68 + 4*t^70 + 4*t^72 + 4*t^74 + 4*t^76 + 4*t^78 + 4*t^80 + 4*t^82 + 4*t^84 + 4*t^86 + 4*t^88 + 4*t^90 + 4*t^92 + 4*t^94 + 4*t^96 + 4*t^98 + 4*t^100 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -x_series t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + t^10 + t^11 + t^12 + t^13 + t^14 + t^15 + t^16 + t^17 + t^18 + t^19 + t^20 + t^21 + t^22 + t^23 + t^24 + t^25 + t^26 + t^27 + t^28 + t^29 + t^30 + t^31 + t^32 + t^33 + t^34 + t^35 + t^36 + t^37 + t^38 + t^39 + t^40 + t^41 + t^42 + t^43 + t^44 + t^45 + t^46 + t^47 + t^48 + t^49 + t^50 -4*t^50 + 3*t^52 + 4*t^54 + 2*t^56 + t^58 + 3*t^60 + 4*t^62 + 2*t^64 + t^66 + 3*t^68 + 4*t^70 + 2*t^72 + t^74 + 3*t^76 + 4*t^78 + 2*t^80 + t^82 + 3*t^84 + 4*t^86 + 2*t^88 + t^90 + 3*t^92 + 4*t^94 + 2*t^96 + t^98 + t^100 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -x_series 4*t^50 + 3*t^52 + 4*t^54 + 2*t^56 + t^58 + 3*t^60 + 4*t^62 + 2*t^64 + t^66 + 3*t^68 + 4*t^70 + 2*t^72 + t^74 + 3*t^76 + 4*t^78 + 2*t^80 + t^82 + 3*t^84 + 4*t^86 + 2*t^88 + t^90 + 3*t^92 + 4*t^94 + 2*t^96 + t^98 + t^100 -4*t^50 + 3*t^52 + 4*t^54 + 2*t^56 + t^58 + 3*t^60 + 4*t^62 + 2*t^64 + t^66 + 3*t^68 + 4*t^70 + 2*t^72 + t^74 + 3*t^76 + 4*t^78 + 2*t^80 + t^82 + 3*t^84 + 4*t^86 + 2*t^88 + t^90 + 3*t^92 + 4*t^94 + 2*t^96 + t^98 + t^100 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: f -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [22], in () -----> 1 f - -NameError: name 'f' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -x_series 2 + 4*t^2 + 4*t^4 + t^10 + 4*t^12 + 4*t^14 + 2*t^20 + 3*t^22 + 3*t^24 + 3*t^30 + 2*t^32 + 2*t^34 + 2*t^50 + 3*t^52 + 3*t^54 + 2*t^60 + 3*t^62 + 3*t^64 + 4*t^70 + t^72 + t^74 + t^80 + 4*t^82 + 4*t^84 -2 + 4*t^2 + 4*t^4 + t^10 + 4*t^12 + 4*t^14 + 2*t^20 + 3*t^22 + 3*t^24 + 3*t^30 + 2*t^32 + 2*t^34 + 2*t^50 + 3*t^52 + 3*t^54 + 2*t^60 + 3*t^62 + 3*t^64 + 4*t^70 + t^72 + t^74 + t^80 + 4*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lnbof_ps_at_infty[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty = 3 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty = 3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty -[?7h[?12l[?25h[?2004l[?7h3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -x_series 4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l2.[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le((C.y)^2)[?7h[?12l[?25h[?25l[?7lx((C.y)^2)[?7h[?12l[?25h[?25l[?7lp((C.y)^2)[?7h[?12l[?25h[?25l[?7la((C.y)^2)[?7h[?12l[?25h[?25l[?7ln((C.y)^2)[?7h[?12l[?25h[?25l[?7ls((C.y)^2)[?7h[?12l[?25h[?25l[?7li((C.y)^2)[?7h[?12l[?25h[?25l[?7lo((C.y)^2)[?7h[?12l[?25h[?25l[?7ln((C.y)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: expansion((C.y)^2, -1, 0, prec=100) -[?7h[?12l[?25h[?2004lx_series 4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?7ht^2 + t^250 + 4*t^252 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexpansion((C.y)^2, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lexpansion((C.y)^2, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7lsage: expansion((C.y)^2, -1, 0, prec=100) -[?7h[?12l[?25h[?2004l[?7ht^2 + t^250 + 4*t^252 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexpansion((C.y)^2, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lexpansion((C.y)^2, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lexpansion((C.y)^2, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)^2, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7lx)^2, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l3, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l , -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l+, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l , -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7lC, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l., -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7lo, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7ln, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7le, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: expansion((C.x)^3 + C.one, -1, 0, prec=100) -[?7h[?12l[?25h[?2004l[?7ht^2 + t^250 + 4*t^252 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd .. -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cdgit status -On branch master -Your branch is up to date with 'origin/master'. - -Changes not staged for commit: - (use "git add ..." to update what will be committed) - (use "git restore ..." to discard changes in working directory) - modified: sage/.run.term-0.term - modified: sage/as_covers/as_form_class.sage - modified: sage/drafty/draft.sage - modified: sage/drafty/superelliptic_drw.sage - modified: sage/init.sage - modified: sage/superelliptic/superelliptic_form_class.sage - -Untracked files: - (use "git add ..." to include in what will be committed) - .crystalline_p2.ipynb.sage-jupyter2 - .deRhamComputation.ipynb.sage-jupyter2 - .elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2 - .git.x11-0.term - .superelliptic.ipynb.sage-jupyter2 - .superelliptic_alpha.ipynb.sage-jupyter2 - .superelliptic_arbitrary_field.ipynb.sage-jupyter2 - git.x11 - sage/as_covers/tests/cartier_test.sage - sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2 - sage/drafty/2gpcovers.sage - sage/drafty/as_cartier.sage - sage/drafty/better_trace.sage - sage/drafty/cartier_image_representation.sage - sage/drafty/convert_superelliptic_into_AS.sage - sage/drafty/draft4.sage - sage/drafty/draft5.sage - sage/drafty/draft6.sage - sage/drafty/draft7.sage - sage/drafty/draft8.sage - sage/drafty/draft_klein_covers.sage - sage/drafty/lift_to_de_rham.sage - sage/drafty/pole_numbers.sage - sage/drafty/regular_on_U0.sage - sage/superelliptic/frobenius_kernel.sage - sage/superelliptic/tests/ - superelliptic_arbitrary_field.ipynb - -no changes added to commit (use "git add" and/or "git commit -a") -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gigit add -u -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""p"r"z"e"d" "d"o"d"a"n"i"e"m" "e"k"s"j"a"p"n"c""""""p"a"n"s"j"i" "w" "d"o"w"o"l"n"y"m" "p"u"n"k"c"i"e" -[master b79484b] przed dodaniem ekspansji w dowolnym punkcie - 6 files changed, 3072 insertions(+), 12 deletions(-) -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push -Username for 'https://git.wmi.amu.edu.pl': jgarnek -Password for 'https://jgarnek@git.wmi.amu.edu.pl': -Enumerating objects: 22, done. -Counting objects: 4% (1/22) Counting objects: 9% (2/22) Counting objects: 13% (3/22) Counting objects: 18% (4/22) Counting objects: 22% (5/22) Counting objects: 27% (6/22) Counting objects: 31% (7/22) Counting objects: 36% (8/22) Counting objects: 40% (9/22) Counting objects: 45% (10/22) Counting objects: 50% (11/22) Counting objects: 54% (12/22) Counting objects: 59% (13/22) Counting objects: 63% (14/22) Counting objects: 68% (15/22) Counting objects: 72% (16/22) Counting objects: 77% (17/22) Counting objects: 81% (18/22) Counting objects: 86% (19/22) Counting objects: 90% (20/22) Counting objects: 95% (21/22) Counting objects: 100% (22/22) Counting objects: 100% (22/22), done. -Delta compression using up to 4 threads -Compressing objects: 8% (1/12) Compressing objects: 16% (2/12) Compressing objects: 25% (3/12) Compressing objects: 33% (4/12) Compressing objects: 41% (5/12) Compressing objects: 50% (6/12) Compressing objects: 58% (7/12) Compressing objects: 66% (8/12) Compressing objects: 75% (9/12) Compressing objects: 83% (10/12) Compressing objects: 91% (11/12) Compressing objects: 100% (12/12) Compressing objects: 100% (12/12), done. -Writing objects: 8% (1/12) Writing objects: 16% (2/12) Writing objects: 25% (3/12) Writing objects: 33% (4/12) Writing objects: 41% (5/12) Writing objects: 50% (6/12) Writing objects: 58% (7/12) Writing objects: 66% (8/12) Writing objects: 75% (9/12) Writing objects: 83% (10/12) Writing objects: 91% (11/12) Writing objects: 100% (12/12) Writing objects: 100% (12/12), 24.44 KiB | 287.00 KiB/s, done. -Total 12 (delta 8), reused 0 (delta 0) -remote: . Processing 1 references -remote: Processed 1 references in total -To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git - 7e8546b..b79484b master -> master -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage/ -]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7ldx.valuation()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()>[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: (C.dx).expansion((-1, 0)) -[?7h[?12l[?25h[?2004l[?7h4*t + t^3 + 3*t^11 + 2*t^13 + 2*t^21 + 3*t^23 + t^31 + 4*t^33 + t^51 + 4*t^53 + 2*t^61 + 3*t^63 + 3*t^71 + 2*t^73 + 4*t^81 + t^83 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.dx).expansion((-1, 0))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx).expansion(-1, 0)[?7h[?12l[?25h[?25l[?7lsage: (C.x).expansion((-1, 0)) -[?7h[?12l[?25h[?2004l[?7h4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduction(C2, y^2*a.omega0.h1)/y^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2range(0, 3)[?7h[?12l[?25h[?25l[?7l range(0, 3)[?7h[?12l[?25h[?25l[?7lirange(0, 3)[?7h[?12l[?25h[?25l[?7lnrange(0, 3)[?7h[?12l[?25h[?25l[?7lin range(0, 3)[?7h[?12l[?25h[?25l[?7lsage: 2 in range(0, 3) -[?7h[?12l[?25h[?2004l[?7hTrue -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduction(C2, y^2*a.omega0.h1)/y^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lirange(0, 3)[?7h[?12l[?25h[?25l[?7lsrange(0, 3)[?7h[?12l[?25h[?25l[?7lirange(0, 3)[?7h[?12l[?25h[?25l[?7lnrange(0, 3)[?7h[?12l[?25h[?25l[?7lsrange(0, 3)[?7h[?12l[?25h[?25l[?7ltrange(0, 3)[?7h[?12l[?25h[?25l[?7larange(0, 3)[?7h[?12l[?25h[?25l[?7lnrange(0, 3)[?7h[?12l[?25h[?25l[?7lcrange(0, 3)[?7h[?12l[?25h[?25l[?7lerange(0, 3)[?7h[?12l[?25h[?25l[?7lisinstance(range(0, 3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: isinstance(range(0, 3), list) -[?7h[?12l[?25h[?2004l[?7hFalse -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(range(0, 3), list)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7llis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lisinstanc(range(0, 3))[?7h[?12l[?25h[?25l[?7l(range(0, 3))[?7h[?12l[?25h[?25l[?7l(range(0, 3))[?7h[?12l[?25h[?25l[?7l(range(0, 3))[?7h[?12l[?25h[?25l[?7l(range(0, 3))[?7h[?12l[?25h[?25l[?7l(range(0, 3))[?7h[?12l[?25h[?25l[?7l(range(0, 3))[?7h[?12l[?25h[?25l[?7lis(range(0, 3))[?7h[?12l[?25h[?25l[?7li(range(0, 3))[?7h[?12l[?25h[?25l[?7l(range(0, 3))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll(range(0, 3))[?7h[?12l[?25h[?25l[?7li(range(0, 3))[?7h[?12l[?25h[?25l[?7ls(range(0, 3))[?7h[?12l[?25h[?25l[?7llist(range(0, 3))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: list(range(0, 3)) -[?7h[?12l[?25h[?2004l[?7h[0, 1, 2] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llist(range(0, 3))[?7h[?12l[?25h[?25l[?7load'iit.sage'[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS3.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.x)^3 + (C.x)^5, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7las_cover(C, [(C.x)^3 + (C.x)^5, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l[], prec = 50)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l [], prec = 50)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l(], prec = 50)[?7h[?12l[?25h[?25l[?7l)], prec = 50)[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7lC)], prec = 50)[?7h[?12l[?25h[?25l[?7l.)], prec = 50)[?7h[?12l[?25h[?25l[?7lx)], prec = 50)[?7h[?12l[?25h[?25l[?7l+)], prec = 50)[?7h[?12l[?25h[?25l[?7lC)], prec = 50)[?7h[?12l[?25h[?25l[?7l.)], prec = 50)[?7h[?12l[?25h[?25l[?7lo)], prec = 50)[?7h[?12l[?25h[?25l[?7ln)], prec = 50)[?7h[?12l[?25h[?25l[?7le)], prec = 50)[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l^], prec = 50)[?7h[?12l[?25h[?25l[?7l(], prec = 50)[?7h[?12l[?25h[?25l[?7l)], prec = 50)[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l0)], prec = 50)[?7h[?12l[?25h[?25l[?7l1)], prec = 50)[?7h[?12l[?25h[?25l[?7l)], prec = 50)[?7h[?12l[?25h[?25l[?7l)], prec = 50)[?7h[?12l[?25h[?25l[?7l-)], prec = 50)[?7h[?12l[?25h[?25l[?7l1)], prec = 50)[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(])[?7h[?12l[?25h[?25l[?7l)])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l-)])[?7h[?12l[?25h[?25l[?7l1)])[?7h[?12l[?25h[?25l[?7l,)])[?7h[?12l[?25h[?25l[?7l )])[?7h[?12l[?25h[?25l[?7l9)])[?7h[?12l[?25h[?25l[?7l)])[?7h[?12l[?25h[?25l[?7l0)])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x+C.one)^(-1)], prec = 50, branch_points = [(-1, 0)]) -[?7h[?12l[?25h[?2004lno 0 -th root; divide by 1 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [11], in () -----> 1 AS = as_cover(C, [(C.x+C.one)**(-Integer(1))], prec = Integer(50), branch_points = [(-Integer(1), Integer(0))]) - -File :45, in __init__(self, C, list_of_fcts, branch_points, prec) - -ValueError: not enough values to unpack (expected 4, got 2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l}[?7h[?12l[?25h[?25l[?7l'}[?7h[?12l[?25h[?25l[?7la}[?7h[?12l[?25h[?25l[?7l'}[?7h[?12l[?25h[?25l[?7l:}[?7h[?12l[?25h[?25l[?7l1}[?7h[?12l[?25h[?25l[?7l,}[?7h[?12l[?25h[?25l[?7l }[?7h[?12l[?25h[?25l[?7l2}[?7h[?12l[?25h[?25l[?7l:}[?7h[?12l[?25h[?25l[?7l'}[?7h[?12l[?25h[?25l[?7lb}[?7h[?12l[?25h[?25l[?7l'}[?7h[?12l[?25h[?25l[?7l}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lll = {'a':1, 2:'b'} -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll = {'a':1, 2:'b'}[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: lll['a'] -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll['a'][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l'][?7h[?12l[?25h[?25l[?7lb'][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lll['b'] -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [14], in () -----> 1 lll['b'] - -KeyError: 'b' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll['b'][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lll[2] -[?7h[?12l[?25h[?2004l[?7h'b' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lor a in xi.coordinates():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: for a in lll: -....: [?7h[?12l[?25h[?25l[?7lprint(lift(a))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print(a) -....: [?7h[?12l[?25h[?25l[?7lsage: for a in lll: -....:  print(a) -....:  -[?7h[?12l[?25h[?2004la -2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.f[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll[2][?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l = {'a':1, 2:'b'}[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l}[?7h[?12l[?25h[?25l[?7l'}[?7h[?12l[?25h[?25l[?7lc}[?7h[?12l[?25h[?25l[?7l'}[?7h[?12l[?25h[?25l[?7l:}[?7h[?12l[?25h[?25l[?7l3}[?7h[?12l[?25h[?25l[?7l}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lll + {'c':3} -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [17], in () -----> 1 lll + {'c':Integer(3)} - -TypeError: unsupported operand type(s) for +: 'dict' and 'dict' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll + {'c':3}[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[2][?7h[?12l[?25h[?25l[?7l'b'][?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: lll['c'] = 3 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll['c'] = 3[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: lll -[?7h[?12l[?25h[?2004l[?7h{'a': 1, 2: 'b', 'c': 3} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l['c'] = 3[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: lll['d'] = [1, 2, 3] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll['d'] = [1, 2, 3][?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: lll -[?7h[?12l[?25h[?2004l[?7h{'a': 1, 2: 'b', 'c': 3, 'd': [1, 2, 3]} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lll[?7h[?12l[?25h[?25l[?7l['d'] = [1, 2, 3][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l['c'] = 3[?7h[?12l[?25h[?25l[?7l + {'c':}[?7h[?12l[?25h[?25l[?7lsage: for a in lll: -....:  print(a)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7llll[2] - [?7h[?12l[?25h[?25l[?7l'b'][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = {'a':1, 2:'b'}[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x+C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x+C.one)^(-1)], prec = 50, branch_points = [(-1, 0)]) -[?7h[?12l[?25h[?2004lno 0 -th root; divide by 1 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [23], in () -----> 1 AS = as_cover(C, [(C.x+C.one)**(-Integer(1))], prec = Integer(50), branch_points = [(-Integer(1), Integer(0))]) - -File :45, in __init__(self, C, list_of_fcts, branch_points, prec) - -ValueError: not enough values to unpack (expected 4, got 2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTraceback (most recent call last): - - File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code - exec(code_obj, self.user_global_ns, self.user_ns) - - Input In [24] in  - load('init.sage') - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :7 in  - - File sage/misc/persist.pyx:175 in sage.misc.persist.load - sage.repl.load.load(filename, globals()) - - File /ext/sage/9.7/src/sage/repl/load.py:272 in load - exec(preparse_file(f.read()) + "\n", globals) - - File :26 - if branch_points = []: - ^ -SyntaxError: invalid syntax. Maybe you meant '==' or ':=' instead of '='? - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x+C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x+C.one)^(-1)], prec = 50, branch_points = [(-1, 0)]) -[?7h[?12l[?25h[?2004lno 2 -th root; divide by 3 ---------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -Input In [26], in () -----> 1 AS = as_cover(C, [(C.x+C.one)**(-Integer(1))], prec = Integer(50), branch_points = [(-Integer(1), Integer(0))]) - -File :48, in __init__(self, C, list_of_fcts, branch_points, prec) - -ValueError: not enough values to unpack (expected 4, got 2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x+C.one)^(-1)[?7h[?12l[?25h[?25l[?7lsage: (C.x+C.one)^(-1) -[?7h[?12l[?25h[?2004l[?7h1/(x + 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x+C.one)^(-1)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x+C.one)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[(-1, 0))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x+C.one)^(-1)).expansion(pt=[(-1, 0)]) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [28], in () -----> 1 ((C.x+C.one)**(-Integer(1))).expansion(pt=[(-Integer(1), Integer(0))]) - -File :144, in expansion(self, pt, prec) - -IndexError: list index out of range -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x+C.one)^(-1)).expansion(pt=[(-1, 0)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(-1, 0))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x+C.one)^(-1)).expansion(pt=(-1, 0)) -[?7h[?12l[?25h[?2004l[?7h3*t^-2 + 4 + 2*t^2 + t^4 + t^6 + t^8 + t^12 + 4*t^14 + 4*t^16 + 3*t^18 + 4*t^20 + 3*t^22 + 4*t^28 + 2*t^30 + 4*t^32 + O(t^48) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x+C.one)^(-1)).expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l3C.x+C.one)^(-1).expansion(pt=(-1, 0)[?7h[?12l[?25h[?25l[?7l*C.x+C.one)^(-1).expansion(pt=(-1, 0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3C.one)^(-1).expansion(pt=(-1, 0)[?7h[?12l[?25h[?25l[?7l^C.one)^(-1).expansion(pt=(-1, 0)[?7h[?12l[?25h[?25l[?7lC.one)^(-1).expansion(pt=(-1, 0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x+C.one)^(-1)).expansion(pt=[(-1, 0)])[?7h[?12l[?25h[?25l[?7lC.x+C.one)^(-1)[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x+C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l3C.x+C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l*C.x+C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)]) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [30], in () -----> 1 AS = as_cover(C, [(Integer(3)*C.x+Integer(3)*C.one)**(-Integer(1))], prec = Integer(50), branch_points = [(-Integer(1), Integer(0))]) - -File :78, in __init__(self, C, list_of_fcts, branch_points, prec) - -File :78, in (.0) - -TypeError: tuple indices must be integers or slices, not tuple -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l + {'c':3}[?7h[?12l[?25h[?25l[?7l=a1, 2:'b'}[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7l{'a':1, 2:'b'}[?7h[?12l[?25h[?25l[?7l}[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2:'b'}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,:'b'}[?7h[?12l[?25h[?25l[?7l :'b'}[?7h[?12l[?25h[?25l[?7l1:'b'}[?7h[?12l[?25h[?25l[?7l():'b'}[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lll = {'a':1, (2, 1):'b'} -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll = {'a':1, (2, 1):'b'}[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: lll -[?7h[?12l[?25h[?2004l[?7h{'a': 1, (2, 1): 'b'} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lll[?7h[?12l[?25h[?25l[?7l = {'a':1, (2, 1):'b'}[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 with the equation: - z^5 - z = 2/(x + 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [36], in () -----> 1 AS.genus() - -File :100, in genus(self) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :100, in (.0) - -KeyError: 0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [41], in () -----> 1 AS.holomorphic_differentials_basis() - -File :139, in holomorphic_differentials_basis(self, threshold) - -File :23, in expansion_at_infty(self, place) - -KeyError: 0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [42], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :29, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :10, in  - -File :318, in a_number(self) - -File :159, in cartier_matrix(self, prec) - -File :139, in holomorphic_differentials_basis(self, threshold) - -AttributeError: 'as_form' object has no attribute 'expansion' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7loa[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [43], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :29, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :10, in  - -File :318, in a_number(self) - -File :159, in cartier_matrix(self, prec) - -File :139, in holomorphic_differentials_basis(self, threshold) - -TypeError: as_form.expansion() got an unexpected keyword argument 'prec' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis)[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004lIncrease precision. -[?7h[(1) * dx, - (z0) * dx, - (z0^2) * dx, - (z0^3) * dx, - (z0^4) * dx, - (1/y) * dx, - (z0/y) * dx, - (z0^2/y) * dx, - (z0^3/y) * dx, - (z0^4/y) * dx, - (x) * dx, - (x*z0) * dx, - (x*z0^2) * dx, - (x*z0^3) * dx, - (x*z0^4) * dx, - (x/y) * dx, - (x*z0/y) * dx, - (x*z0^2/y) * dx, - (x*z0^3/y) * dx, - (x*z0^4/y) * dx, - (x^2) * dx, - (x^2*z0) * dx, - (x^2*z0^2) * dx, - (x^2*z0^3) * dx, - (x^2*z0^4) * dx, - (x^2/y) * dx, - (x^2*z0/y) * dx, - (x^2*z0^2/y) * dx, - (x^2*z0^3/y) * dx, - (x^2*z0^4/y) * dx, - (x^3) * dx, - (x^3*z0) * dx, - (x^3*z0^2) * dx, - (x^3*z0^3) * dx, - (x^3*z0^4) * dx, - (x^3/y) * dx, - (x^3*z0/y) * dx, - (x^3*z0^2/y) * dx, - (x^3*z0^3/y) * dx, - (x^3*z0^4/y) * dx, - (x^4) * dx, - (x^4*z0) * dx, - (x^4*z0^2) * dx, - (x^4*z0^3) * dx, - (x^4*z0^4) * dx, - (x^4/y) * dx, - (x^4*z0/y) * dx, - (x^4*z0^2/y) * dx, - (x^4*z0^3/y) * dx, - (x^4*z0^4/y) * dx, - (x^5) * dx, - (x^5*z0) * dx, - (x^5*z0^2) * dx, - (x^5*z0^3) * dx, - (x^5*z0^4) * dx, - (x^5/y) * dx, - (x^5*z0/y) * dx, - (x^5*z0^2/y) * dx, - (x^5*z0^3/y) * dx, - (x^5*z0^4/y) * dx, - (x^6) * dx, - (x^6*z0) * dx, - (x^6*z0^2) * dx, - (x^6*z0^3) * dx, - (x^6*z0^4) * dx, - (x^6/y) * dx, - (x^6*z0/y) * dx, - (x^6*z0^2/y) * dx, - (x^6*z0^3/y) * dx, - (x^6*z0^4/y) * dx, - (x^7) * dx, - (x^7*z0) * dx, - (x^7*z0^2) * dx, - (x^7*z0^3) * dx, - (x^7*z0^4) * dx, - (x^7/y) * dx, - (x^7*z0/y) * dx, - (x^7*z0^2/y) * dx, - (x^7*z0^3/y) * dx, - (x^7*z0^4/y) * dx, - (x^8) * dx, - (x^8*z0) * dx, - (x^8*z0^2) * dx, - (x^8*z0^3) * dx, - (x^8*z0^4) * dx, - (x^8/y) * dx, - (x^8*z0/y) * dx, - (x^8*z0^2/y) * dx, - (x^8*z0^3/y) * dx, - (x^8*z0^4/y) * dx, - (x^9) * dx, - (x^9*z0) * dx, - (x^9*z0^2) * dx, - (x^9*z0^3) * dx, - (x^9*z0^4) * dx, - (x^9/y) * dx, - (x^9*z0/y) * dx, - (x^9*z0^2/y) * dx, - (x^9*z0^3/y) * dx, - (x^9*z0^4/y) * dx, - (x^10) * dx, - (x^10*z0) * dx, - (x^10*z0^2) * dx, - (x^10*z0^3) * dx, - (x^10*z0^4) * dx, - (x^10/y) * dx, - (x^10*z0/y) * dx, - (x^10*z0^2/y) * dx, - (x^10*z0^3/y) * dx, - (x^10*z0^4/y) * dx, - (x^11) * dx, - (x^11*z0) * dx, - (x^11*z0^2) * dx, - (x^11*z0^3) * dx, - (x^11*z0^4) * dx, - (x^11/y) * dx, - (x^11*z0/y) * dx, - (x^11*z0^2/y) * dx, - (x^11*z0^3/y) * dx, - (x^11*z0^4/y) * dx, - (x^12) * dx, - (x^12*z0) * dx, - (x^12*z0^2) * dx, - (x^12*z0^3) * dx, - (x^12*z0^4) * dx, - (x^12/y) * dx, - (x^12*z0/y) * dx, - (x^12*z0^2/y) * dx, - (x^12*z0^3/y) * dx, - (x^12*z0^4/y) * dx, - (x^13) * dx, - (x^13*z0) * dx, - (x^13*z0^2) * dx, - (x^13*z0^3) * dx, - (x^13*z0^4) * dx, - (x^13/y) * dx, - (x^13*z0/y) * dx, - (x^13*z0^2/y) * dx, - (x^13*z0^3/y) * dx, - (x^13*z0^4/y) * dx, - (x^14) * dx, - (x^14*z0) * dx, - (x^14*z0^2) * dx, - (x^14*z0^3) * dx, - (x^14*z0^4) * dx, - (x^14/y) * dx, - (x^14*z0/y) * dx, - (x^14*z0^2/y) * dx, - (x^14*z0^3/y) * dx, - (x^14*z0^4/y) * dx, - (x^15) * dx, - (x^15*z0) * dx, - (x^15*z0^2) * dx, - (x^15*z0^3) * dx, - (x^15*z0^4) * dx, - (x^15/y) * dx, - (x^15*z0/y) * dx, - (x^15*z0^2/y) * dx, - (x^15*z0^3/y) * dx, - (x^15*z0^4/y) * dx, - (x^16) * dx, - (x^16*z0) * dx, - (x^16*z0^2) * dx, - (x^16*z0^3) * dx, - (x^16*z0^4) * dx, - (x^16/y) * dx, - (x^16*z0/y) * dx, - (x^16*z0^2/y) * dx, - (x^16*z0^3/y) * dx, - (x^16*z0^4/y) * dx, - (x^17) * dx, - (x^17*z0) * dx, - (x^17*z0^2) * dx, - (x^17*z0^3) * dx, - (x^17*z0^4) * dx, - (x^17/y) * dx, - (x^17*z0/y) * dx, - (x^17*z0^2/y) * dx, - (x^17*z0^3/y) * dx, - (x^17*z0^4/y) * dx, - (x^18) * dx, - (x^18*z0) * dx, - (x^18*z0^2) * dx, - (x^18*z0^3) * dx, - (x^18*z0^4) * dx, - (x^18/y) * dx, - (x^18*z0/y) * dx, - (x^18*z0^2/y) * dx, - (x^18*z0^3/y) * dx, - (x^18*z0^4/y) * dx, - (x^19) * dx, - (x^19*z0) * dx, - (x^19*z0^2) * dx, - (x^19*z0^3) * dx, - (x^19*z0^4) * dx, - (x^19/y) * dx, - (x^19*z0/y) * dx, - (x^19*z0^2/y) * dx, - (x^19*z0^3/y) * dx, - (x^19*z0^4/y) * dx, - (x^20) * dx, - (x^20*z0) * dx, - (x^20*z0^2) * dx, - (x^20*z0^3) * dx, - (x^20*z0^4) * dx, - (x^20/y) * dx, - (x^20*z0/y) * dx, - (x^20*z0^2/y) * dx, - (x^20*z0^3/y) * dx, - (x^20*z0^4/y) * dx, - (x^21) * dx, - (x^21*z0) * dx, - (x^21*z0^2) * dx, - (x^21*z0^3) * dx, - (x^21*z0^4) * dx, - (x^21/y) * dx, - (x^21*z0/y) * dx, - (x^21*z0^2/y) * dx, - (x^21*z0^3/y) * dx, - (x^21*z0^4/y) * dx, - (x^22) * dx, - (x^22*z0) * dx, - (x^22*z0^2) * dx, - (x^22*z0^3) * dx, - (x^22*z0^4) * dx, - (x^22/y) * dx, - (x^22*z0/y) * dx, - (x^22*z0^2/y) * dx, - (x^22*z0^3/y) * dx, - (x^22*z0^4/y) * dx, - (x^23) * dx, - (x^23*z0) * dx, - (x^23*z0^2) * dx, - (x^23*z0^3) * dx, - (x^23*z0^4) * dx, - (x^23/y) * dx, - (x^23*z0/y) * dx, - (x^23*z0^2/y) * dx, - (x^23*z0^3/y) * dx, - (x^23*z0^4/y) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l20, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l0, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 200, branch_points = [(-1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 200, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004lIncrease precision. -[?7h[(1) * dx, - (z0) * dx, - (z0^2) * dx, - (z0^3) * dx, - (z0^4) * dx, - (1/y) * dx, - (z0/y) * dx, - (z0^2/y) * dx, - (z0^3/y) * dx, - (z0^4/y) * dx, - (x) * dx, - (x*z0) * dx, - (x*z0^2) * dx, - (x*z0^3) * dx, - (x*z0^4) * dx, - (x/y) * dx, - (x*z0/y) * dx, - (x*z0^2/y) * dx, - (x*z0^3/y) * dx, - (x*z0^4/y) * dx, - (x^2) * dx, - (x^2*z0) * dx, - (x^2*z0^2) * dx, - (x^2*z0^3) * dx, - (x^2*z0^4) * dx, - (x^2/y) * dx, - (x^2*z0/y) * dx, - (x^2*z0^2/y) * dx, - (x^2*z0^3/y) * dx, - (x^2*z0^4/y) * dx, - (x^3) * dx, - (x^3*z0) * dx, - (x^3*z0^2) * dx, - (x^3*z0^3) * dx, - (x^3*z0^4) * dx, - (x^3/y) * dx, - (x^3*z0/y) * dx, - (x^3*z0^2/y) * dx, - (x^3*z0^3/y) * dx, - (x^3*z0^4/y) * dx, - (x^4) * dx, - (x^4*z0) * dx, - (x^4*z0^2) * dx, - (x^4*z0^3) * dx, - (x^4*z0^4) * dx, - (x^4/y) * dx, - (x^4*z0/y) * dx, - (x^4*z0^2/y) * dx, - (x^4*z0^3/y) * dx, - (x^4*z0^4/y) * dx, - (x^5) * dx, - (x^5*z0) * dx, - (x^5*z0^2) * dx, - (x^5*z0^3) * dx, - (x^5*z0^4) * dx, - (x^5/y) * dx, - (x^5*z0/y) * dx, - (x^5*z0^2/y) * dx, - (x^5*z0^3/y) * dx, - (x^5*z0^4/y) * dx, - (x^6) * dx, - (x^6*z0) * dx, - (x^6*z0^2) * dx, - (x^6*z0^3) * dx, - (x^6*z0^4) * dx, - (x^6/y) * dx, - (x^6*z0/y) * dx, - (x^6*z0^2/y) * dx, - (x^6*z0^3/y) * dx, - (x^6*z0^4/y) * dx, - (x^7) * dx, - (x^7*z0) * dx, - (x^7*z0^2) * dx, - (x^7*z0^3) * dx, - (x^7*z0^4) * dx, - (x^7/y) * dx, - (x^7*z0/y) * dx, - (x^7*z0^2/y) * dx, - (x^7*z0^3/y) * dx, - (x^7*z0^4/y) * dx, - (x^8) * dx, - (x^8*z0) * dx, - (x^8*z0^2) * dx, - (x^8*z0^3) * dx, - (x^8*z0^4) * dx, - (x^8/y) * dx, - (x^8*z0/y) * dx, - (x^8*z0^2/y) * dx, - (x^8*z0^3/y) * dx, - (x^8*z0^4/y) * dx, - (x^9) * dx, - (x^9*z0) * dx, - (x^9*z0^2) * dx, - (x^9*z0^3) * dx, - (x^9*z0^4) * dx, - (x^9/y) * dx, - (x^9*z0/y) * dx, - (x^9*z0^2/y) * dx, - (x^9*z0^3/y) * dx, - (x^9*z0^4/y) * dx, - (x^10) * dx, - (x^10*z0) * dx, - (x^10*z0^2) * dx, - (x^10*z0^3) * dx, - (x^10*z0^4) * dx, - (x^10/y) * dx, - (x^10*z0/y) * dx, - (x^10*z0^2/y) * dx, - (x^10*z0^3/y) * dx, - (x^10*z0^4/y) * dx, - (x^11) * dx, - (x^11*z0) * dx, - (x^11*z0^2) * dx, - (x^11*z0^3) * dx, - (x^11*z0^4) * dx, - (x^11/y) * dx, - (x^11*z0/y) * dx, - (x^11*z0^2/y) * dx, - (x^11*z0^3/y) * dx, - (x^11*z0^4/y) * dx, - (x^12) * dx, - (x^12*z0) * dx, - (x^12*z0^2) * dx, - (x^12*z0^3) * dx, - (x^12*z0^4) * dx, - (x^12/y) * dx, - (x^12*z0/y) * dx, - (x^12*z0^2/y) * dx, - (x^12*z0^3/y) * dx, - (x^12*z0^4/y) * dx, - (x^13) * dx, - (x^13*z0) * dx, - (x^13*z0^2) * dx, - (x^13*z0^3) * dx, - (x^13*z0^4) * dx, - (x^13/y) * dx, - (x^13*z0/y) * dx, - (x^13*z0^2/y) * dx, - (x^13*z0^3/y) * dx, - (x^13*z0^4/y) * dx, - (x^14) * dx, - (x^14*z0) * dx, - (x^14*z0^2) * dx, - (x^14*z0^3) * dx, - (x^14*z0^4) * dx, - (x^14/y) * dx, - (x^14*z0/y) * dx, - (x^14*z0^2/y) * dx, - (x^14*z0^3/y) * dx, - (x^14*z0^4/y) * dx, - (x^15) * dx, - (x^15*z0) * dx, - (x^15*z0^2) * dx, - (x^15*z0^3) * dx, - (x^15*z0^4) * dx, - (x^15/y) * dx, - (x^15*z0/y) * dx, - (x^15*z0^2/y) * dx, - (x^15*z0^3/y) * dx, - (x^15*z0^4/y) * dx, - (x^16) * dx, - (x^16*z0) * dx, - (x^16*z0^2) * dx, - (x^16*z0^3) * dx, - (x^16*z0^4) * dx, - (x^16/y) * dx, - (x^16*z0/y) * dx, - (x^16*z0^2/y) * dx, - (x^16*z0^3/y) * dx, - (x^16*z0^4/y) * dx, - (x^17) * dx, - (x^17*z0) * dx, - (x^17*z0^2) * dx, - (x^17*z0^3) * dx, - (x^17*z0^4) * dx, - (x^17/y) * dx, - (x^17*z0/y) * dx, - (x^17*z0^2/y) * dx, - (x^17*z0^3/y) * dx, - (x^17*z0^4/y) * dx, - (x^18) * dx, - (x^18*z0) * dx, - (x^18*z0^2) * dx, - (x^18*z0^3) * dx, - (x^18*z0^4) * dx, - (x^18/y) * dx, - (x^18*z0/y) * dx, - (x^18*z0^2/y) * dx, - (x^18*z0^3/y) * dx, - (x^18*z0^4/y) * dx, - (x^19) * dx, - (x^19*z0) * dx, - (x^19*z0^2) * dx, - (x^19*z0^3) * dx, - (x^19*z0^4) * dx, - (x^19/y) * dx, - (x^19*z0/y) * dx, - (x^19*z0^2/y) * dx, - (x^19*z0^3/y) * dx, - (x^19*z0^4/y) * dx, - (x^20) * dx, - (x^20*z0) * dx, - (x^20*z0^2) * dx, - (x^20*z0^3) * dx, - (x^20*z0^4) * dx, - (x^20/y) * dx, - (x^20*z0/y) * dx, - (x^20*z0^2/y) * dx, - (x^20*z0^3/y) * dx, - (x^20*z0^4/y) * dx, - (x^21) * dx, - (x^21*z0) * dx, - (x^21*z0^2) * dx, - (x^21*z0^3) * dx, - (x^21*z0^4) * dx, - (x^21/y) * dx, - (x^21*z0/y) * dx, - (x^21*z0^2/y) * dx, - (x^21*z0^3/y) * dx, - (x^21*z0^4/y) * dx, - (x^22) * dx, - (x^22*z0) * dx, - (x^22*z0^2) * dx, - (x^22*z0^3) * dx, - (x^22*z0^4) * dx, - (x^22/y) * dx, - (x^22*z0/y) * dx, - (x^22*z0^2/y) * dx, - (x^22*z0^3/y) * dx, - (x^22*z0^4/y) * dx, - (x^23) * dx, - (x^23*z0) * dx, - (x^23*z0^2) * dx, - (x^23*z0^3) * dx, - (x^23*z0^4) * dx, - (x^23/y) * dx, - (x^23*z0/y) * dx, - (x^23*z0^2/y) * dx, - (x^23*z0^3/y) * dx, - (x^23*z0^4/y) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: AS.dx.expansion(pt=(-1, 0)) -[?7h[?12l[?25h[?2004l[?7ht^17 + 2*t^25 + 3*t^33 + 4*t^41 + t^57 + 2*t^65 + 3*t^73 + 4*t^81 + t^97 + 2*t^105 + 3*t^113 + 4*t^121 + t^137 + 2*t^145 + 3*t^153 + 4*t^161 + t^177 + 2*t^185 + 3*t^193 + 4*t^201 + O(t^209) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lx.function[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lverschiebung()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion(pt=(-1, 0)) -[?7h[?12l[?25h[?2004l[?7h4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldx.expansion(pt=(-1, 0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.dx.expansion(pt=(-1, 0)) -[?7h[?12l[?25h[?2004l[?7h4*t + t^3 + 3*t^11 + 2*t^13 + 2*t^21 + 3*t^23 + t^31 + 4*t^33 + t^51 + 4*t^53 + 2*t^61 + 3*t^63 + 3*t^71 + 2*t^73 + 4*t^81 + t^83 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.dx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lAS.dx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lC.x.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7ldx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.dx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0]/AS.x[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7leries[?7h[?12l[?25h[?25l[?7lsage: AS.z_series -[?7h[?12l[?25h[?2004l[?7h{(-1, 0): [t^-2]} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z_series[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lAS.dx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lholomorphc_differentials_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 200, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l.z_series[?7h[?12l[?25h[?25l[?7lsage: AS.z_series -[?7h[?12l[?25h[?2004l[?7h{0: [2*t^2 + 2*t^4 + 2*t^6 + 4*t^8 + t^10 + 3*t^12 + t^14 + t^16 + 3*t^18 + t^20 + 3*t^22 + t^24 + 2*t^26 + 4*t^28 + 2*t^30 + 4*t^32 + 2*t^34 + 3*t^36 + t^38 + t^40 + t^46 + t^48 + 2*t^50 + O(t^52)], - (-1, 0): [t^-2]} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*C.x+3*C.one)^(-1)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((3*C.x+3*C.one)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((3*C.x+3*C.one)^(-1)).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t^2 + 3*t^4 + 2*t^6 + 3*t^10 + 4*t^12 + 4*t^16 + 4*t^18 + O(t^22) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((3*C.x+3*C.one)^(-1)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lAS.z_series[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: AS.z_series[0] -[?7h[?12l[?25h[?2004l[?7h[2*t^2 + 2*t^4 + 2*t^6 + 4*t^8 + t^10 + 3*t^12 + t^14 + t^16 + 3*t^18 + t^20 + 3*t^22 + t^24 + 2*t^26 + 4*t^28 + 2*t^30 + 4*t^32 + 2*t^34 + 3*t^36 + t^38 + t^40 + t^46 + t^48 + 2*t^50 + O(t^52)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z_series[0][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: AS.z_series[0][0] -[?7h[?12l[?25h[?2004l[?7h2*t^2 + 2*t^4 + 2*t^6 + 4*t^8 + t^10 + 3*t^12 + t^14 + t^16 + 3*t^18 + t^20 + 3*t^22 + t^24 + 2*t^26 + 4*t^28 + 2*t^30 + 4*t^32 + 2*t^34 + 3*t^36 + t^38 + t^40 + t^46 + t^48 + 2*t^50 + O(t^52) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z_series[0][0][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*C.x+3*C.one)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z_series[0][0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l()AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l( AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l() AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l( AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l AS.z_series[0][0][?7h[?12l[?25h[?25l[?7lAS.z_series[0][0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.z_series[0][0]^5 - AS.z_series[0][0] -[?7h[?12l[?25h[?2004l[?7h3*t^2 + 3*t^4 + 3*t^6 + t^8 + t^10 + 2*t^12 + 4*t^14 + 4*t^16 + 2*t^18 + t^20 + 2*t^22 + 4*t^24 + 3*t^26 + t^28 + t^32 + 3*t^34 + 2*t^36 + 4*t^38 + 3*t^40 + 4*t^46 + 4*t^48 + 4*t^50 + O(t^52) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lAS.z_series[0][0]^5 - AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l((3*C.x+3*C.one)^(-1)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lAS.z_series[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l.z_series[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lAS.z_series[0][0]^5 - AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l((3*C.x+3*C.one)^(-1)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lAS.z_series[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l.z_series[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l.z_series[?7h[?12l[?25h[?25l[?7l((3*C.x+3*C.one)^(-1)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lAS.z_series[0][?7h[?12l[?25h[?25l[?7l[][0][?7h[?12l[?25h[?25l[?7l[]^5 - AS.z_series[0][0][?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lAS.z_series[0][0]^5 - AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l((3*C.x+3*C.one)^(-1)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lAS.z_series[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(3*C.x+3*C.one)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lAS.z_series[0][0]^5 - AS.z_series[0][0][?7h[?12l[?25h[?25l[?7lsage: AS.z_series[0][0]^5 - AS.z_series[0][0] -[?7h[?12l[?25h[?2004l[?7h2*t^2 + 3*t^4 + 2*t^6 + 3*t^10 + 4*t^12 + 4*t^16 + 4*t^18 + t^22 + t^30 + 4*t^34 + t^36 + 4*t^40 + 2*t^42 + t^46 + t^48 + O(t^52) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((3*C.x+3*C.one)^(-1)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l(3*C.x+3*C.one)^(-1)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: ((3*C.x+3*C.one)^(-1)).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t^2 + 3*t^4 + 2*t^6 + 3*t^10 + 4*t^12 + 4*t^16 + 4*t^18 + O(t^22) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z_series[0][0]^5 - AS.z_series[0][0][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differential_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004lIncrease precision. -[?7h[(x^23*z0^4 + 2*x^23*z0^3 - x^22*z0^4 - 2*x^22*z0^3 + x^21*z0^4 + 2*x^21*z0^3 - 2*x^20*z0^4 - 2*x^20*z0^3 + x^19*z0^4 - x^19*z0^3 + x^20 + 1) * dx, - (2*x^23*z0^4 - 2*x^22*z0^4 + 2*x^21*z0^4 - 2*x^20*z0^4 - x^19*z0^4 - 2*x^19 + z0) * dx, - (z0^2) * dx, - (z0^3) * dx, - (z0^4) * dx, - (1/y) * dx, - (z0/y) * dx, - (z0^2/y) * dx, - (z0^3/y) * dx, - (z0^4/y) * dx, - (-x^23*z0^4 + x^23*z0^3 + x^22*z0^4 + x^23*z0^2 - x^22*z0^3 - 2*x^21*z0^4 - x^22*z0^2 + x^21*z0^3 + x^20*z0^4 + x^21*z0^2 + x^20*z0^3 - x^19*z0^4 - x^20*z0^2 - x^19*z0^3 + x^21 + 2*x^19*z0^2 + x) * dx, - (x^23*z0^4 + x^23*z0^3 - x^22*z0^4 - x^22*z0^3 + x^21*z0^4 + x^21*z0^3 + x^20*z0^4 - x^20*z0^3 - x^19*z0^4 + 2*x^19*z0^3 - 2*x^20 + 2*x^19 + x*z0) * dx, - (x^23*z0^4 - x^22*z0^4 + x^21*z0^4 - x^20*z0^4 + 2*x^19*z0^4 - x^19 + x*z0^2) * dx, - (x*z0^3) * dx, - (x*z0^4) * dx, - ((-2*x^23*z0^4 - x^23*z0^3 + 2*x^22*z0^4 + x^23*z0^2 + x^22*z0^3 + 2*x^21*z0^4 - x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 + x^21*z0^2 - 2*x^20*z0^3 - 2*x^19*z0^4 - x^20*z0^2 + x^21 + 2*x^19*z0^2 - x^20 + x)/y) * dx, - (x*z0/y) * dx, - (x*z0^2/y) * dx, - (x*z0^3/y) * dx, - (x*z0^4/y) * dx, - (x^23*z0^4 + x^23*z0^3 - 2*x^22*z0^4 + 2*x^23*z0^2 - x^22*z0^3 + x^21*z0^4 - 2*x^23*z0 - 2*x^22*z0^2 - 2*x^21*z0^3 - x^20*z0^4 + 2*x^22*z0 + 2*x^21*z0^2 + 2*x^20*z0^3 + x^19*z0^4 + x^22 - 2*x^21*z0 - x^20*z0^2 - 2*x^19*z0^3 + 2*x^20*z0 + x^19*z0 + x^2) * dx, - (x^23*z0^4 + 2*x^23*z0^3 - x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 - 2*x^21*z0^4 + 2*x^22*z0^2 + 2*x^21*z0^3 + 2*x^20*z0^4 - 2*x^21*z0^2 - x^20*z0^3 - 2*x^19*z0^4 + 2*x^20*z0^2 - 2*x^21 + x^19*z0^2 + 2*x^20 - 2*x^19 + x^2*z0) * dx, - (2*x^23*z0^4 - 2*x^23*z0^3 - 2*x^22*z0^4 + 2*x^22*z0^3 + 2*x^21*z0^4 - 2*x^21*z0^3 - x^20*z0^4 + 2*x^20*z0^3 + x^19*z0^3 - x^20 + 2*x^19 + x^2*z0^2) * dx, - (-2*x^23*z0^4 + 2*x^22*z0^4 - 2*x^21*z0^4 + 2*x^20*z0^4 + x^19*z0^4 + 2*x^19 + x^2*z0^3) * dx, - (x^2*z0^4) * dx, - ((-x^23*z0^4 + 2*x^23*z0^3 + 2*x^23*z0^2 - 2*x^22*z0^3 - x^21*z0^4 - 2*x^23*z0 - 2*x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 + 2*x^22*z0 + 2*x^21*z0^2 + x^20*z0^3 - x^19*z0^4 + x^22 - 2*x^21*z0 - x^20*z0^2 + 2*x^20*z0 - 2*x^20 + x^19*z0 + x^2)/y) * dx, - ((-x^23*z0^4 + 2*x^23*z0^3 + x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 + x^21*z0^4 + 2*x^22*z0^2 + 2*x^21*z0^3 - x^20*z0^4 - 2*x^21*z0^2 - x^20*z0^3 - x^19*z0^4 + 2*x^20*z0^2 - 2*x^21 + x^19*z0^2 + 2*x^20 + x^2*z0)/y) * dx, - (x^2*z0^2/y) * dx, - (x^2*z0^3/y) * dx, - (x^2*z0^4/y) * dx, - (-2*x^23*z0^4 + 2*x^23*z0^3 + x^22*z0^4 + x^23*z0^2 - x^21*z0^4 - 2*x^23*z0 - x^22*z0^2 + x^20*z0^4 + 2*x^22*z0 + 2*x^21*z0^2 - x^19*z0^4 + x^22 - 2*x^21*z0 + 2*x^20*z0^2 - x^21 - x^19*z0^2 + x^20 - x^19*z0 - 2*x^19 + x^3) * dx, - (2*x^23*z0^4 + x^23*z0^3 - 2*x^23*z0^2 - x^22*z0^3 - x^23*z0 + 2*x^22*z0^2 + 2*x^21*z0^3 + x^22*z0 - 2*x^21*z0^2 + 2*x^20*z0^3 - 2*x^22 - x^21*z0 - x^19*z0^3 + 2*x^21 + x^20*z0 - x^19*z0^2 - 2*x^20 - 2*x^19*z0 + 2*x^19 + x^3*z0) * dx, - (x^23*z0^4 - 2*x^23*z0^3 - x^22*z0^4 - x^23*z0^2 + 2*x^22*z0^3 + 2*x^21*z0^4 + x^22*z0^2 - 2*x^21*z0^3 + 2*x^20*z0^4 - x^21*z0^2 - x^19*z0^4 + x^20*z0^2 - x^19*z0^3 - x^21 - 2*x^19*z0^2 + 2*x^20 + 2*x^19 + x^3*z0^2) * dx, - (-2*x^23*z0^4 - x^23*z0^3 + 2*x^22*z0^4 + x^22*z0^3 - 2*x^21*z0^4 - x^21*z0^3 + x^20*z0^3 - x^19*z0^4 - 2*x^19*z0^3 + 2*x^20 - x^19 + x^3*z0^3) * dx, - (-x^23*z0^4 + x^22*z0^4 - x^21*z0^4 + x^20*z0^4 - 2*x^19*z0^4 + x^19 + x^3*z0^4) * dx, - ((x^23*z0^4 + 2*x^23*z0^3 - 2*x^22*z0^4 + x^23*z0^2 + 2*x^21*z0^4 - 2*x^23*z0 - x^22*z0^2 - 2*x^20*z0^4 + 2*x^22*z0 + 2*x^21*z0^2 + x^22 - 2*x^21*z0 + 2*x^20*z0^2 - x^21 - x^19*z0^2 + x^20 - x^19*z0 + x^3)/y) * dx, - ((-2*x^23*z0^4 - x^23*z0^3 - x^22*z0^4 - 2*x^23*z0^2 + x^22*z0^3 + x^21*z0^4 - x^23*z0 + 2*x^22*z0^2 + x^22*z0 - 2*x^21*z0^2 - x^20*z0^3 - 2*x^19*z0^4 - 2*x^22 - x^21*z0 + 2*x^21 + x^20*z0 - x^19*z0^2 + 2*x^20 - 2*x^19*z0 + x^3*z0)/y) * dx, - ((2*x^23*z0^4 + x^23*z0^3 - 2*x^22*z0^4 - x^23*z0^2 - x^22*z0^3 - 2*x^21*z0^4 + x^22*z0^2 + x^21*z0^3 + 2*x^20*z0^4 - x^21*z0^2 + 2*x^20*z0^3 + 2*x^19*z0^4 + x^20*z0^2 - x^21 - 2*x^19*z0^2 + x^20 + x^3*z0^2)/y) * dx, - (x^3*z0^3/y) * dx, - (x^3*z0^4/y) * dx, - (2*x^23*z0^4 - x^23*z0^3 - 2*x^22*z0^4 + x^22*z0^3 + 2*x^21*z0^4 + x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 - 2*x^21*z0^2 + x^20*z0^3 - x^19*z0^4 - 2*x^21*z0 - 2*x^20*z0^2 + x^19*z0^3 + x^20*z0 + x^19*z0^2 - x^20 - 2*x^19*z0 + 2*x^19 + x^4) * dx, - (-x^23*z0^4 + x^22*z0^4 + x^22*z0^3 - x^21*z0^4 - 2*x^21*z0^3 + x^20*z0^4 - 2*x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 + x^20*z0^2 + x^19*z0^3 - x^20*z0 - 2*x^19*z0^2 - x^19*z0 + x^4*z0) * dx, - (x^22*z0^4 - 2*x^21*z0^4 + 2*x^23*z0 - 2*x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 + x^20*z0^3 + x^19*z0^4 - x^22 + 2*x^21*z0 - x^20*z0^2 - 2*x^19*z0^3 + 2*x^21 - 2*x^20*z0 - x^19*z0^2 + 2*x^20 - x^19*z0 - x^19 + x^4*z0^2) * dx, - (2*x^23*z0^2 - 2*x^21*z0^4 - 2*x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 - x^20*z0^3 - 2*x^19*z0^4 - 2*x^20*z0^2 - x^19*z0^3 + 2*x^21 - x^19*z0^2 - x^20 + 2*x^19 + x^4*z0^3) * dx, - (2*x^23*z0^3 - 2*x^22*z0^3 + 2*x^21*z0^3 - x^20*z0^4 - 2*x^20*z0^3 - x^19*z0^4 - x^19*z0^3 + x^20 + x^19 + x^4*z0^4) * dx, - ((x^23*z0^3 - x^22*z0^3 + x^22*z0^2 + x^21*z0^3 - x^20*z0^4 - 2*x^21*z0^2 - x^20*z0^3 - x^19*z0^4 - 2*x^21*z0 - 2*x^20*z0^2 + x^20*z0 + x^19*z0^2 - 2*x^19*z0 + x^4)/y) * dx, - ((2*x^23*z0^3 - x^22*z0^3 - x^20*z0^4 - 2*x^21*z0^2 + x^20*z0^3 + 2*x^19*z0^4 + x^20*z0^2 - x^20*z0 - 2*x^19*z0^2 + x^20 - x^19*z0 + x^4*z0)/y) * dx, - ((2*x^23*z0^4 + x^23*z0^3 - x^22*z0^4 - x^22*z0^3 + 2*x^23*z0 - x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 + 2*x^19*z0^4 - x^22 + 2*x^21*z0 - x^20*z0^2 + 2*x^21 - 2*x^20*z0 - x^19*z0^2 - x^19*z0 + x^4*z0^2)/y) * dx, - ((x^23*z0^4 - 2*x^23*z0^3 - x^22*z0^4 + 2*x^23*z0^2 + 2*x^22*z0^3 - x^21*z0^4 - 2*x^22*z0^2 - 2*x^21*z0^3 + x^20*z0^4 + 2*x^21*z0^2 + x^20*z0^3 + x^19*z0^4 - 2*x^20*z0^2 + 2*x^21 - x^19*z0^2 - 2*x^20 + x^4*z0^3)/y) * dx, - (x^4*z0^4/y) * dx, - (-2*x^23*z0^4 + 2*x^23*z0^3 + 2*x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 - 2*x^21*z0^4 + x^22*z0^2 + 2*x^21*z0^3 - x^20*z0^4 - 2*x^22*z0 - 2*x^19*z0^4 + x^21*z0 - x^20*z0^2 - 2*x^19*z0^3 - x^21 - 2*x^20*z0 - x^19*z0^2 + 2*x^20 + x^5) * dx, - (2*x^23*z0^4 - 2*x^23*z0^3 - 2*x^22*z0^4 + x^22*z0^3 + 2*x^21*z0^4 - 2*x^22*z0^2 + x^21*z0^2 - x^20*z0^3 - 2*x^19*z0^4 - x^21*z0 - 2*x^20*z0^2 - x^19*z0^3 - x^20*z0 - x^19 + x^5*z0) * dx, - (-2*x^23*z0^4 + x^22*z0^4 - 2*x^22*z0^3 - 2*x^23*z0 + x^21*z0^3 - x^20*z0^4 + 2*x^22*z0 - x^21*z0^2 - 2*x^20*z0^3 - x^19*z0^4 + x^22 - 2*x^21*z0 - x^20*z0^2 - 2*x^21 - x^20*z0 - 2*x^20 - 2*x^19*z0 + x^5*z0^2) * dx, - (-2*x^22*z0^4 - 2*x^23*z0^2 + x^21*z0^4 + x^23*z0 + 2*x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 - x^22*z0 - 2*x^21*z0^2 - x^20*z0^3 + 2*x^22 + x^21*z0 - x^20*z0^2 - x^21 - x^20*z0 - 2*x^19*z0^2 + 2*x^20 + 2*x^19*z0 + x^5*z0^3) * dx, - (-2*x^23*z0^3 + x^23*z0^2 + 2*x^22*z0^3 - x^21*z0^4 - x^22*z0^2 - 2*x^21*z0^3 - x^20*z0^4 + x^21*z0^2 - x^20*z0^3 - x^20*z0^2 - 2*x^19*z0^3 + x^21 + 2*x^19*z0^2 + x^20 + x^5*z0^4) * dx, - ((x^23*z0^4 - 2*x^23*z0^3 - x^22*z0^4 - 2*x^23*z0^2 + 2*x^22*z0^3 + x^21*z0^4 + x^22*z0^2 - 2*x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 - x^20*z0^3 + x^19*z0^4 + x^21*z0 - x^20*z0^2 - x^21 - 2*x^20*z0 - x^19*z0^2 + x^5)/y) * dx, - ((x^23*z0^3 - 2*x^22*z0^3 - 2*x^22*z0^2 - 2*x^21*z0^3 - 2*x^20*z0^4 + x^21*z0^2 + x^20*z0^3 - x^21*z0 - 2*x^20*z0^2 - x^20*z0 - x^20 + x^5*z0)/y) * dx, - ((-2*x^23*z0^4 + x^22*z0^4 - 2*x^22*z0^3 - 2*x^23*z0 + x^21*z0^3 - x^20*z0^4 + 2*x^22*z0 - x^21*z0^2 - 2*x^20*z0^3 - x^19*z0^4 + x^22 - 2*x^21*z0 - x^20*z0^2 - 2*x^21 - x^20*z0 - 2*x^20 - 2*x^19*z0 + x^5*z0^2)/y) * dx, - ((-2*x^22*z0^4 - 2*x^23*z0^2 + x^21*z0^4 + x^23*z0 + 2*x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 - x^22*z0 - 2*x^21*z0^2 - x^20*z0^3 + 2*x^22 + x^21*z0 - x^20*z0^2 - x^21 - x^20*z0 - 2*x^19*z0^2 + 2*x^20 + 2*x^19*z0 + x^5*z0^3)/y) * dx, - ((-2*x^23*z0^4 - x^23*z0^3 + 2*x^22*z0^4 + x^23*z0^2 + x^22*z0^3 + 2*x^21*z0^4 - x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 + x^21*z0^2 - 2*x^20*z0^3 - 2*x^19*z0^4 - x^20*z0^2 + x^21 + 2*x^19*z0^2 - x^20 + x^5*z0^4)/y) * dx, - (2*x^23*z0^4 + 2*x^23*z0^3 - 2*x^22*z0^4 + 2*x^23*z0^2 - 2*x^22*z0^3 - x^21*z0^4 + 2*x^23*z0 - x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 + 2*x^22*z0 - x^20*z0^3 + 2*x^19*z0^4 - x^22 + 2*x^21*z0 - 2*x^20*z0^2 + x^19*z0^3 + 2*x^21 + x^20*z0 - x^19*z0^2 - 2*x^19*z0 + x^6) * dx, - (2*x^23*z0^4 + 2*x^23*z0^3 - 2*x^22*z0^4 + 2*x^23*z0^2 - x^22*z0^3 - x^21*z0^4 + 2*x^22*z0^2 - x^20*z0^4 - x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 - x^21*z0 + x^20*z0^2 - x^19*z0^3 - 2*x^19*z0^2 - x^20 + x^19 + x^6*z0) * dx, - (2*x^23*z0^4 + 2*x^23*z0^3 - x^22*z0^4 + 2*x^22*z0^3 + 2*x^23*z0 - x^22*z0^2 + 2*x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 - x^21*z0^2 + x^20*z0^3 - x^19*z0^4 - x^22 - x^21*z0 - 2*x^19*z0^3 + 2*x^21 - 2*x^20*z0 + x^20 + 2*x^19*z0 + 2*x^19 + x^6*z0^2) * dx, - (2*x^23*z0^4 + 2*x^22*z0^4 + 2*x^23*z0^2 - x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 - 2*x^22*z0^2 - x^21*z0^3 + x^20*z0^4 + 2*x^22*z0 - x^21*z0^2 - 2*x^19*z0^4 + x^22 - 2*x^21*z0 - 2*x^20*z0^2 - 2*x^20*z0 + 2*x^19*z0^2 + 2*x^20 + 2*x^19*z0 + 2*x^19 + x^6*z0^3) * dx, - (2*x^23*z0^3 - x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 - x^21*z0^4 - 2*x^23*z0 + 2*x^22*z0^2 - x^21*z0^3 + 2*x^22*z0 - 2*x^21*z0^2 - 2*x^20*z0^3 + x^22 - 2*x^21*z0 - 2*x^20*z0^2 + 2*x^19*z0^3 + x^21 + 2*x^20*z0 + 2*x^19*z0^2 + x^19*z0 + x^6*z0^4) * dx, - ((-2*x^23*z0^4 - x^23*z0^3 + 2*x^22*z0^4 + 2*x^23*z0^2 + x^22*z0^3 + 2*x^23*z0 - x^22*z0^2 + x^21*z0^3 + x^20*z0^4 + 2*x^22*z0 + 2*x^20*z0^3 - 2*x^19*z0^4 - x^22 + 2*x^21*z0 - 2*x^20*z0^2 + 2*x^21 + x^20*z0 - x^19*z0^2 + x^20 - 2*x^19*z0 + x^6)/y) * dx, - ((2*x^23*z0^4 - 2*x^22*z0^4 + 2*x^23*z0^2 + x^22*z0^3 - x^21*z0^4 + 2*x^22*z0^2 - 2*x^21*z0^3 - x^22*z0 + 2*x^21*z0^2 + 2*x^19*z0^4 - x^21*z0 + x^20*z0^2 - 2*x^19*z0^2 - 2*x^20 + x^6*z0)/y) * dx, - ((2*x^23*z0^4 - 2*x^23*z0^3 - x^22*z0^4 + x^22*z0^3 + 2*x^23*z0 - x^22*z0^2 - 2*x^21*z0^3 - 2*x^22*z0 - x^21*z0^2 + x^19*z0^4 - x^22 - x^21*z0 + 2*x^21 - 2*x^20*z0 - x^20 + 2*x^19*z0 + x^6*z0^2)/y) * dx, - ((-x^23*z0^4 + 2*x^23*z0^2 - x^22*z0^3 - x^21*z0^4 - 2*x^23*z0 - 2*x^22*z0^2 - x^21*z0^3 - x^20*z0^4 + 2*x^22*z0 - x^21*z0^2 + 2*x^19*z0^4 + x^22 - 2*x^21*z0 - 2*x^20*z0^2 - 2*x^20*z0 + 2*x^19*z0^2 + 2*x^20 + 2*x^19*z0 + x^6*z0^3)/y) * dx, - ((2*x^23*z0^4 + x^23*z0^3 + 2*x^22*z0^4 - 2*x^23*z0^2 - x^22*z0^3 + x^21*z0^4 - 2*x^23*z0 + 2*x^22*z0^2 - 2*x^21*z0^3 + x^20*z0^4 + 2*x^22*z0 - 2*x^21*z0^2 - x^20*z0^3 + 2*x^19*z0^4 + x^22 - 2*x^21*z0 - 2*x^20*z0^2 + x^21 + 2*x^20*z0 + 2*x^19*z0^2 + 2*x^20 + x^19*z0 + x^6*z0^4)/y) * dx, - (-2*x^23*z0^4 - x^23*z0^3 - x^22*z0^4 - 2*x^22*z0^3 - 2*x^21*z0^4 - 2*x^23*z0 - x^22*z0^2 + 2*x^20*z0^4 + x^22*z0 - x^21*z0^2 - 2*x^19*z0^4 + x^22 + 2*x^21*z0 - 2*x^20*z0^2 + x^21 + 2*x^20*z0 - x^20 + 2*x^19 + x^7) * dx, - (-x^23*z0^4 - 2*x^22*z0^4 - 2*x^23*z0^2 - x^22*z0^3 + x^22*z0^2 - x^21*z0^3 - 2*x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 + x^21*z0 + 2*x^20*z0^2 - x^21 - x^20*z0 + x^20 + 2*x^19*z0 - x^19 + x^7*z0) * dx, - (-2*x^23*z0^3 - x^22*z0^4 + x^22*z0^3 - x^21*z0^4 - 2*x^23*z0 - 2*x^22*z0^2 + 2*x^21*z0^3 - 2*x^20*z0^4 - x^22*z0 + x^21*z0^2 + 2*x^20*z0^3 + x^22 - 2*x^21*z0 - x^20*z0^2 + 2*x^21 + 2*x^20*z0 + 2*x^19*z0^2 + x^20 - 2*x^19*z0 + x^19 + x^7*z0^2) * dx, - (-2*x^23*z0^4 + x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 - x^22*z0^2 + x^21*z0^3 + 2*x^20*z0^4 + 2*x^22*z0 - 2*x^21*z0^2 - x^20*z0^3 + x^22 - x^21*z0 + 2*x^20*z0^2 + 2*x^19*z0^3 + x^21 + x^20*z0 - 2*x^19*z0^2 - 2*x^20 - x^19*z0 + 2*x^19 + x^7*z0^3) * dx, - (-2*x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 - x^22*z0^3 + x^21*z0^4 + x^23*z0 + 2*x^22*z0^2 - 2*x^21*z0^3 - x^20*z0^4 - x^22*z0 - x^21*z0^2 + 2*x^20*z0^3 + 2*x^19*z0^4 + 2*x^22 + x^21*z0 + x^20*z0^2 - 2*x^19*z0^3 - x^21 + 2*x^20*z0 - x^19*z0^2 + x^20 + 2*x^19 + x^7*z0^4) * dx, - ((-x^23*z0^3 + 2*x^22*z0^4 - 2*x^22*z0^3 - 2*x^23*z0 - x^22*z0^2 + x^22*z0 - x^21*z0^2 + 2*x^19*z0^4 + x^22 + 2*x^21*z0 - 2*x^20*z0^2 + x^21 + 2*x^20*z0 - x^20 + x^7)/y) * dx, - ((-2*x^23*z0^4 - x^22*z0^4 - 2*x^23*z0^2 - x^22*z0^3 - x^21*z0^4 + x^22*z0^2 - x^21*z0^3 + x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 - 2*x^19*z0^4 + x^21*z0 + 2*x^20*z0^2 - x^21 - x^20*z0 + x^20 + 2*x^19*z0 + x^7*z0)/y) * dx, - ((x^23*z0^4 - 2*x^23*z0^3 - 2*x^22*z0^4 + x^22*z0^3 - 2*x^23*z0 - 2*x^22*z0^2 + 2*x^21*z0^3 + 2*x^20*z0^4 - x^22*z0 + x^21*z0^2 + 2*x^20*z0^3 + 2*x^19*z0^4 + x^22 - 2*x^21*z0 - x^20*z0^2 + 2*x^21 + 2*x^20*z0 + 2*x^19*z0^2 + x^20 - 2*x^19*z0 + x^7*z0^2)/y) * dx, - ((2*x^23*z0^4 - x^23*z0^3 + 2*x^22*z0^4 - 2*x^23*z0^2 - x^22*z0^3 + x^21*z0^4 - 2*x^23*z0 - x^22*z0^2 + x^20*z0^4 + 2*x^22*z0 - 2*x^21*z0^2 + x^19*z0^4 + x^22 - x^21*z0 + 2*x^20*z0^2 + x^21 + x^20*z0 - 2*x^19*z0^2 - x^19*z0 + x^7*z0^3)/y) * dx, - ((-x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 + x^21*z0^4 + x^23*z0 + 2*x^22*z0^2 - x^21*z0^3 + x^20*z0^4 - x^22*z0 - x^21*z0^2 + x^20*z0^3 - x^19*z0^4 + 2*x^22 + x^21*z0 + x^20*z0^2 - x^21 + 2*x^20*z0 - x^19*z0^2 - x^20 + x^7*z0^4)/y) * dx, - (-x^23*z0^4 + 2*x^23*z0^3 - 2*x^22*z0^4 + x^23*z0^2 + x^22*z0^3 + 2*x^21*z0^4 + x^23*z0 + 2*x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 + 2*x^22*z0 + x^20*z0^3 + 2*x^19*z0^4 + 2*x^22 + 2*x^21*z0 - 2*x^20*z0^2 - x^19*z0^3 - 2*x^21 - x^19*z0^2 - 2*x^20 + 2*x^19*z0 - 2*x^19 + x^8) * dx, - (2*x^23*z0^4 + x^23*z0^3 + x^22*z0^4 + x^23*z0^2 + 2*x^22*z0^3 - x^21*z0^4 + 2*x^23*z0 + 2*x^22*z0^2 + x^20*z0^4 + 2*x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 - x^19*z0^4 - x^22 - 2*x^21*z0 - x^19*z0^3 + x^21 - 2*x^20*z0 + 2*x^19*z0^2 - x^20 - 2*x^19*z0 + x^19 + x^8*z0) * dx, - (x^23*z0^4 + x^23*z0^3 + 2*x^22*z0^4 + 2*x^23*z0^2 + 2*x^22*z0^3 - x^23*z0 + 2*x^22*z0^2 + 2*x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 - 2*x^21*z0^2 - x^19*z0^4 - 2*x^22 + 2*x^21*z0 - 2*x^20*z0^2 + 2*x^19*z0^3 - 2*x^20*z0 - 2*x^19*z0^2 + 2*x^20 + 2*x^19*z0 + x^19 + x^8*z0^2) * dx, - (x^23*z0^4 + 2*x^23*z0^3 + 2*x^22*z0^4 - x^23*z0^2 + 2*x^22*z0^3 + 2*x^21*z0^4 + x^23*z0 - 2*x^22*z0^2 - 2*x^21*z0^3 + 2*x^21*z0^2 - 2*x^20*z0^3 + 2*x^19*z0^4 + 2*x^22 - 2*x^20*z0^2 - 2*x^19*z0^3 + 2*x^21 + 2*x^19*z0^2 - 2*x^20 - 2*x^19 + x^8*z0^3) * dx, - (2*x^23*z0^4 - x^23*z0^3 + 2*x^22*z0^4 + x^23*z0^2 - 2*x^22*z0^3 - 2*x^21*z0^4 - 2*x^23*z0 + 2*x^21*z0^3 - 2*x^20*z0^4 + 2*x^22*z0 - 2*x^20*z0^3 - 2*x^19*z0^4 + x^22 + x^21*z0 + 2*x^19*z0^3 - x^21 + x^20*z0 - x^20 + 2*x^19*z0 + 2*x^19 + x^8*z0^4) * dx, - ((x^23*z0^4 + x^22*z0^4 + x^23*z0^2 - 2*x^22*z0^3 - x^21*z0^4 + x^23*z0 + 2*x^22*z0^2 + 2*x^21*z0^3 + 2*x^20*z0^4 + 2*x^22*z0 - 2*x^20*z0^3 + 2*x^19*z0^4 + 2*x^22 + 2*x^21*z0 - 2*x^20*z0^2 - 2*x^21 - x^19*z0^2 + 2*x^20 + 2*x^19*z0 + x^8)/y) * dx, - ((2*x^23*z0^4 - x^23*z0^3 + x^22*z0^4 + x^23*z0^2 - x^22*z0^3 - x^21*z0^4 + 2*x^23*z0 + 2*x^22*z0^2 - 2*x^21*z0^3 + 2*x^20*z0^4 + 2*x^22*z0 + 2*x^21*z0^2 - x^22 - 2*x^21*z0 + x^21 - 2*x^20*z0 + 2*x^19*z0^2 - 2*x^20 - 2*x^19*z0 + x^8*z0)/y) * dx, - ((-x^23*z0^4 - x^22*z0^4 + 2*x^23*z0^2 - 2*x^22*z0^3 - 2*x^21*z0^4 - x^23*z0 + 2*x^22*z0^2 + x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 - 2*x^21*z0^2 + x^20*z0^3 - 2*x^19*z0^4 - 2*x^22 + 2*x^21*z0 - 2*x^20*z0^2 - 2*x^20*z0 - 2*x^19*z0^2 - x^20 + 2*x^19*z0 + x^8*z0^2)/y) * dx, - ((2*x^23*z0^4 - 2*x^23*z0^3 + x^22*z0^4 - x^23*z0^2 + x^22*z0^3 - 2*x^21*z0^4 + x^23*z0 - 2*x^22*z0^2 - x^21*z0^3 + x^20*z0^4 + 2*x^21*z0^2 + 2*x^20*z0^3 + x^19*z0^4 + 2*x^22 - 2*x^20*z0^2 + 2*x^21 + 2*x^19*z0^2 + x^20 + x^8*z0^3)/y) * dx, - ((x^23*z0^4 - 2*x^23*z0^3 - 2*x^22*z0^4 + x^23*z0^2 - x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 + x^21*z0^3 + 2*x^20*z0^4 + 2*x^22*z0 - x^20*z0^3 - x^19*z0^4 + x^22 + x^21*z0 - x^21 + x^20*z0 + x^20 + 2*x^19*z0 + x^8*z0^4)/y) * dx, - (2*x^23*z0^4 - 2*x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 + 2*x^22*z0^3 + 2*x^21*z0^4 - x^22*z0^2 - 2*x^21*z0^3 - 2*x^20*z0^4 - x^22*z0 - x^21*z0^2 + 2*x^20*z0^3 - x^19*z0^4 - 2*x^21*z0 - 2*x^20*z0^2 + 2*x^19*z0^3 + x^21 - x^20*z0 + x^19*z0^2 + 2*x^19 + x^9) * dx, - (-2*x^23*z0^4 - 2*x^23*z0^3 + 2*x^22*z0^4 - x^22*z0^3 - 2*x^21*z0^4 - x^22*z0^2 - x^21*z0^3 + 2*x^20*z0^4 - 2*x^21*z0^2 - 2*x^20*z0^3 + 2*x^19*z0^4 + x^21*z0 - x^20*z0^2 + x^19*z0^3 - x^19*z0 + x^9*z0) * dx, - (-2*x^23*z0^4 - x^22*z0^4 - x^22*z0^3 - x^21*z0^4 - x^23*z0 - 2*x^21*z0^3 - 2*x^20*z0^4 + x^22*z0 + x^21*z0^2 - x^20*z0^3 + x^19*z0^4 - 2*x^22 - x^21*z0 - x^21 + x^20*z0 - x^19*z0^2 - x^20 - 2*x^19*z0 - 2*x^19 + x^9*z0^2) * dx, - (-x^22*z0^4 - x^23*z0^2 - 2*x^21*z0^4 + 2*x^23*z0 + x^22*z0^2 + x^21*z0^3 - x^20*z0^4 - 2*x^22*z0 - x^21*z0^2 - x^22 + 2*x^21*z0 + x^20*z0^2 - x^19*z0^3 + x^21 - 2*x^20*z0 - 2*x^19*z0^2 - 2*x^19*z0 - 2*x^19 + x^9*z0^3) * dx, - (-x^23*z0^3 + 2*x^23*z0^2 + x^22*z0^3 + x^21*z0^4 - 2*x^22*z0^2 - x^21*z0^3 - 2*x^22*z0 + 2*x^21*z0^2 + x^20*z0^3 - x^19*z0^4 - x^21*z0 - 2*x^20*z0^2 - 2*x^19*z0^3 - 2*x^21 - x^20*z0 - 2*x^19*z0^2 - 2*x^20 - 2*x^19*z0 + x^9*z0^4) * dx, - ((x^23*z0^4 + 2*x^23*z0^3 - x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 + x^21*z0^4 - x^22*z0^2 + 2*x^21*z0^3 + 2*x^20*z0^4 - x^22*z0 - x^21*z0^2 - 2*x^20*z0^3 - 2*x^21*z0 - 2*x^20*z0^2 + x^21 - x^20*z0 + x^19*z0^2 + 2*x^20 + x^9)/y) * dx, - ((-x^23*z0^4 + x^22*z0^4 + 2*x^22*z0^3 - x^21*z0^4 - x^22*z0^2 + x^21*z0^3 - 2*x^21*z0^2 + x^20*z0^3 - 2*x^19*z0^4 + x^21*z0 - x^20*z0^2 + x^20 - x^19*z0 + x^9*z0)/y) * dx, - ((x^23*z0^4 + x^22*z0^4 - x^22*z0^3 + 2*x^21*z0^4 - x^23*z0 - 2*x^21*z0^3 + x^22*z0 + x^21*z0^2 - x^20*z0^3 + 2*x^19*z0^4 - 2*x^22 - x^21*z0 - x^21 + x^20*z0 - x^19*z0^2 - x^20 - 2*x^19*z0 + x^9*z0^2)/y) * dx, - ((2*x^23*z0^4 - 2*x^23*z0^3 + 2*x^22*z0^4 - x^23*z0^2 + 2*x^22*z0^3 + 2*x^23*z0 + x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 - x^21*z0^2 + 2*x^20*z0^3 - x^22 + 2*x^21*z0 + x^20*z0^2 + x^21 - 2*x^20*z0 - 2*x^19*z0^2 - x^20 - 2*x^19*z0 + x^9*z0^3)/y) * dx, - ((-2*x^23*z0^4 + 2*x^22*z0^4 + 2*x^23*z0^2 - x^21*z0^4 - 2*x^22*z0^2 - x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 + 2*x^19*z0^4 - x^21*z0 - 2*x^20*z0^2 - 2*x^21 - x^20*z0 - 2*x^19*z0^2 + x^20 - 2*x^19*z0 + x^9*z0^4)/y) * dx, - (-2*x^23*z0^4 - 2*x^23*z0^3 + 2*x^22*z0^4 - 2*x^23*z0^2 + 2*x^22*z0^3 - 2*x^21*z0^4 - 2*x^23*z0 - 2*x^21*z0^3 - x^20*z0^4 - x^22*z0 + 2*x^21*z0^2 + x^20*z0^3 - 2*x^19*z0^4 + x^22 - 2*x^21*z0 + 2*x^20*z0^2 - x^19*z0^3 + x^20*z0 + 2*x^20 - 2*x^19*z0 + x^10) * dx, - (-2*x^23*z0^4 - 2*x^23*z0^3 + 2*x^22*z0^4 - 2*x^23*z0^2 - 2*x^21*z0^4 - x^22*z0^2 + 2*x^21*z0^3 + x^20*z0^4 + x^22*z0 - 2*x^21*z0^2 + 2*x^20*z0^3 - x^19*z0^4 + x^20*z0^2 - x^20*z0 - 2*x^19*z0^2 - x^19 + x^10*z0) * dx, - (-2*x^23*z0^4 - 2*x^23*z0^3 - x^22*z0^3 + 2*x^21*z0^4 + x^23*z0 + x^22*z0^2 - 2*x^21*z0^3 + 2*x^20*z0^4 - x^22*z0 + x^20*z0^3 + 2*x^22 + x^21*z0 - x^20*z0^2 - 2*x^19*z0^3 + x^21 - 2*x^20*z0 + x^20 + x^19*z0 + x^10*z0^2) * dx, - (-2*x^23*z0^4 - x^22*z0^4 + x^23*z0^2 + x^22*z0^3 - 2*x^21*z0^4 - x^22*z0^2 + x^20*z0^4 + x^21*z0^2 - x^20*z0^3 - 2*x^19*z0^4 - 2*x^20*z0^2 + x^21 + x^20*z0 + x^19*z0^2 + 2*x^20 + 2*x^19*z0 - 2*x^19 + x^10*z0^3) * dx, - (x^23*z0^3 + x^22*z0^4 - x^22*z0^3 - x^23*z0 + x^21*z0^3 - x^20*z0^4 - 2*x^22*z0 - 2*x^20*z0^3 - 2*x^22 + x^20*z0^2 + x^19*z0^3 - 2*x^21 + 2*x^20*z0 + 2*x^19*z0^2 + 2*x^19*z0 + x^10*z0^4) * dx, - ((2*x^23*z0^4 + x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 - x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 + x^21*z0^3 + x^20*z0^4 - x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 + 2*x^19*z0^4 + x^22 - 2*x^21*z0 + 2*x^20*z0^2 + x^20*z0 + x^20 - 2*x^19*z0 + x^10)/y) * dx, - ((2*x^23*z0^4 - 2*x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 + 2*x^21*z0^4 - x^22*z0^2 + 2*x^21*z0^3 + 2*x^20*z0^4 + x^22*z0 - 2*x^21*z0^2 + 2*x^20*z0^3 + 2*x^19*z0^4 + x^20*z0^2 - x^20*z0 - 2*x^19*z0^2 + x^10*z0)/y) * dx, - ((x^23*z0^4 - x^23*z0^3 + 2*x^22*z0^4 - 2*x^22*z0^3 + x^23*z0 + x^22*z0^2 - x^21*z0^3 + x^20*z0^4 - x^22*z0 - 2*x^19*z0^4 + 2*x^22 + x^21*z0 - x^20*z0^2 + x^21 - 2*x^20*z0 - x^20 + x^19*z0 + x^10*z0^2)/y) * dx, - ((x^23*z0^4 + x^22*z0^4 + x^23*z0^2 + x^22*z0^3 + x^21*z0^4 - x^22*z0^2 - 2*x^20*z0^4 + x^21*z0^2 - x^20*z0^3 - x^19*z0^4 - 2*x^20*z0^2 + x^21 + x^20*z0 + x^19*z0^2 + 2*x^20 + 2*x^19*z0 + x^10*z0^3)/y) * dx, - ((x^23*z0^4 - 2*x^23*z0^3 + 2*x^22*z0^3 + x^21*z0^4 - x^23*z0 - 2*x^21*z0^3 + 2*x^20*z0^4 - 2*x^22*z0 + x^20*z0^3 + x^19*z0^4 - 2*x^22 + x^20*z0^2 - 2*x^21 + 2*x^20*z0 + 2*x^19*z0^2 + x^20 + 2*x^19*z0 + x^10*z0^4)/y) * dx, - (2*x^23*z0^4 + x^23*z0^3 - 2*x^22*z0^4 - x^23*z0^2 - x^22*z0^3 - x^21*z0^4 - 2*x^23*z0 - 2*x^22*z0^2 - 2*x^20*z0^4 - x^22*z0 + x^21*z0^2 + 2*x^19*z0^4 + x^22 + x^20*z0^2 + x^21 - x^20*z0 + x^20 - 2*x^19 + x^11) * dx, - (x^23*z0^4 - x^23*z0^3 - x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 - x^22*z0^2 + x^21*z0^3 + x^22*z0 + x^20*z0^3 - 2*x^21*z0 - x^20*z0^2 + x^20*z0 - x^20 - 2*x^19*z0 + x^19 + x^11*z0) * dx, - (-x^23*z0^4 - 2*x^23*z0^3 - 2*x^22*z0^4 - x^22*z0^3 + x^21*z0^4 - x^23*z0 + x^22*z0^2 + x^20*z0^4 + x^22*z0 - 2*x^21*z0^2 - x^20*z0^3 - 2*x^22 - 2*x^21*z0 + x^20*z0^2 - x^21 + x^20*z0 - 2*x^19*z0^2 + 2*x^20 - x^19*z0 + 2*x^19 + x^11*z0^2) * dx, - (-2*x^23*z0^4 - x^22*z0^4 - x^23*z0^2 + x^22*z0^3 - 2*x^23*z0 + x^22*z0^2 - 2*x^21*z0^3 - x^20*z0^4 + 2*x^22*z0 - 2*x^21*z0^2 + x^20*z0^3 + x^22 - x^21*z0 + x^20*z0^2 - 2*x^19*z0^3 + 2*x^21 - x^20*z0 - x^19*z0^2 - 2*x^20 + x^19*z0 + x^19 + x^11*z0^3) * dx, - (-x^23*z0^3 + x^22*z0^4 - 2*x^23*z0^2 + x^22*z0^3 - 2*x^21*z0^4 - 2*x^23*z0 + 2*x^22*z0^2 - 2*x^21*z0^3 + x^20*z0^4 - x^21*z0^2 + x^20*z0^3 - 2*x^19*z0^4 + x^22 + 2*x^21*z0 - x^20*z0^2 - x^19*z0^3 + 2*x^21 + 2*x^20*z0 + x^19*z0^2 - 2*x^20 + x^19*z0 + x^11*z0^4) * dx, - ((x^23*z0^3 - x^23*z0^2 - x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 - 2*x^22*z0^2 - x^22*z0 + x^21*z0^2 - 2*x^19*z0^4 + x^22 + x^20*z0^2 + x^21 - x^20*z0 + x^20 + x^11)/y) * dx, - ((2*x^23*z0^4 - x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 + x^21*z0^4 - x^22*z0^2 + x^21*z0^3 - x^20*z0^4 + x^22*z0 + x^20*z0^3 + 2*x^19*z0^4 - 2*x^21*z0 - x^20*z0^2 + x^20*z0 - x^20 - 2*x^19*z0 + x^11*z0)/y) * dx, - ((x^23*z0^4 - 2*x^23*z0^3 + x^22*z0^4 - x^22*z0^3 - 2*x^21*z0^4 - x^23*z0 + x^22*z0^2 - x^20*z0^4 + x^22*z0 - 2*x^21*z0^2 - x^20*z0^3 - x^19*z0^4 - 2*x^22 - 2*x^21*z0 + x^20*z0^2 - x^21 + x^20*z0 - 2*x^19*z0^2 + 2*x^20 - x^19*z0 + x^11*z0^2)/y) * dx, - ((2*x^23*z0^4 + x^23*z0^3 - x^23*z0^2 - x^21*z0^4 - 2*x^23*z0 + x^22*z0^2 - x^21*z0^3 + 2*x^20*z0^4 + 2*x^22*z0 - 2*x^21*z0^2 + x^22 - x^21*z0 + x^20*z0^2 + 2*x^21 - x^20*z0 - x^19*z0^2 + x^20 + x^19*z0 + x^11*z0^3)/y) * dx, - ((-x^23*z0^4 + 2*x^23*z0^3 + 2*x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 + 2*x^22*z0^2 + x^21*z0^3 - 2*x^20*z0^4 - x^21*z0^2 - 2*x^20*z0^3 + 2*x^19*z0^4 + x^22 + 2*x^21*z0 - x^20*z0^2 + 2*x^21 + 2*x^20*z0 + x^19*z0^2 + 2*x^20 + x^19*z0 + x^11*z0^4)/y) * dx, - (-2*x^23*z0^4 - x^22*z0^4 + x^23*z0^2 - x^22*z0^3 - 2*x^21*z0^4 + x^23*z0 - 2*x^22*z0^2 + x^21*z0^3 + 2*x^20*z0^4 - 2*x^22*z0 - x^21*z0^2 - x^20*z0^3 - 2*x^19*z0^4 + 2*x^22 + x^21*z0 + 2*x^20*z0^2 + x^19*z0^3 - 2*x^20*z0 + 2*x^19*z0^2 - x^20 + x^19*z0 - 2*x^19 + x^12) * dx, - (x^23*z0^3 - x^22*z0^4 + x^23*z0^2 - 2*x^22*z0^3 + x^21*z0^4 - 2*x^22*z0^2 - x^21*z0^3 - x^20*z0^4 - x^22*z0 + x^21*z0^2 + 2*x^20*z0^3 + x^19*z0^4 - 2*x^20*z0^2 + 2*x^19*z0^3 - x^21 - x^20*z0 + x^19*z0^2 + x^20 - 2*x^19*z0 - x^19 + x^12*z0) * dx, - (x^23*z0^4 + x^23*z0^3 - 2*x^22*z0^4 - 2*x^22*z0^3 - x^21*z0^4 + x^23*z0 - x^22*z0^2 + x^21*z0^3 + 2*x^20*z0^4 - 2*x^22*z0 - 2*x^20*z0^3 + 2*x^19*z0^4 + 2*x^22 + x^21*z0 - x^20*z0^2 + x^19*z0^3 - x^21 - x^20*z0 - 2*x^19*z0^2 + x^19*z0 + x^19 + x^12*z0^2) * dx, - (x^23*z0^4 - 2*x^22*z0^4 + x^23*z0^2 - x^22*z0^3 + x^21*z0^4 - x^23*z0 - 2*x^22*z0^2 - 2*x^20*z0^4 + 2*x^22*z0 + x^21*z0^2 - x^20*z0^3 + x^19*z0^4 - 2*x^22 + x^21*z0 - x^20*z0^2 - 2*x^19*z0^3 + 2*x^21 - x^20*z0 + x^19*z0^2 + 2*x^20 + x^19*z0 + x^19 + x^12*z0^3) * dx, - (x^23*z0^3 - x^22*z0^4 - x^23*z0^2 - 2*x^22*z0^3 - x^23*z0 + 2*x^22*z0^2 + x^21*z0^3 - x^20*z0^4 - 2*x^22*z0 + x^21*z0^2 - x^20*z0^3 - 2*x^19*z0^4 - 2*x^22 + x^21*z0 - x^20*z0^2 + x^19*z0^3 + 2*x^21 + 2*x^20*z0 + x^19*z0^2 + x^20 - x^19 + x^12*z0^4) * dx, - ((2*x^23*z0^4 + 2*x^23*z0^3 + x^23*z0^2 + 2*x^22*z0^3 + 2*x^21*z0^4 + x^23*z0 - 2*x^22*z0^2 - 2*x^21*z0^3 + 2*x^20*z0^4 - 2*x^22*z0 - x^21*z0^2 + 2*x^20*z0^3 + 2*x^22 + x^21*z0 + 2*x^20*z0^2 - 2*x^20*z0 + 2*x^19*z0^2 + x^19*z0 + x^12)/y) * dx, - ((x^23*z0^4 - 2*x^22*z0^4 + x^23*z0^2 - x^22*z0^3 + 2*x^21*z0^4 - 2*x^22*z0^2 - 2*x^21*z0^3 + x^20*z0^4 - x^22*z0 + x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 - 2*x^20*z0^2 - x^21 - x^20*z0 + x^19*z0^2 - 2*x^20 - 2*x^19*z0 + x^12*z0)/y) * dx, - ((-2*x^23*z0^4 - 2*x^23*z0^3 + x^22*z0^4 + x^22*z0^3 + x^21*z0^4 + x^23*z0 - x^22*z0^2 - 2*x^21*z0^3 - x^20*z0^4 - 2*x^22*z0 + x^20*z0^3 + 2*x^22 + x^21*z0 - x^20*z0^2 - x^21 - x^20*z0 - 2*x^19*z0^2 + x^20 + x^19*z0 + x^12*z0^2)/y) * dx, - ((x^23*z0^3 - x^22*z0^4 + x^23*z0^2 - 2*x^22*z0^3 - x^23*z0 - 2*x^22*z0^2 + x^21*z0^3 + x^20*z0^4 + 2*x^22*z0 + x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 - 2*x^22 + x^21*z0 - x^20*z0^2 + 2*x^21 - x^20*z0 + x^19*z0^2 + x^19*z0 + x^12*z0^3)/y) * dx, - ((-2*x^23*z0^3 - x^22*z0^4 - x^23*z0^2 + x^22*z0^3 - x^23*z0 + 2*x^22*z0^2 - 2*x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 + x^21*z0^2 + 2*x^20*z0^3 + 2*x^19*z0^4 - 2*x^22 + x^21*z0 - x^20*z0^2 + 2*x^21 + 2*x^20*z0 + x^19*z0^2 + 2*x^20 + x^12*z0^4)/y) * dx, - (-x^23*z0^4 - 2*x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 + 2*x^22*z0^3 + 2*x^21*z0^4 + x^23*z0 - x^22*z0^2 - 2*x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 + 2*x^20*z0^3 + 2*x^19*z0^4 + 2*x^22 + x^21*z0 + 2*x^20*z0^2 - 2*x^19*z0^3 + 2*x^21 - 2*x^20*z0 - x^19*z0^2 + x^19 + x^13) * dx, - (-2*x^23*z0^4 - 2*x^23*z0^3 + 2*x^22*z0^4 + x^23*z0^2 - x^22*z0^3 - 2*x^21*z0^4 + 2*x^23*z0 - 2*x^22*z0^2 + 2*x^21*z0^3 + 2*x^20*z0^4 + 2*x^22*z0 + x^21*z0^2 + 2*x^20*z0^3 - 2*x^19*z0^4 - x^22 + 2*x^21*z0 - 2*x^20*z0^2 - x^19*z0^3 + x^21 - x^20 + x^19*z0 + x^19 + x^13*z0) * dx, - (-2*x^23*z0^4 + x^23*z0^3 - x^22*z0^4 + 2*x^23*z0^2 - 2*x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 + 2*x^22*z0^2 + x^21*z0^3 + 2*x^20*z0^4 + x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 - x^19*z0^4 + x^22 - x^21*z0 - 2*x^21 + x^20*z0 + x^19*z0^2 - 2*x^20 - x^19*z0 + x^19 + x^13*z0^2) * dx, - (x^23*z0^4 + 2*x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 + 2*x^22*z0^3 + x^21*z0^4 + x^22*z0^2 + 2*x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 - x^21*z0^2 + 2*x^21*z0 + x^20*z0^2 + x^19*z0^3 - x^21 - 2*x^20*z0 - x^19*z0^2 - x^20 + 2*x^19*z0 + x^19 + x^13*z0^3) * dx, - (2*x^23*z0^4 - 2*x^23*z0^3 + 2*x^22*z0^4 + x^22*z0^3 + 2*x^21*z0^4 - 2*x^22*z0^2 - x^21*z0^3 - x^22*z0 + 2*x^21*z0^2 + x^20*z0^3 + x^19*z0^4 - x^21*z0 - 2*x^20*z0^2 - x^19*z0^3 - 2*x^21 - 2*x^20*z0 + 2*x^19*z0^2 + 2*x^20 + x^19 + x^13*z0^4) * dx, - ((-2*x^23*z0^4 - x^23*z0^3 - x^22*z0^4 - 2*x^23*z0^2 + x^22*z0^3 + x^21*z0^4 + x^23*z0 - x^22*z0^2 - x^21*z0^3 + x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 + x^20*z0^3 + 2*x^19*z0^4 + 2*x^22 + x^21*z0 + 2*x^20*z0^2 + 2*x^21 - 2*x^20*z0 - x^19*z0^2 - 2*x^20 + x^13)/y) * dx, - ((-2*x^23*z0^4 + x^23*z0^3 + 2*x^22*z0^4 + x^23*z0^2 + x^22*z0^3 - 2*x^21*z0^4 + 2*x^23*z0 - 2*x^22*z0^2 - 2*x^20*z0^4 + 2*x^22*z0 + x^21*z0^2 - x^20*z0^3 - x^19*z0^4 - x^22 + 2*x^21*z0 - 2*x^20*z0^2 + x^21 - 2*x^20 + x^19*z0 + x^13*z0)/y) * dx, - ((-x^23*z0^4 + x^23*z0^3 - 2*x^22*z0^4 + 2*x^23*z0^2 - 2*x^22*z0^3 - 2*x^21*z0^4 - 2*x^23*z0 + 2*x^22*z0^2 + x^21*z0^3 + x^20*z0^4 + x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 + x^22 - x^21*z0 - 2*x^21 + x^20*z0 + x^19*z0^2 - 2*x^20 - x^19*z0 + x^13*z0^2)/y) * dx, - ((-2*x^23*z0^4 - x^23*z0^3 + x^22*z0^4 - 2*x^23*z0^2 - 2*x^21*z0^4 + x^22*z0^2 - x^21*z0^3 - 2*x^22*z0 - x^21*z0^2 - 2*x^20*z0^3 - 2*x^19*z0^4 + 2*x^21*z0 + x^20*z0^2 - x^21 - 2*x^20*z0 - x^19*z0^2 + 2*x^19*z0 + x^13*z0^3)/y) * dx, - ((2*x^23*z0^4 + x^23*z0^3 + 2*x^22*z0^4 - 2*x^22*z0^3 + 2*x^21*z0^4 - 2*x^22*z0^2 + 2*x^21*z0^3 + x^20*z0^4 - x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 + 2*x^19*z0^4 - x^21*z0 - 2*x^20*z0^2 - 2*x^21 - 2*x^20*z0 + 2*x^19*z0^2 + x^20 + x^13*z0^4)/y) * dx, - (-x^23*z0^4 - x^23*z0^3 + x^22*z0^4 - 2*x^23*z0^2 + x^22*z0^3 - x^21*z0^4 + 2*x^23*z0 - 2*x^22*z0^2 - x^21*z0^3 + x^20*z0^4 + 2*x^22*z0 + x^21*z0^2 + x^20*z0^3 - 2*x^19*z0^4 - x^22 + 2*x^21*z0 + x^19*z0^3 - 2*x^21 + x^20*z0 - 2*x^20 + 2*x^19*z0 + x^14) * dx, - (-x^23*z0^4 - 2*x^23*z0^3 + x^22*z0^4 + 2*x^23*z0^2 - 2*x^22*z0^3 - x^21*z0^4 + 2*x^22*z0^2 + x^21*z0^3 + x^20*z0^4 - x^22*z0 + 2*x^21*z0^2 + x^19*z0^4 - 2*x^21*z0 + x^20*z0^2 - 2*x^20*z0 + 2*x^19*z0^2 - x^19*z0 + x^14*z0) * dx, - (-2*x^23*z0^4 + 2*x^23*z0^3 - 2*x^22*z0^4 + 2*x^22*z0^3 + x^21*z0^4 + 2*x^23*z0 - x^22*z0^2 + 2*x^21*z0^3 - 2*x^22*z0 - 2*x^21*z0^2 + x^20*z0^3 - x^22 + 2*x^21*z0 - 2*x^20*z0^2 + 2*x^19*z0^3 + 2*x^21 - 2*x^20*z0 - x^19*z0^2 + 2*x^20 - x^19*z0 - x^19 + x^14*z0^2) * dx, - (2*x^23*z0^4 + 2*x^22*z0^4 + 2*x^23*z0^2 - x^22*z0^3 + 2*x^21*z0^4 + 2*x^23*z0 - 2*x^22*z0^2 - 2*x^21*z0^3 + x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 + 2*x^19*z0^4 - x^22 + 2*x^21*z0 - 2*x^20*z0^2 - x^19*z0^3 - x^21 - 2*x^20*z0 - x^19*z0^2 + x^20 - 2*x^19*z0 + x^19 + x^14*z0^3) * dx, - (2*x^23*z0^3 - x^22*z0^4 + 2*x^23*z0^2 - 2*x^22*z0^3 - 2*x^21*z0^4 - x^23*z0 - 2*x^22*z0^2 + 2*x^21*z0^3 - 2*x^20*z0^4 - x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 - x^19*z0^4 - 2*x^22 - 2*x^21*z0 - 2*x^20*z0^2 - x^19*z0^3 + 2*x^21 - 2*x^19*z0^2 + x^20 + 2*x^19 + x^14*z0^4) * dx, - ((x^23*z0^3 - 2*x^23*z0^2 - x^22*z0^3 + 2*x^23*z0 - 2*x^22*z0^2 + x^21*z0^3 - x^20*z0^4 + 2*x^22*z0 + x^21*z0^2 - x^20*z0^3 - x^19*z0^4 - x^22 + 2*x^21*z0 - 2*x^21 + x^20*z0 - x^20 + 2*x^19*z0 + x^14)/y) * dx, - ((-x^23*z0^4 - 2*x^23*z0^3 + x^22*z0^4 + 2*x^23*z0^2 - 2*x^22*z0^3 - x^21*z0^4 + 2*x^22*z0^2 + x^21*z0^3 + x^20*z0^4 - x^22*z0 + 2*x^21*z0^2 + x^19*z0^4 - 2*x^21*z0 + x^20*z0^2 - 2*x^20*z0 + 2*x^19*z0^2 - x^19*z0 + x^14*z0)/y) * dx, - ((-x^23*z0^4 + x^23*z0^3 + 2*x^22*z0^4 - 2*x^22*z0^3 + 2*x^21*z0^4 + 2*x^23*z0 - x^22*z0^2 + x^21*z0^3 + 2*x^20*z0^4 - 2*x^22*z0 - 2*x^21*z0^2 + 2*x^20*z0^3 - x^22 + 2*x^21*z0 - 2*x^20*z0^2 + 2*x^21 - 2*x^20*z0 - x^19*z0^2 - x^20 - x^19*z0 + x^14*z0^2)/y) * dx, - ((2*x^23*z0^4 - 2*x^23*z0^3 + 2*x^22*z0^4 + 2*x^23*z0^2 + x^22*z0^3 + 2*x^21*z0^4 + 2*x^23*z0 - 2*x^22*z0^2 + x^21*z0^3 + 2*x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 - 2*x^19*z0^4 - x^22 + 2*x^21*z0 - 2*x^20*z0^2 - x^21 - 2*x^20*z0 - x^19*z0^2 - 2*x^19*z0 + x^14*z0^3)/y) * dx, - ((x^23*z0^4 - 2*x^22*z0^4 + 2*x^23*z0^2 - x^21*z0^4 - x^23*z0 - 2*x^22*z0^2 - 2*x^20*z0^4 - x^22*z0 + 2*x^21*z0^2 + 2*x^19*z0^4 - 2*x^22 - 2*x^21*z0 - 2*x^20*z0^2 + 2*x^21 - 2*x^19*z0^2 + x^14*z0^4)/y) * dx, - (x^23*z0^4 - 2*x^23*z0^3 - x^22*z0^4 + 2*x^22*z0^3 + x^21*z0^4 + x^23*z0 - x^22*z0^2 - 2*x^21*z0^3 - 2*x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 - x^20*z0^3 + x^19*z0^4 + 2*x^22 - 2*x^20*z0^2 - x^21 - 2*x^20*z0 + x^19*z0^2 - x^20 + x^19*z0 + 2*x^19 + x^15) * dx, - (-2*x^23*z0^4 + 2*x^22*z0^4 + x^23*z0^2 - x^22*z0^3 - 2*x^21*z0^4 - 2*x^22*z0^2 + 2*x^21*z0^3 - x^20*z0^4 + 2*x^22*z0 - 2*x^20*z0^3 - x^21*z0 - 2*x^20*z0^2 + x^19*z0^3 - 2*x^20*z0 + x^19*z0^2 + 2*x^19*z0 - 2*x^19 + x^15*z0) * dx, - (x^23*z0^3 - x^22*z0^4 - 2*x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 + 2*x^22*z0^2 - 2*x^20*z0^4 + 2*x^22*z0 - x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 + x^22 - 2*x^21*z0 - 2*x^20*z0^2 + x^19*z0^3 - 2*x^21 - x^20*z0 + 2*x^19*z0^2 - 2*x^20 - 2*x^19*z0 + x^15*z0^2) * dx, - (x^23*z0^4 - 2*x^22*z0^4 - 2*x^23*z0^2 + 2*x^22*z0^3 - x^23*z0 + 2*x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 + x^22*z0 - 2*x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 - 2*x^22 - x^21*z0 - x^20*z0^2 + 2*x^19*z0^3 + 2*x^21 + 2*x^20*z0 - 2*x^19*z0^2 - 2*x^19 + x^15*z0^3) * dx, - (-2*x^23*z0^3 + 2*x^22*z0^4 - x^23*z0^2 + 2*x^22*z0^3 - x^21*z0^4 + x^22*z0^2 - 2*x^21*z0^3 - 2*x^20*z0^4 + 2*x^22*z0 - x^21*z0^2 - x^20*z0^3 + 2*x^19*z0^4 + x^21*z0 + 2*x^20*z0^2 - 2*x^19*z0^3 - 2*x^21 - x^20*z0 - 2*x^19*z0 - 2*x^19 + x^15*z0^4) * dx, - ((-2*x^23*z0^4 - 2*x^23*z0^3 + 2*x^22*z0^4 + 2*x^22*z0^3 - 2*x^21*z0^4 + x^23*z0 - x^22*z0^2 - 2*x^21*z0^3 + x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 - x^20*z0^3 + 2*x^22 - 2*x^20*z0^2 - x^21 - 2*x^20*z0 + x^19*z0^2 - x^20 + x^19*z0 + x^15)/y) * dx, - ((2*x^23*z0^4 + 2*x^23*z0^3 - 2*x^22*z0^4 + x^23*z0^2 + 2*x^22*z0^3 + 2*x^21*z0^4 - 2*x^22*z0^2 - x^21*z0^3 - x^20*z0^4 + 2*x^22*z0 + x^20*z0^3 + 2*x^19*z0^4 - x^21*z0 - 2*x^20*z0^2 - 2*x^20*z0 + x^19*z0^2 + x^20 + 2*x^19*z0 + x^15*z0)/y) * dx, - ((x^23*z0^4 - 2*x^23*z0^3 - 2*x^22*z0^4 + x^22*z0^3 - 2*x^21*z0^4 - 2*x^23*z0 + 2*x^22*z0^2 + 2*x^21*z0^3 + x^20*z0^4 + 2*x^22*z0 - x^21*z0^2 + x^20*z0^3 + 2*x^19*z0^4 + x^22 - 2*x^21*z0 - 2*x^20*z0^2 - 2*x^21 - x^20*z0 + 2*x^19*z0^2 - x^20 - 2*x^19*z0 + x^15*z0^2)/y) * dx, - ((x^23*z0^4 - x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 - x^23*z0 + 2*x^22*z0^2 - 2*x^21*z0^3 + x^20*z0^4 + x^22*z0 - 2*x^21*z0^2 - x^20*z0^3 - x^19*z0^4 - 2*x^22 - x^21*z0 - x^20*z0^2 + 2*x^21 + 2*x^20*z0 - 2*x^19*z0^2 + 2*x^20 + x^15*z0^3)/y) * dx, - ((x^23*z0^4 - x^23*z0^3 + x^22*z0^4 - x^23*z0^2 + x^22*z0^3 + x^22*z0^2 - x^21*z0^3 - x^20*z0^4 + 2*x^22*z0 - x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 + x^21*z0 + 2*x^20*z0^2 - 2*x^21 - x^20*z0 - 2*x^20 - 2*x^19*z0 + x^15*z0^4)/y) * dx, - (-x^23*z0^4 + x^22*z0^4 - 2*x^23*z0^2 - 2*x^21*z0^4 - 2*x^23*z0 - 2*x^22*z0^2 + 2*x^21*z0^3 + x^20*z0^4 + 2*x^21*z0^2 + 2*x^20*z0^3 - x^19*z0^4 + x^22 - 2*x^21*z0 + 2*x^20*z0^2 - 2*x^19*z0^3 + 2*x^21 + x^20*z0 - 2*x^19*z0^2 - x^20 - x^19*z0 + x^19 + x^16) * dx, - (-2*x^23*z0^3 - 2*x^23*z0^2 - 2*x^22*z0^3 + 2*x^21*z0^4 + 2*x^21*z0^3 + 2*x^20*z0^4 + x^22*z0 - 2*x^21*z0^2 + 2*x^20*z0^3 - 2*x^19*z0^4 + x^21*z0 + x^20*z0^2 - 2*x^19*z0^3 - x^20*z0 - x^19*z0^2 - 2*x^20 + x^19*z0 + 2*x^19 + x^16*z0) * dx, - (-2*x^23*z0^4 - 2*x^23*z0^3 - 2*x^22*z0^4 + 2*x^21*z0^4 + 2*x^23*z0 + x^22*z0^2 - 2*x^21*z0^3 + 2*x^20*z0^4 - 2*x^22*z0 + x^21*z0^2 + x^20*z0^3 - 2*x^19*z0^4 - x^22 - x^21*z0 - x^20*z0^2 - x^19*z0^3 + 2*x^21 - 2*x^20*z0 + x^19*z0^2 + x^20 + 2*x^19*z0 - x^19 + x^16*z0^2) * dx, - (-2*x^23*z0^4 + 2*x^23*z0^2 + x^22*z0^3 - 2*x^21*z0^4 - 2*x^22*z0^2 + x^21*z0^3 + x^20*z0^4 - x^21*z0^2 - x^20*z0^3 - x^19*z0^4 + x^21*z0 - 2*x^20*z0^2 + x^19*z0^3 + 2*x^21 + x^20*z0 + 2*x^19*z0^2 + x^20 - x^19*z0 - x^19 + x^16*z0^3) * dx, - (2*x^23*z0^3 + x^22*z0^4 - 2*x^22*z0^3 + x^21*z0^4 - x^23*z0 - x^21*z0^3 - x^20*z0^4 - x^22*z0 + x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 - 2*x^22 + x^21*z0 + x^20*z0^2 + 2*x^19*z0^3 + x^20*z0 - x^19*z0^2 - 2*x^20 - x^19*z0 + x^16*z0^4 + 2*x^19) * dx, - ((-2*x^23*z0^4 + x^23*z0^3 + 2*x^22*z0^4 - 2*x^23*z0^2 - x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 - 2*x^22*z0^2 - 2*x^21*z0^3 - x^20*z0^4 + 2*x^21*z0^2 + x^20*z0^3 - x^19*z0^4 + x^22 - 2*x^21*z0 + 2*x^20*z0^2 + 2*x^21 + x^20*z0 - 2*x^19*z0^2 + 2*x^20 - x^19*z0 + x^16)/y) * dx, - ((-x^23*z0^3 - 2*x^23*z0^2 + 2*x^22*z0^3 + 2*x^21*z0^4 - 2*x^21*z0^3 - x^20*z0^4 + x^22*z0 - 2*x^21*z0^2 + x^20*z0^3 + x^21*z0 + x^20*z0^2 - x^20*z0 - x^19*z0^2 + x^20 + x^19*z0 + x^16*z0)/y) * dx, - ((x^23*z0^4 + x^23*z0^3 + 2*x^22*z0^3 + 2*x^23*z0 + x^22*z0^2 + x^21*z0^3 - 2*x^22*z0 + x^21*z0^2 - 2*x^20*z0^3 - x^22 - x^21*z0 - x^20*z0^2 + 2*x^21 - 2*x^20*z0 + x^19*z0^2 + 2*x^19*z0 + x^16*z0^2)/y) * dx, - ((-2*x^23*z0^4 + 2*x^23*z0^3 + 2*x^23*z0^2 - x^22*z0^3 - 2*x^21*z0^4 - 2*x^22*z0^2 - 2*x^21*z0^3 - x^21*z0^2 + 2*x^20*z0^3 - 2*x^19*z0^4 + x^21*z0 - 2*x^20*z0^2 + 2*x^21 + x^20*z0 + 2*x^19*z0^2 + 2*x^20 - x^19*z0 + x^16*z0^3)/y) * dx, - ((-x^23*z0^4 + x^23*z0^3 + 2*x^22*z0^4 - x^22*z0^3 - x^23*z0 - 2*x^21*z0^3 - 2*x^20*z0^4 - x^22*z0 + x^21*z0^2 - x^20*z0^3 + 2*x^19*z0^4 - 2*x^22 + x^21*z0 + x^20*z0^2 + x^20*z0 - x^19*z0^2 - x^19*z0 + x^16*z0^4)/y) * dx, - (x^23*z0^4 + 2*x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 + x^21*z0^4 - x^23*z0 + 2*x^22*z0^2 - x^21*z0^3 - x^20*z0^4 - x^22*z0 + 2*x^21*z0^2 + x^20*z0^3 + x^19*z0^4 - 2*x^22 - 2*x^20*z0^2 - x^19*z0^3 - 2*x^21 + 2*x^19*z0^2 + 2*x^20 - 2*x^19 + x^17) * dx, - (2*x^23*z0^4 - 2*x^23*z0^3 - x^23*z0^2 + 2*x^22*z0^3 - x^21*z0^4 - x^22*z0^2 + 2*x^21*z0^3 + x^20*z0^4 + 2*x^22*z0 - 2*x^20*z0^3 - x^19*z0^4 - 2*x^21*z0 + 2*x^19*z0^3 - 2*x^21 + 2*x^20*z0 + 2*x^20 - 2*x^19*z0 - 2*x^19 + x^17*z0) * dx, - (-2*x^23*z0^4 - x^23*z0^3 + 2*x^22*z0^4 - x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 + 2*x^22*z0^2 - 2*x^20*z0^4 - x^22*z0 - 2*x^21*z0^2 + 2*x^19*z0^4 + x^22 - 2*x^21*z0 + 2*x^20*z0^2 + 2*x^21 + 2*x^20*z0 - 2*x^19*z0^2 - 2*x^20 - 2*x^19*z0 + 2*x^19 + x^17*z0^2) * dx, - (-x^23*z0^4 - x^22*z0^4 - 2*x^23*z0^2 + 2*x^22*z0^3 + x^23*z0 - x^22*z0^2 - 2*x^21*z0^3 - 2*x^21*z0^2 + 2*x^20*z0^3 + 2*x^22 + 2*x^21*z0 + 2*x^20*z0^2 - 2*x^19*z0^3 + x^21 - 2*x^20*z0 - 2*x^19*z0^2 - x^20 + 2*x^19*z0 + x^17*z0^3 + x^19) * dx, - (-2*x^23*z0^3 + 2*x^22*z0^4 + x^23*z0^2 - x^22*z0^3 - 2*x^21*z0^4 - x^23*z0 - 2*x^21*z0^3 + 2*x^20*z0^4 + x^22*z0 + 2*x^21*z0^2 + 2*x^20*z0^3 - 2*x^19*z0^4 - 2*x^22 + x^21*z0 - 2*x^20*z0^2 - 2*x^19*z0^3 - x^20*z0 + 2*x^19*z0^2 + x^17*z0^4 + x^19*z0) * dx, - ((-2*x^23*z0^4 + x^22*z0^4 - 2*x^23*z0^2 + 2*x^22*z0^3 - 2*x^21*z0^4 - x^23*z0 + 2*x^22*z0^2 + 2*x^21*z0^3 - 2*x^20*z0^4 - x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 - 2*x^22 - 2*x^20*z0^2 - 2*x^21 + 2*x^19*z0^2 + x^20 + x^17)/y) * dx, - ((2*x^23*z0^4 + 2*x^23*z0^3 - x^23*z0^2 - 2*x^22*z0^3 - x^21*z0^4 - x^22*z0^2 + x^21*z0^3 - x^20*z0^4 + 2*x^22*z0 - x^20*z0^3 + 2*x^19*z0^4 - 2*x^21*z0 - 2*x^21 + 2*x^20*z0 - x^20 - 2*x^19*z0 + x^17*z0)/y) * dx, - ((-x^23*z0^3 - x^22*z0^3 - x^21*z0^4 - 2*x^23*z0 + 2*x^22*z0^2 + x^20*z0^4 - x^22*z0 - 2*x^21*z0^2 + x^19*z0^4 + x^22 - 2*x^21*z0 + 2*x^20*z0^2 + 2*x^21 + 2*x^20*z0 - 2*x^19*z0^2 - 2*x^20 - 2*x^19*z0 + x^17*z0^2)/y) * dx, - ((-2*x^23*z0^4 + x^23*z0^3 - 2*x^23*z0^2 + x^22*z0^3 - x^21*z0^4 + x^23*z0 - x^22*z0^2 - x^21*z0^3 - 2*x^20*z0^4 - 2*x^21*z0^2 + x^20*z0^3 + 2*x^22 + 2*x^21*z0 + 2*x^20*z0^2 + x^21 - 2*x^20*z0 - 2*x^19*z0^2 + 2*x^20 + 2*x^19*z0 + x^17*z0^3)/y) * dx, - ((-2*x^23*z0^4 - x^23*z0^3 - x^22*z0^4 + x^23*z0^2 - 2*x^22*z0^3 + x^21*z0^4 - x^23*z0 - x^21*z0^3 + x^20*z0^4 + x^22*z0 + 2*x^21*z0^2 + x^20*z0^3 + x^19*z0^4 - 2*x^22 + x^21*z0 - 2*x^20*z0^2 - x^20*z0 + 2*x^19*z0^2 + x^17*z0^4 - 2*x^20 + x^19*z0)/y) * dx, - (-2*x^23*z0^4 - 2*x^23*z0^3 + x^22*z0^4 - 2*x^23*z0^2 + x^22*z0^3 - x^21*z0^4 - 2*x^23*z0 + x^22*z0^2 - x^21*z0^3 + x^20*z0^4 + x^22*z0 - x^21*z0^2 + x^20*z0^3 - x^19*z0^4 + x^22 - x^21*z0 + x^20*z0^2 - x^19*z0^3 - x^21 + x^20*z0 - x^19*z0^2 + x^20 - x^19*z0 - x^19 + x^18) * dx, - (-2*x^23*z0^4 - 2*x^23*z0^3 + x^22*z0^4 - 2*x^23*z0^2 + x^22*z0^3 - x^21*z0^4 - x^23*z0 + x^22*z0^2 - x^21*z0^3 + x^20*z0^4 + x^22*z0 - x^21*z0^2 + x^20*z0^3 - x^19*z0^4 - 2*x^22 - x^21*z0 + x^20*z0^2 - x^19*z0^3 + 2*x^21 + x^20*z0 - x^19*z0^2 - 2*x^20 - x^19*z0 + 2*x^19 + x^18*z0) * dx, - (-2*x^23*z0^4 - 2*x^23*z0^3 + x^22*z0^4 - x^23*z0^2 + x^22*z0^3 - x^21*z0^4 - x^23*z0 + x^22*z0^2 - x^21*z0^3 + x^20*z0^4 - 2*x^22*z0 - x^21*z0^2 + x^20*z0^3 - x^19*z0^4 - 2*x^22 + 2*x^21*z0 + x^20*z0^2 - x^19*z0^3 + 2*x^21 - 2*x^20*z0 - x^19*z0^2 - 2*x^20 + 2*x^19*z0 + x^18*z0^2 + 2*x^19) * dx, - (-2*x^23*z0^4 - x^23*z0^3 + x^22*z0^4 - x^23*z0^2 + x^22*z0^3 - x^21*z0^4 - x^23*z0 - 2*x^22*z0^2 - x^21*z0^3 + x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 + x^20*z0^3 - x^19*z0^4 - 2*x^22 + 2*x^21*z0 - 2*x^20*z0^2 - x^19*z0^3 + 2*x^21 - 2*x^20*z0 + 2*x^19*z0^2 + x^18*z0^3 - 2*x^20 + 2*x^19*z0 + 2*x^19) * dx, - (-x^23*z0^4 - x^23*z0^3 + x^22*z0^4 - x^23*z0^2 - 2*x^22*z0^3 - x^21*z0^4 - x^23*z0 - 2*x^22*z0^2 + 2*x^21*z0^3 + x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 - x^19*z0^4 - 2*x^22 + 2*x^21*z0 - 2*x^20*z0^2 + 2*x^19*z0^3 + x^18*z0^4 + 2*x^21 - 2*x^20*z0 + 2*x^19*z0^2 - 2*x^20 + 2*x^19*z0 + 2*x^19) * dx, - ((x^23*z0^4 + x^23*z0^3 - 2*x^22*z0^4 - 2*x^23*z0^2 - 2*x^22*z0^3 + 2*x^21*z0^4 - 2*x^23*z0 + x^22*z0^2 + 2*x^21*z0^3 - x^20*z0^4 + x^22*z0 - x^21*z0^2 - 2*x^20*z0^3 + x^19*z0^4 + x^22 - x^21*z0 + x^20*z0^2 - x^21 + x^20*z0 - x^19*z0^2 - x^19*z0 + x^18)/y) * dx, - ((-x^23*z0^4 + x^23*z0^3 - 2*x^23*z0^2 - 2*x^22*z0^3 - x^23*z0 + x^22*z0^2 + 2*x^21*z0^3 + x^20*z0^4 + x^22*z0 - x^21*z0^2 - 2*x^20*z0^3 + 2*x^19*z0^4 - 2*x^22 - x^21*z0 + x^20*z0^2 + 2*x^21 + x^20*z0 - x^19*z0^2 + 2*x^20 - x^19*z0 + x^18*z0)/y) * dx, - ((-x^23*z0^4 + x^23*z0^3 - x^23*z0^2 - 2*x^22*z0^3 - x^23*z0 + x^22*z0^2 + 2*x^21*z0^3 + x^20*z0^4 - 2*x^22*z0 - x^21*z0^2 - 2*x^20*z0^3 + 2*x^19*z0^4 - 2*x^22 + 2*x^21*z0 + x^20*z0^2 + 2*x^21 - 2*x^20*z0 - x^19*z0^2 + 2*x^20 + 2*x^19*z0 + x^18*z0^2)/y) * dx, - ((-x^23*z0^4 + 2*x^23*z0^3 - x^23*z0^2 - 2*x^22*z0^3 - x^23*z0 - 2*x^22*z0^2 + 2*x^21*z0^3 + x^20*z0^4 - 2*x^22*z0 + 2*x^21*z0^2 - 2*x^20*z0^3 + 2*x^19*z0^4 - 2*x^22 + 2*x^21*z0 - 2*x^20*z0^2 + 2*x^21 - 2*x^20*z0 + 2*x^19*z0^2 + x^18*z0^3 + 2*x^20 + 2*x^19*z0)/y) * dx, - ((-2*x^23*z0^4 - 2*x^23*z0^3 + 2*x^22*z0^4 - x^23*z0^2 - x^22*z0^3 - 2*x^21*z0^4 - x^23*z0 - 2*x^22*z0^2 + x^21*z0^3 - 2*x^22*z0 + 2*x^21*z0^2 - x^20*z0^3 - 2*x^22 + 2*x^21*z0 - 2*x^20*z0^2 + x^18*z0^4 + 2*x^21 - 2*x^20*z0 + 2*x^19*z0^2 + 2*x^19*z0)/y) * dx, - ((-x^23*z0^4 + x^22*z0^4 - x^21*z0^4 + x^20*z0^4 - 2*x^19*z0^4 + x^19)/y) * dx, - ((-x^23*z0^4 - 2*x^23*z0^3 + x^22*z0^4 + 2*x^22*z0^3 - x^21*z0^4 - 2*x^21*z0^3 + 2*x^20*z0^4 + 2*x^20*z0^3 - x^19*z0^4 + x^19*z0^3 - x^20)/y) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7len(decompoition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7llen[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lle[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7leAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lnAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7llen(AS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: len(AS.holomorphic_differentials_basis()) -[?7h[?12l[?25h[?2004lIncrease precision. -[?7h192 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(AS.holomorphic_differentials_basis())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llenAS.holomorphic_diferentials_basis()[-1][?7h[?12l[?25h[?25l[?7lAS.holomorphic_diferentials_basis()[-1][?7h[?12l[?25h[?25l[?7lAS.holomorphic_diferentials_basis()[-1][?7h[?12l[?25h[?25l[?7lAS.holomorphic_diferentials_basis()[-1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loAS.holomorphic_diferentials_basis()[-1][?7h[?12l[?25h[?25l[?7lmAS.holomorphic_diferentials_basis()[-1][?7h[?12l[?25h[?25l[?7l AS.holomorphic_diferentials_basis()[-1][?7h[?12l[?25h[?25l[?7l=AS.holomorphic_diferentials_basis()[-1][?7h[?12l[?25h[?25l[?7l AS.holomorphic_diferentials_basis()[-1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[-1] -[?7h[?12l[?25h[?2004lIncrease precision. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[-1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om -[?7h[?12l[?25h[?2004l[?7h((-x^23*z0^4 - 2*x^23*z0^3 + x^22*z0^4 + 2*x^22*z0^3 - x^21*z0^4 - 2*x^21*z0^3 + 2*x^20*z0^4 + 2*x^20*z0^3 - x^19*z0^4 + x^19*z0^3 - x^20)/y) * dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.jth_component(1)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.expansion(pt = 0) -[?7h[?12l[?25h[?2004l[?7h3 + 2*t^6 + 4*t^8 + O(t^10) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion(pt = 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l-))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l,))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7l0))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om.expansion(pt = (-1, 0)) -[?7h[?12l[?25h[?2004l[?7ht^4 + 2*t^6 + 3*t^12 + 4*t^14 + t^16 + t^20 + 4*t^22 + 2*t^26 + 3*t^44 + O(t^46) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((3*C.x+3*C.one)^(-1)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC.x+C.one)^(-1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn()[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7ht^-1 + 4*t^5 + 3*t^11 + 3*t^17 + O(t^19) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lomexpansion(pt = (-1, 0))[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_differentials_basis()[-1][?7h[?12l[?25h[?25l[?7llen(AS.holomorphic_diferentials_basis())[?7h[?12l[?25h[?25l[?7lAS.holomrphic_dfferentials_bais()[?7h[?12l[?25h[?25l[?7llen(AS.hlomorphc_differential_basis())[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_diferentials_basis()[-1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion(pt = 0)[?7h[?12l[?25h[?25l[?7l(-1, 0))[?7h[?12l[?25h[?25l[?7l(Cy/C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lomexpansion(pt = (-1, 0))[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_differentials_basis()[-1][?7h[?12l[?25h[?25l[?7llen(AS.holomorphic_diferentials_basis())[?7h[?12l[?25h[?25l[?7lAS.holomrphic_dfferentials_bais()[?7h[?12l[?25h[?25l[?7l((3*C.x+3*C.one)^(-1)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lAS.z_series[0][0]^5 - AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l = as_cover(C, [(3*C.x+3*C.on)^(-1)], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lC], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l.], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7ly], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l/], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lC], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l.], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7lx], prec = 50, branch_points = [(-1, 0)])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l(])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l0])[?7h[?12l[?25h[?25l[?7l)])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [74], in () -----> 1 AS.holomorphic_differentials_basis() - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l20, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [76], in () -----> 1 AS.holomorphic_differentials_basis() - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y/C.x], prec = 500, branch_points = [(-1, 0), (1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y/C.x], prec = 500, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [78], in () -----> 1 AS.holomorphic_differentials_basis() - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 15) -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [79], in () -----> 1 AS.holomorphic_differentials_basis(threshold = Integer(15)) - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 15)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 20) -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [80], in () -----> 1 AS.holomorphic_differentials_basis(threshold = Integer(20)) - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l30)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 30) -[?7h[?12l[?25h[?2004lI haven't found all forms. ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [81], in () -----> 1 AS.holomorphic_differentials_basis(threshold = Integer(30)) - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 30)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l15[?7h[?12l[?25h[?25l[?7l20[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 30)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lseries[?7h[?12l[?25h[?25l[?7lsage: AS.x_series -[?7h[?12l[?25h[?2004l[?7h{0: t^-10 + 3*t^-6 + t^-2 + t^20 + 4*t^24 + t^40 + 4*t^44 + 2*t^50 + t^60 + 4*t^64 + 4*t^70 + t^80 + 4*t^84 + t^90 + t^100 + 4*t^104 + 2*t^110 + 3*t^114 + 2*t^118 + t^120 + t^122 + 4*t^124 + 3*t^140 + 2*t^148 + 2*t^150 + 3*t^160 + 2*t^168 + 4*t^174 + 3*t^180 + 2*t^188 + 3*t^190 + 3*t^194 + 3*t^200 + 2*t^208 + 2*t^218 + 3*t^220 + t^222 + 2*t^228 + 4*t^230 + t^234 + t^244 + 4*t^248 + 2*t^250 + t^260 + 3*t^264 + 2*t^268 + t^270 + 4*t^272 + 3*t^274 + t^280 + 3*t^284 + 2*t^288 + t^290 + 4*t^292 + 4*t^294 + t^298 + t^300 + 3*t^304 + 2*t^308 + 4*t^312 + 3*t^314 + 4*t^318 + 4*t^320 + t^322 + 2*t^328 + t^330 + 4*t^332 + t^334 + 3*t^338 + 2*t^340 + 4*t^348 + 3*t^350 + 4*t^352 + 2*t^354 + 4*t^358 + 3*t^360 + 2*t^372 + 2*t^374 + 3*t^384 + 2*t^392 + 3*t^394 + 3*t^398 + 3*t^404 + 2*t^410 + 2*t^412 + 2*t^414 + 3*t^418 + 4*t^420 + t^422 + 4*t^424 + t^430 + 2*t^432 + 4*t^438 + 4*t^440 + 2*t^444 + 2*t^448 + 2*t^452 + t^454 + 2*t^458 + 4*t^460 + t^464 + t^468 + 2*t^470 + 4*t^472 + t^474 + t^488 + O(t^490), - (-1, - 0): 4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 + 3*t^250 + 4*t^252 + 3*t^254 + t^260 + 3*t^262 + t^264 + 4*t^270 + 2*t^272 + 4*t^274 + 2*t^280 + t^282 + 2*t^284 + 2*t^300 + t^302 + 2*t^304 + 4*t^310 + 2*t^312 + 4*t^314 + t^320 + 3*t^322 + t^324 + 3*t^330 + 4*t^332 + 3*t^334 + 2*t^500 + t^502 + 2*t^504 + 4*t^510 + 2*t^512 + 4*t^514 + t^520 + 3*t^522 + t^524 + 3*t^530 + 4*t^532 + 3*t^534 + 3*t^550 + 4*t^552 + 3*t^554 + t^560 + 3*t^562 + t^564 + 4*t^570 + 2*t^572 + 4*t^574 + 2*t^580 + t^582 + 2*t^584 + t^750 + 3*t^752 + t^754 + 2*t^760 + t^762 + 2*t^764 + 3*t^770 + 4*t^772 + 3*t^774 + 4*t^780 + 2*t^782 + 4*t^784 + 4*t^800 + 2*t^802 + 4*t^804 + 3*t^810 + 4*t^812 + 3*t^814 + 2*t^820 + t^822 + 2*t^824 + t^830 + 3*t^832 + t^834, - (1, - 0): 1 + 3*t^2 + 4*t^4 + 4*t^6 + 4*t^8 + 4*t^10 + 4*t^12 + 4*t^14 + 4*t^16 + 4*t^18 + 4*t^20 + 4*t^22 + 4*t^24 + 4*t^26 + 4*t^28 + 4*t^30 + 4*t^32 + 4*t^34 + 4*t^36 + 4*t^38 + 4*t^40 + 4*t^42 + 4*t^44 + 4*t^46 + 4*t^48 + 4*t^50 + 4*t^52 + 4*t^54 + 4*t^56 + 4*t^58 + 4*t^60 + 4*t^62 + 4*t^64 + 4*t^66 + 4*t^68 + 4*t^70 + 4*t^72 + 4*t^74 + 4*t^76 + 4*t^78 + 4*t^80 + 4*t^82 + 4*t^84 + 4*t^86 + 4*t^88 + 4*t^90 + 4*t^92 + 4*t^94 + 4*t^96 + 4*t^98 + 4*t^100 + 4*t^102 + 4*t^104 + 4*t^106 + 4*t^108 + 4*t^110 + 4*t^112 + 4*t^114 + 4*t^116 + 4*t^118 + 4*t^120 + 4*t^122 + 4*t^124 + 4*t^126 + 4*t^128 + 4*t^130 + 4*t^132 + 4*t^134 + 4*t^136 + 4*t^138 + 4*t^140 + 4*t^142 + 4*t^144 + 4*t^146 + 4*t^148 + 4*t^150 + 4*t^152 + 4*t^154 + 4*t^156 + 4*t^158 + 4*t^160 + 4*t^162 + 4*t^164 + 4*t^166 + 4*t^168 + 4*t^170 + 4*t^172 + 4*t^174 + 4*t^176 + 4*t^178 + 4*t^180 + 4*t^182 + 4*t^184 + 4*t^186 + 4*t^188 + 4*t^190 + 4*t^192 + 4*t^194 + 4*t^196 + 4*t^198 + 4*t^200 + 4*t^202 + 4*t^204 + 4*t^206 + 4*t^208 + 4*t^210 + 4*t^212 + 4*t^214 + 4*t^216 + 4*t^218 + 4*t^220 + 4*t^222 + 4*t^224 + 4*t^226 + 4*t^228 + 4*t^230 + 4*t^232 + 4*t^234 + 4*t^236 + 4*t^238 + 4*t^240 + 4*t^242 + 4*t^244 + 4*t^246 + 4*t^248 + 4*t^250 + 4*t^252 + 4*t^254 + 4*t^256 + 4*t^258 + 4*t^260 + 4*t^262 + 4*t^264 + 4*t^266 + 4*t^268 + 4*t^270 + 4*t^272 + 4*t^274 + 4*t^276 + 4*t^278 + 4*t^280 + 4*t^282 + 4*t^284 + 4*t^286 + 4*t^288 + 4*t^290 + 4*t^292 + 4*t^294 + 4*t^296 + 4*t^298 + 4*t^300 + 4*t^302 + 4*t^304 + 4*t^306 + 4*t^308 + 4*t^310 + 4*t^312 + 4*t^314 + 4*t^316 + 4*t^318 + 4*t^320 + 4*t^322 + 4*t^324 + 4*t^326 + 4*t^328 + 4*t^330 + 4*t^332 + 4*t^334 + 4*t^336 + 4*t^338 + 4*t^340 + 4*t^342 + 4*t^344 + 4*t^346 + 4*t^348 + 4*t^350 + 4*t^352 + 4*t^354 + 4*t^356 + 4*t^358 + 4*t^360 + 4*t^362 + 4*t^364 + 4*t^366 + 4*t^368 + 4*t^370 + 4*t^372 + 4*t^374 + 4*t^376 + 4*t^378 + 4*t^380 + 4*t^382 + 4*t^384 + 4*t^386 + 4*t^388 + 4*t^390 + 4*t^392 + 4*t^394 + 4*t^396 + 4*t^398 + 4*t^400 + 4*t^402 + 4*t^404 + 4*t^406 + 4*t^408 + 4*t^410 + 4*t^412 + 4*t^414 + 4*t^416 + 4*t^418 + 4*t^420 + 4*t^422 + 4*t^424 + 4*t^426 + 4*t^428 + 4*t^430 + 4*t^432 + 4*t^434 + 4*t^436 + 4*t^438 + 4*t^440 + 4*t^442 + 4*t^444 + 4*t^446 + 4*t^448 + 4*t^450 + 4*t^452 + 4*t^454 + 4*t^456 + 4*t^458 + 4*t^460 + 4*t^462 + 4*t^464 + 4*t^466 + 4*t^468 + 4*t^470 + 4*t^472 + 4*t^474 + 4*t^476 + 4*t^478 + 4*t^480 + 4*t^482 + 4*t^484 + 4*t^486 + 4*t^488 + 4*t^490 + 4*t^492 + 4*t^494 + 4*t^496 + 4*t^498 + 4*t^500 + 4*t^502 + 4*t^504 + 4*t^506 + 4*t^508 + 4*t^510 + 4*t^512 + 4*t^514 + 4*t^516 + 4*t^518 + 4*t^520 + 4*t^522 + 4*t^524 + 4*t^526 + 4*t^528 + 4*t^530 + 4*t^532 + 4*t^534 + 4*t^536 + 4*t^538 + 4*t^540 + 4*t^542 + 4*t^544 + 4*t^546 + 4*t^548 + 4*t^550 + 4*t^552 + 4*t^554 + 4*t^556 + 4*t^558 + 4*t^560 + 4*t^562 + 4*t^564 + 4*t^566 + 4*t^568 + 4*t^570 + 4*t^572 + 4*t^574 + 4*t^576 + 4*t^578 + 4*t^580 + 4*t^582 + 4*t^584 + 4*t^586 + 4*t^588 + 4*t^590 + 4*t^592 + 4*t^594 + 4*t^596 + 4*t^598 + 4*t^600 + 4*t^602 + 4*t^604 + 4*t^606 + 4*t^608 + 4*t^610 + 4*t^612 + 4*t^614 + 4*t^616 + 4*t^618 + 4*t^620 + 4*t^622 + 4*t^624 + 4*t^626 + 4*t^628 + 4*t^630 + 4*t^632 + 4*t^634 + 4*t^636 + 4*t^638 + 4*t^640 + 4*t^642 + 4*t^644 + 4*t^646 + 4*t^648 + 4*t^650 + 4*t^652 + 4*t^654 + 4*t^656 + 4*t^658 + 4*t^660 + 4*t^662 + 4*t^664 + 4*t^666 + 4*t^668 + 4*t^670 + 4*t^672 + 4*t^674 + 4*t^676 + 4*t^678 + 4*t^680 + 4*t^682 + 4*t^684 + 4*t^686 + 4*t^688 + 4*t^690 + 4*t^692 + 4*t^694 + 4*t^696 + 4*t^698 + 4*t^700 + 4*t^702 + 4*t^704 + 4*t^706 + 4*t^708 + 4*t^710 + 4*t^712 + 4*t^714 + 4*t^716 + 4*t^718 + 4*t^720 + 4*t^722 + 4*t^724 + 4*t^726 + 4*t^728 + 4*t^730 + 4*t^732 + 4*t^734 + 4*t^736 + 4*t^738 + 4*t^740 + 4*t^742 + 4*t^744 + 4*t^746 + 4*t^748 + 4*t^750 + 4*t^752 + 4*t^754 + 4*t^756 + 4*t^758 + 4*t^760 + 4*t^762 + 4*t^764 + 4*t^766 + 4*t^768 + 4*t^770 + 4*t^772 + 4*t^774 + 4*t^776 + 4*t^778 + 4*t^780 + 4*t^782 + 4*t^784 + 4*t^786 + 4*t^788 + 4*t^790 + 4*t^792 + 4*t^794 + 4*t^796 + 4*t^798 + 4*t^800 + 4*t^802 + 4*t^804 + 4*t^806 + 4*t^808 + 4*t^810 + 4*t^812 + 4*t^814 + 4*t^816 + 4*t^818 + 4*t^820 + 4*t^822 + 4*t^824 + 4*t^826 + 4*t^828 + 4*t^830 + 4*t^832 + 4*t^834 + 4*t^836 + 4*t^838 + 4*t^840 + 4*t^842 + 4*t^844 + 4*t^846 + 4*t^848 + 4*t^850 + 4*t^852 + 4*t^854 + 4*t^856 + 4*t^858 + 4*t^860 + 4*t^862 + 4*t^864 + 4*t^866 + 4*t^868 + 4*t^870 + 4*t^872 + 4*t^874 + 4*t^876 + 4*t^878 + 4*t^880 + 4*t^882 + 4*t^884 + 4*t^886 + 4*t^888 + 4*t^890 + 4*t^892 + 4*t^894 + 4*t^896 + 4*t^898 + 4*t^900 + 4*t^902 + 4*t^904 + 4*t^906 + 4*t^908 + 4*t^910 + 4*t^912 + 4*t^914 + 4*t^916 + 4*t^918 + 4*t^920 + 4*t^922 + 4*t^924 + 4*t^926 + 4*t^928 + 4*t^930 + 4*t^932 + 4*t^934 + 4*t^936 + 4*t^938 + 4*t^940 + 4*t^942 + 4*t^944 + 4*t^946 + 4*t^948 + 4*t^950 + 4*t^952 + 4*t^954 + 4*t^956 + 4*t^958 + 4*t^960 + 4*t^962 + 4*t^964 + 4*t^966 + 4*t^968 + 4*t^970 + 4*t^972 + 4*t^974 + 4*t^976 + 4*t^978 + 4*t^980 + 4*t^982 + 4*t^984 + 4*t^986 + 4*t^988 + 4*t^990 + 4*t^992 + 4*t^994 + 4*t^996 + 4*t^998 + 4*t^1000} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.x_series[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0][0]^5 - AS.z_series[0][0][?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: AS.z_series -[?7h[?12l[?25h[?2004l[?7h{0: [t^-1], - (-1, - 0): [t + 2*t^3 + 4*t^5 + 4*t^7 + 4*t^11 + 3*t^13 + 4*t^15 + t^17 + 4*t^25 + 4*t^35 + 2*t^51 + 4*t^53 + 3*t^57 + 3*t^61 + t^63 + 2*t^65 + 2*t^67 + 4*t^75 + t^85 + 3*t^101 + t^103 + 4*t^105 + 2*t^107 + 2*t^111 + 4*t^113 + t^115 + 3*t^117 + 4*t^125 + 4*t^151 + 3*t^153 + 2*t^155 + t^157 + t^161 + 2*t^163 + 3*t^165 + 4*t^167 + 4*t^175 + 4*t^251 + 3*t^253 + 4*t^255 + t^257 + t^261 + 2*t^263 + 2*t^265 + 4*t^267 + 3*t^285 + 3*t^301 + t^303 + 2*t^305 + 2*t^307 + 2*t^311 + 4*t^313 + 2*t^315 + 3*t^317 + 2*t^325 + 2*t^335 + 2*t^351 + 4*t^353 + t^355 + 3*t^357 + 3*t^361 + t^363 + 4*t^365 + 2*t^367 + 4*t^375 + t^401 + 2*t^403 + 3*t^405 + 4*t^407 + 4*t^411 + 3*t^413 + 2*t^415 + t^417 + t^425 + O(t^501)], - (1, - 0): [4*t + 3*t^3 + 4*t^5 + 2*t^7 + t^9 + t^11 + 2*t^13 + 3*t^15 + 3*t^17 + 4*t^19 + 4*t^21 + 3*t^23 + 4*t^25 + 2*t^27 + t^29 + t^31 + 2*t^33 + 2*t^35 + 3*t^37 + 4*t^39 + 4*t^41 + 3*t^43 + t^45 + 2*t^47 + t^49 + t^51 + 2*t^53 + t^55 + 3*t^57 + 4*t^59 + 4*t^61 + 3*t^63 + 2*t^65 + 2*t^67 + t^69 + t^71 + 2*t^73 + 3*t^75 + 3*t^77 + 4*t^79 + 4*t^81 + 3*t^83 + 3*t^85 + 2*t^87 + t^89 + t^91 + 2*t^93 + 4*t^95 + 3*t^97 + 4*t^99 + 4*t^101 + 3*t^103 + 4*t^105 + 2*t^107 + t^109 + t^111 + 2*t^113 + 3*t^115 + 3*t^117 + 4*t^119 + 4*t^121 + 3*t^123 + 4*t^125 + 2*t^127 + t^129 + t^131 + 2*t^133 + 2*t^135 + 3*t^137 + 4*t^139 + 4*t^141 + 3*t^143 + t^145 + 2*t^147 + t^149 + t^151 + 2*t^153 + t^155 + 3*t^157 + 4*t^159 + 4*t^161 + 3*t^163 + 2*t^165 + 2*t^167 + t^169 + t^171 + 2*t^173 + 2*t^175 + 3*t^177 + 4*t^179 + 4*t^181 + 3*t^183 + 3*t^185 + 2*t^187 + t^189 + t^191 + 2*t^193 + 4*t^195 + 3*t^197 + 4*t^199 + 4*t^201 + 3*t^203 + 4*t^205 + 2*t^207 + t^209 + t^211 + 2*t^213 + 3*t^215 + 3*t^217 + 4*t^219 + 4*t^221 + 3*t^223 + t^225 + 2*t^227 + t^229 + t^231 + 2*t^233 + 2*t^235 + 3*t^237 + 4*t^239 + 4*t^241 + 3*t^243 + t^245 + 2*t^247 + t^249 + t^251 + 2*t^253 + t^255 + 3*t^257 + 4*t^259 + 4*t^261 + 3*t^263 + 2*t^265 + 2*t^267 + t^269 + t^271 + 2*t^273 + t^275 + 3*t^277 + 4*t^279 + 4*t^281 + 3*t^283 + 3*t^285 + 2*t^287 + t^289 + t^291 + 2*t^293 + 4*t^295 + 3*t^297 + 4*t^299 + 4*t^301 + 3*t^303 + 4*t^305 + 2*t^307 + t^309 + t^311 + 2*t^313 + 3*t^315 + 3*t^317 + 4*t^319 + 4*t^321 + 3*t^323 + 2*t^325 + 2*t^327 + t^329 + t^331 + 2*t^333 + 2*t^335 + 3*t^337 + 4*t^339 + 4*t^341 + 3*t^343 + t^345 + 2*t^347 + t^349 + t^351 + 2*t^353 + t^355 + 3*t^357 + 4*t^359 + 4*t^361 + 3*t^363 + 2*t^365 + 2*t^367 + t^369 + t^371 + 2*t^373 + 3*t^375 + 3*t^377 + 4*t^379 + 4*t^381 + 3*t^383 + 3*t^385 + 2*t^387 + t^389 + t^391 + 2*t^393 + 4*t^395 + 3*t^397 + 4*t^399 + 4*t^401 + 3*t^403 + 4*t^405 + 2*t^407 + t^409 + t^411 + 2*t^413 + 3*t^415 + 3*t^417 + 4*t^419 + 4*t^421 + 3*t^423 + 3*t^425 + 2*t^427 + t^429 + t^431 + 2*t^433 + 2*t^435 + 3*t^437 + 4*t^439 + 4*t^441 + 3*t^443 + t^445 + 2*t^447 + t^449 + t^451 + 2*t^453 + t^455 + 3*t^457 + 4*t^459 + 4*t^461 + 3*t^463 + 2*t^465 + 2*t^467 + t^469 + t^471 + 2*t^473 + 4*t^475 + 3*t^477 + 4*t^479 + 4*t^481 + 3*t^483 + 3*t^485 + 2*t^487 + t^489 + t^491 + 2*t^493 + 4*t^495 + 3*t^497 + 4*t^499 + O(t^501)]} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(AS.holomorphic_differentials_basis())[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.z_series[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis(threshold = 30)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l15[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 500, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l(C.y/C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.z_series[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis(threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 30) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [86], in () -----> 1 AS.holomorphic_differentials_basis(threshold = Integer(30)) - -File :146, in holomorphic_differentials_basis(self, threshold) - -TypeError: can only concatenate str (not "int") to str -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 30)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 30)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 30) -[?7h[?12l[?25h[?2004lI haven't found all forms, only 5 of 9 ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [89], in () -----> 1 AS.holomorphic_differentials_basis(threshold = Integer(30)) - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 30)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l40)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 40) -[?7h[?12l[?25h[?2004lI haven't found all forms, only 5 of 9 ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [90], in () -----> 1 AS.holomorphic_differentials_basis(threshold = Integer(40)) - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 40)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 40)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 40) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [93], in () -----> 1 AS.holomorphic_differentials_basis(threshold = Integer(40)) - -File :143, in holomorphic_differentials_basis(self, threshold) - -File :398, in holomorphic_combinations(S) - -IndexError: list index out of range -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 40)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 20) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [94], in () -----> 1 AS.holomorphic_differentials_basis(threshold = Integer(20)) - -File :143, in holomorphic_differentials_basis(self, threshold) - -File :398, in holomorphic_combinations(S) - -IndexError: list index out of range -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 50, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l20, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l0, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l0, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 20) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [96], in () -----> 1 AS.holomorphic_differentials_basis(threshold = Integer(20)) - -File :143, in holomorphic_differentials_basis(self, threshold) - -File :398, in holomorphic_combinations(S) - -IndexError: list index out of range -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 20) -[?7h[?12l[?25h[?2004lI haven't found all forms, only 5 of 9 ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [99], in () -----> 1 AS.holomorphic_differentials_basis(threshold = Integer(20)) - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], prec = 20, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 20, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 20, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l], prec = 20, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y], prec = 200) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 20) -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, - (1/y) * dx, - (z0/y) * dx, - (z0^2/y) * dx, - (z0^3/y) * dx, - (z0^4/y) * dx, - (x/y) * dx, - (x*z0/y) * dx, - (x*z0^2/y) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis(threshold = 20) -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, - (1/y) * dx, - (z0/y) * dx, - (z0^2/y) * dx, - (z0^3/y) * dx, - (z0^4/y) * dx, - (x/y) * dx, - (x*z0/y) * dx, - (x*z0^2/y) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l2(threshold = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis2(threshold = 20) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [104], in () -----> 1 AS.holomorphic_differentials_basis2(threshold = Integer(20)) - -AttributeError: 'as_cover' object has no attribute 'holomorphic_differentials_basis2' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7ld.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7la.sage')[?7h[?12l[?25h[?25l[?7ld.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7l/.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lf.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7l/.sage')[?7h[?12l[?25h[?25l[?7l2.sage')[?7h[?12l[?25h[?25l[?7lg.sage')[?7h[?12l[?25h[?25l[?7lp.sage')[?7h[?12l[?25h[?25l[?7lc.sage')[?7h[?12l[?25h[?25l[?7lo.sage')[?7h[?12l[?25h[?25l[?7lv.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('draft/2gpcovers.sage') -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -OSError Traceback (most recent call last) -Input In [105], in () -----> 1 load('draft/2gpcovers.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:244, in load(filename, globals, attach) - 242 break - 243 else: ---> 244 raise IOError('did not find file %r to load or attach' % filename) - 246 ext = os.path.splitext(fpath)[1].lower() - 247 if ext == '.py': - -OSError: did not find file 'draft/2gpcovers.sage' to load or attach -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('draft/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7l/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis2(threshold = 20) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [107], in () -----> 1 AS.holomorphic_differentials_basis2(threshold = Integer(20)) - -AttributeError: 'as_cover' object has no attribute 'holomorphic_differentials_basis2' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7lsage: as_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7lAS.hlomorphic_differentials_basi2(threshold = 20)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis2(threshold = 20) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [109], in () -----> 1 AS.holomorphic_differentials_basis2(threshold = Integer(20)) - -AttributeError: 'as_cover' object has no attribute 'holomorphic_differentials_basis2' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lsage: as_cover( - C= %%! AS3  - branch_points= AA AbelianGroup  - list_of_fcts= AS AbelianGroupMorphism > - prec= AS1 AbelianGroupWithValues  - [?7h[?12l[?25h[?25l[?7l - - - -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lini[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7las_cver.holomorphic_differential_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7lsage: as_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2 -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7las_cver.holomorphic_differential_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7lAS.hlomorphic_differentials_basi2(threshold = 20)[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7l/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7l(threshold = 20)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y], prec = 200) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7las_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis2(threshold = 20) -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, - (1/y) * dx, - (z0/y) * dx, - (z0^2/y) * dx, - (z0^3/y) * dx, - (z0^4/y) * dx, - (x/y) * dx, - (x*z0/y) * dx, - (x*z0^2/y) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7las_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7las_cver.holomorphic_differential_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7lAS.hlomorphic_differentials_basi2(threshold = 20)[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7l/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7l(threshold = 20)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis2(threshold = 20) -[?7h[?12l[?25h[?2004lIncrease precision. -[?7h[((-x^61*z0^3 + x^58*y^2*z0^3 + 2*x^59*z0^3 + x^60*z0 + 2*x^58*z0^3 - 2*x^56*y^2*z0^3 - 2*x^59*z0 - x^57*y^2*z0 + x^57*z0^3 - x^55*y^2*z0^3 + 2*x^56*y^2*z0 - 2*x^56*z0^3 - x^54*y^2*z0^3 - x^57*z0 - 2*x^55*z0^3 + 2*x^56*z0 - x^54*z0^3 + 2*x^53*z0^3 + x^54*z0 + 2*x^52*z0^3 - 2*x^53*z0 + x^51*z0^3 - 2*x^50*z0^3 - x^51*z0 - 2*x^49*z0^3 + 2*x^50*z0 - x^48*z0^3 + 2*x^47*z0^3 + x^48*z0 + 2*x^46*z0^3 - 2*x^47*z0 + x^45*z0^3 - 2*x^44*z0^3 - x^45*z0 - 2*x^43*z0^3 + 2*x^44*z0 - x^42*z0^3 + x^41*z0^3 - x^39*y*z0^4 + x^42*z0 + 2*x^40*y*z0^2 + 2*x^40*z0^3 - 2*x^38*y*z0^4 - 2*x^41*z0 - x^39*z0^3 - 2*x^37*y*z0^4 + 2*x^40*z0 - x^38*y*z0^2 - 2*x^38*z0^3 + x^36*y*z0^4 - x^39*y + 2*x^37*z0^3 - 2*x^35*y*z0^4 - x^38*y + x^36*y*z0^2 + 2*x^36*z0^3 + 2*x^34*y*z0^4 - x^37*z0 + x^35*y*z0^2 + 2*x^35*z0^3 - x^33*y*z0^4 - x^36*y - x^36*z0 - 2*x^34*y*z0^2 - 2*x^34*z0^3 - 2*x^32*y*z0^4 + 2*x^35*y - 2*x^35*z0 + x^33*y*z0^2 - 2*x^31*y*z0^4 - 2*x^34*y - x^32*y*z0^2 - x^32*z0^3 - 2*x^33*y + 2*x^33*z0 - x^31*y*z0^2 + 2*x^31*z0^3 - x^29*y*z0^4 + x^32*z0 + x^30*z0^3 + x^28*y*z0^4 + 2*x^31*y + x^31*z0 + x^29*y*z0^2 - 2*x^29*z0^3 + 2*x^27*y*z0^4 - 2*x^30*y + x^30*z0 - 2*x^28*y*z0^2 + x^28*z0^3 + x^26*y*z0^4 - x^29*y - 2*x^27*y*z0^2 - 2*x^27*z0^3 - x^28*y + x^28*z0 - 2*x^26*y*z0^2 + 2*x^24*y*z0^4 - 2*x^27*y - x^27*z0 - 2*x^25*y*z0^2 - x^25*z0^3 - x^23*y*z0^4 - 2*x^26*y - x^26*z0 - 2*x^24*y*z0^2 - 2*x^24*z0^3 + x^22*y*z0^4 - x^25*y - x^25*z0 + 2*x^23*y*z0^2 - x^23*z0^3 - x^21*y*z0^4 - 2*x^24*y + 2*x^24*z0 - x^23*y - x^23*z0 + x^21*y*z0^2 - 2*x^21*z0^3 + x^19*y*z0^4 + 2*x^22*y + 2*x^21*y - 2*x^21*z0 - 2*x^19*y*z0^2 - 2*x^19*z0^3 - 2*x^20*y + x^20*z0 - x^18*y*z0^2 - 2*x^18*z0^3 + 2*x^16*y*z0^4 + 2*x^19*y - 2*x^19*z0 - 2*x^17*y*z0^2 - 2*x^17*z0^3 - 2*x^18*y + x^18*z0 - x^16*z0^3 - 2*x^14*y*z0^4 + x^17*y - 2*x^15*y*z0^2 + 2*x^13*y*z0^4 - 2*x^16*z0 - 2*x^14*y*z0^2 + 2*x^14*z0^3 + 2*x^12*y*z0^4 - 2*x^15*z0 + 2*x^13*y*z0^2 - x^13*z0^3 + 2*x^11*y*z0^4 - 2*x^14*y - 2*x^14*z0 - x^12*y*z0^2 + x^12*z0^3 + 2*x^10*y*z0^4 + 2*x^11*z0^3 - 2*x^12*y - 2*x^10*y*z0^2 + 2*x^10*z0^3 - x^8*y*z0^4 - 2*x^11*z0 + x^9*y*z0^2 - x^9*z0^3 - x^7*y*z0^4 - x^10*y - 2*x^10*z0 + x^8*y*z0^2 + x^6*y*z0^4 + x^9*y - x^9*z0 + x^7*y*z0^2 + x^7*z0^3 + x^5*y*z0^4 + 2*x^8*y - x^8*z0 - 2*x^6*y*z0^2 + 2*x^6*z0^3 + 2*x^4*y*z0^4 + 2*x^7*y + x^7*z0 + x^5*z0^3 - 2*x^3*y*z0^4 - x^6*y + x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^2*y*z0^4 + 2*x^5*y - 2*x^5*z0 - 2*x^3*y*z0^2 + 2*x^3*z0^3 + 2*x^4*y - 2*x^4*z0 - x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y - 2*x^3*z0 + 2*x^2*z0 + y)/y) * dx, - ((x^61*z0^4 - 2*x^60*z0^4 - x^58*y^2*z0^4 - 2*x^59*z0^4 + 2*x^57*y^2*z0^4 - 2*x^60*z0^2 - x^58*z0^4 + 2*x^56*y^2*z0^4 - 2*x^61 + 2*x^57*y^2*z0^2 + 2*x^57*z0^4 + x^60 + 2*x^58*y^2 + 2*x^56*z0^4 - x^57*y^2 + 2*x^57*z0^2 + x^55*z0^4 + 2*x^58 - 2*x^54*z0^4 - x^57 - 2*x^53*z0^4 - 2*x^54*z0^2 - x^52*z0^4 - 2*x^55 + 2*x^51*z0^4 + x^54 + 2*x^50*z0^4 + 2*x^51*z0^2 + x^49*z0^4 + 2*x^52 - 2*x^48*z0^4 - x^51 - 2*x^47*z0^4 - 2*x^48*z0^2 - x^46*z0^4 - 2*x^49 + 2*x^45*z0^4 + x^48 + 2*x^44*z0^4 + 2*x^45*z0^2 + x^43*z0^4 + 2*x^46 - 2*x^42*z0^4 - x^45 - 2*x^41*z0^4 - 2*x^42*z0^2 - 2*x^40*y*z0^3 + 2*x^40*z0^4 - 2*x^43 + x^39*z0^4 + x^42 - x^38*y*z0^3 - x^39*y*z0 + 2*x^39*z0^2 - x^37*y*z0^3 + x^37*z0^4 - 2*x^40 + x^38*y*z0 + 2*x^36*z0^4 + 2*x^39 + x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 - x^35*z0^4 + x^38 + 2*x^36*y*z0 - 2*x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 - 2*x^37 - x^35*y*z0 - 2*x^35*z0^2 + 2*x^33*y*z0^3 + x^33*z0^4 - x^36 + 2*x^34*y*z0 - x^34*z0^2 + 2*x^35 - 2*x^33*y*z0 + x^31*y*z0^3 - x^31*z0^4 - x^34 + 2*x^32*y*z0 + 2*x^32*z0^2 - x^30*y*z0^3 - x^31*z0^2 - 2*x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^32 + x^30*y*z0 + x^30*z0^2 + x^28*y*z0^3 - x^28*z0^4 + x^31 - 2*x^29*y*z0 + x^27*y*z0^3 + x^27*z0^4 - x^28*y*z0 + x^28*z0^2 + 2*x^26*y*z0^3 + 2*x^27*y*z0 - 2*x^27*z0^2 - x^28 - x^26*y*z0 - 2*x^26*z0^2 + x^24*y*z0^3 - x^24*z0^4 - x^25*z0^2 + 2*x^23*y*z0^3 + x^23*z0^4 - x^26 + x^24*y*z0 - 2*x^24*z0^2 + x^22*z0^4 + x^23*y*z0 - 2*x^23*z0^2 + x^21*y*z0^3 - 2*x^21*z0^4 + x^24 + 2*x^22*y*z0 - 2*x^20*y*z0^3 - 2*x^20*z0^4 + x^23 - x^21*y*z0 + x^21*z0^2 - 2*x^19*y*z0^3 - x^19*z0^4 - 2*x^22 - x^18*z0^4 - x^21 - x^19*y*z0 - 2*x^19*z0^2 + x^17*y*z0^3 + x^17*z0^4 - x^20 - 2*x^18*y*z0 - 2*x^18*z0^2 - x^16*y*z0^3 + 2*x^16*z0^4 + 2*x^19 + x^17*y*z0 + x^17*z0^2 - x^15*y*z0^3 + x^15*z0^4 - x^18 + x^16*y*z0 - x^14*y*z0^3 + x^14*z0^4 - x^17 + 2*x^15*y*z0 - x^15*z0^2 + 2*x^13*z0^4 + x^14*y*z0 - x^14*z0^2 - 2*x^12*y*z0^3 + x^12*z0^4 + x^15 - 2*x^13*y*z0 - x^13*z0^2 + x^11*y*z0^3 + 2*x^11*z0^4 + x^14 - 2*x^12*y*z0 + x^12*z0^2 + 2*x^10*y*z0^3 - 2*x^13 - 2*x^9*y*z0^3 + x^9*z0^4 - x^12 + x^10*z0^2 + 2*x^8*y*z0^3 + x^8*z0^4 - 2*x^11 + x^9*y*z0 + 2*x^9*z0^2 + x^7*y*z0^3 + x^10 - 2*x^8*y*z0 + 2*x^8*z0^2 - 2*x^6*y*z0^3 - x^6*z0^4 + x^9 + 2*x^7*y*z0 - 2*x^7*z0^2 - x^5*y*z0^3 - x^8 + x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - x^7 + 2*x^5*y*z0 + x^3*y*z0^3 + x^3*z0^4 - 2*x^6 + x^4*z0^2 - 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*z0^2 - 2*x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 + 2*x^2 + y*z0)/y) * dx, - ((2*x^61*z0^3 + x^60*z0^3 - 2*x^58*y^2*z0^3 - 2*x^61*z0 + x^59*z0^3 - x^57*y^2*z0^3 - 2*x^60*z0 + 2*x^58*y^2*z0 + x^58*z0^3 - x^56*y^2*z0^3 - x^59*z0 + 2*x^57*y^2*z0 + x^57*z0^3 + 2*x^55*y^2*z0^3 + 2*x^58*z0 + x^56*y^2*z0 - x^56*z0^3 - 2*x^54*y^2*z0^3 + 2*x^57*z0 - x^55*z0^3 + x^56*z0 - x^54*z0^3 - 2*x^55*z0 + x^53*z0^3 - 2*x^54*z0 + x^52*z0^3 - x^53*z0 + x^51*z0^3 + 2*x^52*z0 - x^50*z0^3 + 2*x^51*z0 - x^49*z0^3 + x^50*z0 - x^48*z0^3 - 2*x^49*z0 + x^47*z0^3 - 2*x^48*z0 + x^46*z0^3 - x^47*z0 + x^45*z0^3 + 2*x^46*z0 - x^44*z0^3 + 2*x^45*z0 - x^43*z0^3 + x^44*z0 - x^42*z0^3 - 2*x^43*z0 - 2*x^41*z0^3 + 2*x^39*y*z0^4 - 2*x^42*z0 + x^40*y*z0^2 + x^40*z0^3 - 2*x^38*y*z0^4 + 2*x^41*z0 - 2*x^39*y*z0^2 + x^37*y*z0^4 - x^40*y - 2*x^40*z0 + 2*x^38*y*z0^2 - x^38*z0^3 - 2*x^36*y*z0^4 + 2*x^39*z0 - x^37*y*z0^2 + x^37*z0^3 - x^38*y + x^38*z0 + 2*x^36*y*z0^2 - 2*x^36*z0^3 - 2*x^34*y*z0^4 - 2*x^37*y + x^35*y*z0^2 + 2*x^33*y*z0^4 + 2*x^36*y - x^34*y*z0^2 - 2*x^34*z0^3 - x^32*y*z0^4 - x^35*y + 2*x^35*z0 + 2*x^33*y*z0^2 + x^33*z0^3 + 2*x^31*y*z0^4 - 2*x^34*y + x^34*z0 - 2*x^32*y*z0^2 - x^32*z0^3 + 2*x^30*y*z0^4 + x^33*y - x^33*z0 - 2*x^31*y*z0^2 - 2*x^31*z0^3 - x^29*y*z0^4 + x^32*y + 2*x^32*z0 + x^30*y*z0^2 + x^30*z0^3 - 2*x^28*y*z0^4 - 2*x^31*z0 - 2*x^29*y*z0^2 + x^29*z0^3 + x^27*y*z0^4 - x^28*y*z0^2 - 2*x^26*y*z0^4 + x^29*y + x^29*z0 + 2*x^27*y*z0^2 + 2*x^25*y*z0^4 - x^28*y - x^28*z0 + x^26*z0^3 + 2*x^27*y - 2*x^27*z0 - 2*x^23*y*z0^4 - 2*x^26*y + 2*x^26*z0 - x^24*y*z0^2 + x^24*z0^3 + x^25*y + 2*x^23*y*z0^2 - x^24*y + x^24*z0 + 2*x^22*z0^3 - 2*x^20*y*z0^4 + 2*x^23*y - 2*x^23*z0 - 2*x^21*z0^3 + 2*x^19*y*z0^4 - 2*x^22*y + 2*x^22*z0 - x^20*y*z0^2 - 2*x^20*z0^3 + x^21*z0 - x^19*y*z0^2 - x^17*y*z0^4 + x^20*y - 2*x^18*y*z0^2 + x^18*z0^3 + 2*x^16*y*z0^4 + 2*x^19*y - x^17*y*z0^2 - 2*x^17*z0^3 - x^15*y*z0^4 - 2*x^18*y - x^18*z0 + 2*x^16*y*z0^2 - 2*x^16*z0^3 - 2*x^14*y*z0^4 - x^17*z0 - x^15*y*z0^2 - x^16*y - 2*x^16*z0 + x^14*z0^3 + 2*x^12*y*z0^4 - 2*x^15*y + x^15*z0 + 2*x^13*y*z0^2 - 2*x^11*y*z0^4 - x^14*z0 + 2*x^12*z0^3 + 2*x^10*y*z0^4 + 2*x^13*y + x^13*z0 - x^11*y*z0^2 + 2*x^11*z0^3 + x^10*z0^3 + 2*x^8*y*z0^4 - 2*x^9*y*z0^2 - 2*x^9*z0^3 + x^7*y*z0^4 + x^10*y - 2*x^10*z0 + x^8*y*z0^2 + x^8*z0^3 + 2*x^6*y*z0^4 - x^9*z0 + x^7*y*z0^2 + x^7*z0^3 + 2*x^5*y*z0^4 - x^8*z0 + x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^4*y*z0^4 + 2*x^7*z0 + 2*x^5*z0^3 + 2*x^3*y*z0^4 + 2*x^6*z0 - x^4*y*z0^2 + x^2*y*z0^4 + 2*x^5*z0 + x^3*y*z0^2 - 2*x^3*z0^3 - 2*x^4*y + 2*x^2*z0^3 - x^2*y + y*z0^2)/y) * dx, - ((2*x^61*z0^4 - 2*x^58*y^2*z0^4 + 2*x^61*z0^2 - x^59*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 + x^61 + x^57*y^2*z0^2 - x^58*y^2 - 2*x^58*z0^2 + x^56*z0^4 + x^57*z0^2 + 2*x^55*z0^4 - x^58 + 2*x^55*z0^2 - x^53*z0^4 - x^54*z0^2 - 2*x^52*z0^4 + x^55 - 2*x^52*z0^2 + x^50*z0^4 + x^51*z0^2 + 2*x^49*z0^4 - x^52 + 2*x^49*z0^2 - x^47*z0^4 - x^48*z0^2 - 2*x^46*z0^4 + x^49 - 2*x^46*z0^2 + x^44*z0^4 + x^45*z0^2 + 2*x^43*z0^4 - x^46 + 2*x^43*z0^2 - x^41*z0^4 - x^42*z0^2 + x^40*y*z0^3 - 2*x^40*z0^4 + x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + x^40*y*z0 - 2*x^40*z0^2 - 2*x^38*y*z0^3 - x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 + 2*x^40 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 - x^39 - x^37*y*z0 + x^37*z0^2 + x^35*y*z0^3 - 2*x^35*z0^4 - 2*x^38 - 2*x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 - 2*x^34*z0^4 + x^37 - x^35*y*z0 - x^33*y*z0^3 - 2*x^33*z0^4 + 2*x^36 + x^34*y*z0 - 2*x^32*y*z0^3 + x^32*z0^4 - x^35 - x^33*y*z0 + 2*x^33*z0^2 + x^31*y*z0^3 - x^31*z0^4 + x^34 + 2*x^32*y*z0 + 2*x^32*z0^2 + 2*x^30*y*z0^3 + x^30*z0^4 + x^33 + x^31*z0^2 + 2*x^29*y*z0^3 - 2*x^30*z0^2 - 2*x^28*y*z0^3 + x^28*z0^4 - x^31 - 2*x^29*y*z0 - x^29*z0^2 + x^27*y*z0^3 - 2*x^27*z0^4 - x^30 - x^28*y*z0 - x^28*z0^2 - x^26*z0^4 - 2*x^29 + x^27*y*z0 + 2*x^27*z0^2 - 2*x^25*z0^4 - x^28 - x^26*y*z0 + 2*x^26*z0^2 - 2*x^24*y*z0^3 - x^24*z0^4 - x^27 + x^25*y*z0 - x^25*z0^2 - 2*x^23*y*z0^3 + 2*x^23*z0^4 - x^24*y*z0 - 2*x^24*z0^2 - 2*x^22*y*z0^3 - 2*x^22*z0^4 + 2*x^25 - 2*x^23*y*z0 - x^23*z0^2 - 2*x^21*y*z0^3 - 2*x^21*z0^4 - 2*x^24 - x^22*y*z0 + x^20*z0^4 + x^23 + x^21*y*z0 + x^21*z0^2 - x^19*y*z0^3 + x^19*z0^4 + 2*x^22 + 2*x^20*y*z0 - x^18*z0^4 - 2*x^21 - 2*x^19*z0^2 + x^17*z0^4 + 2*x^20 - x^18*y*z0 + 2*x^18*z0^2 - x^16*y*z0^3 - x^16*z0^4 - x^19 + 2*x^17*y*z0 - x^17*z0^2 - x^15*y*z0^3 - 2*x^15*z0^4 + 2*x^18 + 2*x^16*y*z0 + 2*x^16*z0^2 - x^14*y*z0^3 - 2*x^14*z0^4 - 2*x^17 - x^15*y*z0 + x^15*z0^2 - x^13*y*z0^3 + 2*x^13*z0^4 + 2*x^16 + x^14*y*z0 + 2*x^14*z0^2 + 2*x^12*y*z0^3 + x^15 - 2*x^13*y*z0 - 2*x^13*z0^2 - 2*x^11*y*z0^3 - 2*x^12*y*z0 - x^12*z0^2 + 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 + 2*x^11*y*z0 - 2*x^9*z0^4 + x^12 - x^10*z0^2 + x^8*y*z0^3 - 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 + x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 + x^8*y*z0 - x^8*z0^2 + x^6*y*z0^3 - 2*x^6*z0^4 + x^9 - x^7*y*z0 - x^7*z0^2 + 2*x^5*y*z0^3 + 2*x^5*z0^4 + x^6*y*z0 + 2*x^4*y*z0^3 - x^4*z0^4 - 2*x^7 + 2*x^5*z0^2 + x^3*y*z0^3 - x^3*z0^4 + x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 - 2*x^2*z0^4 + x^3*z0^2 - 2*x^2*y*z0 + x^2*z0^2 + y*z0^3 - 2*x^2)/y) * dx, - ((-2*x^61*z0^3 + 2*x^60*z0^3 + 2*x^58*y^2*z0^3 + 2*x^61*z0 + x^59*z0^3 - 2*x^57*y^2*z0^3 + x^60*z0 - 2*x^58*y^2*z0 - x^56*y^2*z0^3 - x^59*z0 - x^57*y^2*z0 + 2*x^57*z0^3 + 2*x^55*y^2*z0^3 - 2*x^58*z0 + x^56*y^2*z0 - x^56*z0^3 + x^54*y^2*z0^3 - x^57*z0 + x^56*z0 - 2*x^54*z0^3 + 2*x^55*z0 + x^53*z0^3 + x^54*z0 - x^53*z0 + 2*x^51*z0^3 - 2*x^52*z0 - x^50*z0^3 - x^51*z0 + x^50*z0 - 2*x^48*z0^3 + 2*x^49*z0 + x^47*z0^3 + x^48*z0 - x^47*z0 + 2*x^45*z0^3 - 2*x^46*z0 - x^44*z0^3 - x^45*z0 + x^44*z0 - 2*x^42*z0^3 + 2*x^43*z0 - x^41*z0^3 - 2*x^39*y*z0^4 + x^42*z0 - x^40*y*z0^2 - 2*x^40*z0^3 + x^41*z0 + 2*x^39*y*z0^2 + x^37*y*z0^4 + x^40*y - 2*x^40*z0 + x^38*y*z0^2 + x^38*z0^3 + x^36*y*z0^4 - x^39*y - 2*x^37*y*z0^2 + 2*x^37*z0^3 - x^35*y*z0^4 + x^38*y - x^38*z0 - x^36*y*z0^2 - 2*x^36*z0^3 + 2*x^34*y*z0^4 + 2*x^37*y + 2*x^37*z0 + x^33*y*z0^4 + x^36*y + 2*x^36*z0 + 2*x^34*y*z0^2 + x^34*z0^3 + x^32*y*z0^4 - x^35*y + 2*x^35*z0 + x^33*z0^3 - 2*x^31*y*z0^4 + x^34*y + 2*x^34*z0 - x^32*y*z0^2 + 2*x^32*z0^3 - 2*x^30*y*z0^4 + x^33*z0 + 2*x^31*y*z0^2 - 2*x^29*y*z0^4 + 2*x^32*y - x^32*z0 + x^30*z0^3 - x^31*y + 2*x^31*z0 + 2*x^29*y*z0^2 - x^27*y*z0^4 + x^30*y - 2*x^30*z0 + x^28*y*z0^2 - x^28*z0^3 - 2*x^26*y*z0^4 - 2*x^29*y + 2*x^27*z0^3 - x^25*y*z0^4 - x^28*y - x^28*z0 - x^26*y*z0^2 - 2*x^26*z0^3 - 2*x^24*y*z0^4 - x^27*y - 2*x^27*z0 + x^25*y*z0^2 + 2*x^25*z0^3 + 2*x^23*y*z0^4 + 2*x^26*y + 2*x^26*z0 + x^24*z0^3 - x^25*y + x^25*z0 + x^23*y*z0^2 + x^23*z0^3 - x^21*y*z0^4 - x^24*y - x^24*z0 + x^22*y*z0^2 - x^22*z0^3 + x^20*y*z0^4 + x^23*y + 2*x^21*y*z0^2 - 2*x^21*z0^3 - x^19*y*z0^4 - 2*x^22*y - x^22*z0 + x^20*y*z0^2 + 2*x^20*z0^3 - x^18*y*z0^4 - 2*x^21*z0 - 2*x^19*z0^3 + x^17*y*z0^4 + x^20*y - 2*x^20*z0 + 2*x^18*y*z0^2 + x^18*z0^3 + 2*x^16*y*z0^4 + 2*x^19*y + 2*x^19*z0 - x^17*y*z0^2 + x^15*y*z0^4 + 2*x^18*y + 2*x^18*z0 + 2*x^16*y*z0^2 + 2*x^16*z0^3 - 2*x^14*y*z0^4 + 2*x^17*y - 2*x^17*z0 + 2*x^15*z0^3 - 2*x^13*y*z0^4 + 2*x^16*y - x^14*y*z0^2 + x^14*z0^3 + 2*x^12*y*z0^4 + 2*x^15*y + 2*x^15*z0 - x^13*y*z0^2 + 2*x^13*z0^3 - 2*x^11*y*z0^4 + 2*x^14*y - 2*x^14*z0 - x^12*y*z0^2 - x^12*z0^3 + 2*x^10*y*z0^4 + 2*x^13*y - 2*x^13*z0 - x^11*y*z0^2 + x^11*z0^3 - x^9*y*z0^4 + 2*x^12*y + x^12*z0 - 2*x^10*y*z0^2 - 2*x^10*z0^3 + x^8*y*z0^4 + 2*x^11*y - 2*x^11*z0 + 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - 2*x^10*y + 2*x^8*y*z0^2 + 2*x^8*z0^3 - x^6*y*z0^4 + 2*x^9*y - 2*x^7*y*z0^2 + x^7*z0^3 + x^8*y - 2*x^8*z0 - x^6*z0^3 + 2*x^7*y - x^7*z0 - x^5*y*z0^2 - x^5*z0^3 + 2*x^3*y*z0^4 - 2*x^6*y - 2*x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 + 2*x^5*z0 + x^3*y*z0^2 - x^3*z0^3 + x^4*y + x^4*z0 + 2*x^2*y*z0^2 - x^2*z0^3 + y*z0^4 + x^3*y - x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((-x^3 + y^2)/y) * dx, - ((-x^3*z0 + y^2*z0)/y) * dx, - ((-x^3*z0^2 + y^2*z0^2)/y) * dx, - ((-x^3*z0^3 + y^2*z0^3)/y) * dx, - ((-x^3*z0^4 + y^2*z0^4)/y) * dx, - ((x^61*z0^3 - x^60*z0^3 - x^58*y^2*z0^3 - 2*x^61*z0 - 2*x^59*z0^3 + x^57*y^2*z0^3 - 2*x^60*z0 + 2*x^58*y^2*z0 + 2*x^56*y^2*z0^3 - x^59*z0 + 2*x^57*y^2*z0 - x^55*y^2*z0^3 + 2*x^58*z0 + x^56*y^2*z0 + 2*x^56*z0^3 + x^54*y^2*z0^3 + 2*x^57*z0 + x^56*z0 - 2*x^55*z0 - 2*x^53*z0^3 - 2*x^54*z0 - x^53*z0 + 2*x^52*z0 + 2*x^50*z0^3 + 2*x^51*z0 + x^50*z0 - 2*x^49*z0 - 2*x^47*z0^3 - 2*x^48*z0 - x^47*z0 + 2*x^46*z0 + 2*x^44*z0^3 + 2*x^45*z0 + x^44*z0 - 2*x^43*z0 - x^41*z0^3 + x^39*y*z0^4 - 2*x^42*z0 - 2*x^40*y*z0^2 - 2*x^40*z0^3 - x^38*y*z0^4 + 2*x^41*z0 - 2*x^39*y*z0^2 - x^39*z0^3 - 2*x^37*y*z0^4 - x^40*y + x^40*z0 - x^38*y*z0^2 + 2*x^38*z0^3 - x^36*y*z0^4 - 2*x^39*y + 2*x^39*z0 + x^37*y*z0^2 - 2*x^37*z0^3 - 2*x^35*y*z0^4 + x^38*y + x^38*z0 + 2*x^36*y*z0^2 + 2*x^34*y*z0^4 - 2*x^37*y + x^37*z0 + 2*x^35*z0^3 + 2*x^33*y*z0^4 - x^36*y - x^34*y*z0^2 - x^34*z0^3 - 2*x^32*y*z0^4 + 2*x^35*y + 2*x^35*z0 + x^33*y*z0^2 + 2*x^33*z0^3 - x^31*y*z0^4 + x^34*z0 - 2*x^32*z0^3 + 2*x^33*y - 2*x^33*z0 + 2*x^31*z0^3 + x^29*y*z0^4 - 2*x^32*z0 + 2*x^30*z0^3 - x^28*y*z0^4 - x^31*y - 2*x^31*z0 + 2*x^29*y*z0^2 - x^29*z0^3 + 2*x^27*y*z0^4 - 2*x^30*y + x^30*z0 + 2*x^28*y*z0^2 - x^28*z0^3 + x^26*y*z0^4 - x^29*y - x^29*z0 + 2*x^27*y*z0^2 - x^27*z0^3 - x^25*y*z0^4 + x^28*y - 2*x^26*y*z0^2 + 2*x^26*z0^3 + x^24*y*z0^4 - 2*x^27*z0 + x^25*y*z0^2 - 2*x^25*z0^3 - x^23*y*z0^4 + x^26*y - x^26*z0 - x^24*y*z0^2 + x^24*z0^3 - x^22*y*z0^4 - x^25*y - 2*x^25*z0 + 2*x^23*y*z0^2 + 2*x^23*z0^3 + x^21*y*z0^4 + 2*x^24*y + x^24*z0 - x^22*y*z0^2 + 2*x^20*y*z0^4 + 2*x^23*y - x^23*z0 - x^21*y*z0^2 - x^21*z0^3 - 2*x^19*y*z0^4 + x^22*y - 2*x^22*z0 - x^20*y*z0^2 - x^20*z0^3 + x^21*y - x^21*z0 + 2*x^19*y*z0^2 + x^19*z0^3 - 2*x^17*y*z0^4 - 2*x^20*z0 + x^18*y*z0^2 - 2*x^18*z0^3 - x^16*y*z0^4 - 2*x^19*y - 2*x^19*z0 - x^17*y*z0^2 - 2*x^15*y*z0^4 + 2*x^18*y - 2*x^18*z0 - 2*x^16*y*z0^2 + x^14*y*z0^4 + x^17*y + 2*x^17*z0 + x^15*z0^3 + x^13*y*z0^4 - x^16*z0 - 2*x^14*y*z0^2 - 2*x^14*z0^3 + 2*x^12*y*z0^4 - x^15*y - 2*x^15*z0 + 2*x^13*y*z0^2 + 2*x^13*z0^3 + x^11*y*z0^4 + x^14*y - 2*x^14*z0 - 2*x^12*y*z0^2 + x^12*z0^3 + 2*x^10*y*z0^4 - 2*x^13*y - x^11*y*z0^2 - 2*x^9*y*z0^4 + x^12*y + x^12*z0 - x^10*y*z0^2 + 2*x^8*y*z0^4 + 2*x^11*z0 + 2*x^9*y*z0^2 + 2*x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y - 2*x^10*z0 + 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*y - 2*x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 + x^5*y*z0^4 + 2*x^8*y + 2*x^8*z0 - x^6*y*z0^2 + x^4*y*z0^4 + 2*x^7*y - 2*x^5*y*z0^2 + 2*x^3*y*z0^4 - 2*x^6*y - x^6*z0 + 2*x^4*y*z0^2 + x^4*z0^3 - x^2*y*z0^4 + x^5*y + 2*x^5*z0 + x^3*y*z0^2 - 2*x^3*z0^3 + 2*x^4*y + 2*x^4*z0 + 2*x^2*z0^3 + 2*x^3*y - 2*x^3*z0 - x^2*y + x^2*z0 + x*y)/y) * dx, - ((-2*x^61*z0^4 + x^60*z0^4 + 2*x^58*y^2*z0^4 + 2*x^61*z0^2 + x^59*z0^4 - x^57*y^2*z0^4 + 2*x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^58*z0^4 - x^56*y^2*z0^4 - 2*x^61 - 2*x^57*y^2*z0^2 - x^57*z0^4 + 2*x^58*y^2 - 2*x^58*z0^2 - x^56*z0^4 - 2*x^57*z0^2 - 2*x^55*z0^4 + 2*x^58 + x^54*z0^4 + 2*x^55*z0^2 + x^53*z0^4 + 2*x^54*z0^2 + 2*x^52*z0^4 - 2*x^55 - x^51*z0^4 - 2*x^52*z0^2 - x^50*z0^4 - 2*x^51*z0^2 - 2*x^49*z0^4 + 2*x^52 + x^48*z0^4 + 2*x^49*z0^2 + x^47*z0^4 + 2*x^48*z0^2 + 2*x^46*z0^4 - 2*x^49 - x^45*z0^4 - 2*x^46*z0^2 - x^44*z0^4 - 2*x^45*z0^2 - 2*x^43*z0^4 + 2*x^46 + x^42*z0^4 + 2*x^43*z0^2 - 2*x^41*z0^4 + 2*x^42*z0^2 - x^40*y*z0^3 + x^40*z0^4 - 2*x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + x^40*y*z0 + 2*x^40*z0^2 - x^38*z0^4 + 2*x^41 + 2*x^39*y*z0 + x^39*z0^2 + 2*x^37*y*z0^3 + 2*x^37*z0^4 + 2*x^40 - x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 - 2*x^36*z0^4 - 2*x^39 - x^37*y*z0 + x^35*z0^4 + x^38 + x^36*y*z0 - x^36*z0^2 + 2*x^34*y*z0^3 - x^37 + x^35*y*z0 + x^35*z0^2 - 2*x^33*y*z0^3 - 2*x^33*z0^4 + 2*x^36 + 2*x^34*y*z0 - 2*x^34*z0^2 + 2*x^32*z0^4 - 2*x^35 + 2*x^33*y*z0 - x^32*y*z0 + x^32*z0^2 + 2*x^30*y*z0^3 - x^33 - 2*x^31*y*z0 + 2*x^31*z0^2 - x^29*y*z0^3 + 2*x^29*z0^4 + x^32 - x^30*y*z0 - x^30*z0^2 - x^28*z0^4 + 2*x^29*y*z0 + x^27*y*z0^3 + x^30 + 2*x^28*z0^2 - 2*x^26*y*z0^3 - x^26*z0^4 + x^29 - 2*x^27*z0^2 - x^25*y*z0^3 + x^25*z0^4 - 2*x^28 - x^26*z0^2 - x^24*y*z0^3 - 2*x^25*y*z0 - x^25*z0^2 - x^23*z0^4 - 2*x^26 - 2*x^24*y*z0 + x^22*y*z0^3 + 2*x^25 + 2*x^23*y*z0 - x^23*z0^2 - x^21*y*z0^3 + x^21*z0^4 - 2*x^24 + 2*x^22*y*z0 - 2*x^20*y*z0^3 - x^20*z0^4 + 2*x^23 - 2*x^21*y*z0 - 2*x^21*z0^2 - 2*x^19*z0^4 + x^22 - x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 - 2*x^18*z0^4 - 2*x^21 + x^19*y*z0 - x^19*z0^2 + x^17*y*z0^3 + x^17*z0^4 + x^20 + 2*x^18*y*z0 + 2*x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^16*z0^4 - 2*x^19 + 2*x^15*z0^4 - 2*x^18 - 2*x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 + 2*x^15*y*z0 - 2*x^15*z0^2 + 2*x^13*y*z0^3 + x^13*z0^4 - 2*x^16 - x^14*y*z0 + x^14*z0^2 - 2*x^12*y*z0^3 - x^12*z0^4 + x^15 - 2*x^13*y*z0 + 2*x^13*z0^2 + 2*x^11*y*z0^3 + x^11*z0^4 - x^14 - x^12*y*z0 + x^12*z0^2 + 2*x^10*y*z0^3 - 2*x^13 - 2*x^11*y*z0 + x^11*z0^2 - x^9*y*z0^3 + x^9*z0^4 - 2*x^10*y*z0 - 2*x^8*z0^4 + 2*x^11 - 2*x^9*z0^2 - 2*x^7*y*z0^3 - x^7*z0^4 - x^10 + x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 + x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 - 2*x^5*z0^4 + x^6*y*z0 - x^6*z0^2 + x^7 - x^5*z0^2 - x^3*y*z0^3 - 2*x^3*z0^4 - x^6 - x^4*z0^2 - 2*x^2*y*z0^3 - x^2*z0^4 + x^3*y*z0 + x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 - x^3 + x*y*z0 + 2*x^2)/y) * dx, - ((-x^60*z0^3 + 2*x^61*z0 + x^59*z0^3 + x^57*y^2*z0^3 - x^60*z0 - 2*x^58*y^2*z0 - x^58*z0^3 - x^56*y^2*z0^3 + x^59*z0 + x^57*y^2*z0 - x^57*z0^3 + x^55*y^2*z0^3 - 2*x^58*z0 - x^56*y^2*z0 - x^56*z0^3 + 2*x^54*y^2*z0^3 + x^57*z0 + x^55*z0^3 - x^56*z0 + x^54*z0^3 + 2*x^55*z0 + x^53*z0^3 - x^54*z0 - x^52*z0^3 + x^53*z0 - x^51*z0^3 - 2*x^52*z0 - x^50*z0^3 + x^51*z0 + x^49*z0^3 - x^50*z0 + x^48*z0^3 + 2*x^49*z0 + x^47*z0^3 - x^48*z0 - x^46*z0^3 + x^47*z0 - x^45*z0^3 - 2*x^46*z0 - x^44*z0^3 + x^45*z0 + x^43*z0^3 - x^44*z0 + x^42*z0^3 + 2*x^43*z0 + x^41*z0^3 - x^42*z0 + x^40*z0^3 - 2*x^38*y*z0^4 - 2*x^41*z0 + 2*x^39*y*z0^2 + 2*x^39*z0^3 - x^37*y*z0^4 + x^40*y + x^40*z0 - 2*x^38*y*z0^2 + 2*x^36*y*z0^4 + 2*x^39*y + x^39*z0 + x^37*z0^3 + 2*x^35*y*z0^4 + 2*x^38*y - x^38*z0 - 2*x^36*y*z0^2 + x^36*z0^3 + 2*x^37*y + 2*x^37*z0 + 2*x^35*y*z0^2 - 2*x^35*z0^3 + 2*x^33*y*z0^4 - x^36*y + 2*x^36*z0 - 2*x^34*y*z0^2 - x^34*z0^3 - 2*x^32*y*z0^4 - 2*x^35*y + 2*x^35*z0 - x^33*z0^3 + x^31*y*z0^4 + 2*x^34*y - 2*x^32*y*z0^2 - x^32*z0^3 + x^30*y*z0^4 + x^33*y - 2*x^33*z0 + x^31*y*z0^2 + x^31*z0^3 - x^29*y*z0^4 + x^32*y - x^32*z0 - 2*x^30*y*z0^2 + 2*x^30*z0^3 - x^28*y*z0^4 - x^31*y + x^31*z0 + x^29*y*z0^2 - x^29*z0^3 + x^27*y*z0^4 + x^30*y - x^30*z0 + 2*x^28*y*z0^2 - 2*x^28*z0^3 - x^29*y - 2*x^29*z0 + 2*x^27*y*z0^2 - 2*x^27*z0^3 + 2*x^25*y*z0^4 + x^28*y + 2*x^28*z0 + 2*x^26*y*z0^2 + 2*x^26*z0^3 - x^24*y*z0^4 + 2*x^27*y - x^27*z0 + 2*x^25*y*z0^2 - 2*x^25*z0^3 - 2*x^23*y*z0^4 + x^26*y - x^26*z0 + x^25*z0 + x^23*y*z0^2 - x^24*y + x^24*z0 - 2*x^22*y*z0^2 + 2*x^22*z0^3 + x^23*y + 2*x^21*y*z0^2 + x^21*z0^3 + 2*x^19*y*z0^4 - x^22*z0 + x^20*y*z0^2 + 2*x^20*z0^3 - x^18*y*z0^4 + x^21*y - 2*x^21*z0 + x^19*y*z0^2 + 2*x^19*z0^3 + x^17*y*z0^4 + x^18*y*z0^2 + x^16*y*z0^4 - x^19*y + 2*x^19*z0 + x^17*y*z0^2 + 2*x^17*z0^3 - x^15*y*z0^4 + x^18*y + 2*x^18*z0 - 2*x^16*y*z0^2 - x^16*z0^3 - x^14*y*z0^4 - x^17*y + x^17*z0 + x^15*y*z0^2 - x^15*z0^3 - x^13*y*z0^4 + x^16*y - 2*x^16*z0 - x^14*y*z0^2 + x^14*z0^3 + x^12*y*z0^4 - 2*x^15*y - 2*x^15*z0 + 2*x^13*y*z0^2 - 2*x^13*z0^3 - x^11*y*z0^4 - 2*x^14*y + x^12*y*z0^2 - x^12*z0^3 + 2*x^10*y*z0^4 - 2*x^11*y*z0^2 + 2*x^11*z0^3 + 2*x^12*y + 2*x^12*z0 - 2*x^10*z0^3 - x^8*y*z0^4 - 2*x^11*z0 + x^9*y*z0^2 - x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y + x^8*z0^3 + x^6*y*z0^4 - 2*x^9*z0 + x^7*y*z0^2 + 2*x^7*z0^3 + 2*x^5*y*z0^4 - 2*x^8*y - 2*x^8*z0 + 2*x^6*z0^3 + x^4*y*z0^4 + x^7*y - 2*x^7*z0 + 2*x^5*y*z0^2 - 2*x^5*z0^3 - 2*x^3*y*z0^4 - 2*x^6*y + x^6*z0 + 2*x^4*y*z0^2 - 2*x^2*y*z0^4 + 2*x^5*y - x^5*z0 - x^3*y*z0^2 + 2*x^3*z0^3 - 2*x^4*y + x^4*z0 - 2*x^2*z0^3 + x^3*y + x^3*z0 + x*y*z0^2 + 2*x^2*y)/y) * dx, - ((-x^60*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 + 2*x^61 - x^57*y^2*z0^2 + x^57*z0^4 - 2*x^58*y^2 - x^57*z0^2 - 2*x^58 - x^54*z0^4 + x^54*z0^2 + 2*x^55 + x^51*z0^4 - x^51*z0^2 - 2*x^52 - x^48*z0^4 + x^48*z0^2 + 2*x^49 + x^45*z0^4 - x^45*z0^2 - 2*x^46 - x^42*z0^4 + x^41*z0^4 + x^42*z0^2 + x^40*z0^4 + 2*x^43 - x^39*z0^4 - 2*x^40*z0^2 + 2*x^38*z0^4 + x^41 - x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 + x^37*z0^4 - 2*x^38*y*z0 + x^36*z0^4 - 2*x^39 - x^37*y*z0 + 2*x^37*z0^2 + 2*x^35*y*z0^3 + 2*x^38 - x^36*y*z0 + x^36*z0^2 + x^34*y*z0^3 + x^34*z0^4 + x^37 - 2*x^35*y*z0 + 2*x^35*z0^2 - 2*x^33*y*z0^3 + x^36 + 2*x^34*y*z0 + 2*x^34*z0^2 - x^32*y*z0^3 + 2*x^32*z0^4 - 2*x^33*y*z0 + 2*x^31*y*z0^3 - 2*x^31*z0^4 + x^34 - x^32*y*z0 - x^32*z0^2 + 2*x^30*z0^4 - x^33 - 2*x^31*y*z0 - x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^32 - x^30*y*z0 - x^30*z0^2 - x^28*y*z0^3 + x^28*z0^4 - 2*x^31 + x^29*y*z0 - x^29*z0^2 - 2*x^27*y*z0^3 - x^27*z0^4 - x^30 - x^28*y*z0 + 2*x^28*z0^2 + x^26*y*z0^3 + x^26*z0^4 + x^29 + x^27*y*z0 + 2*x^27*z0^2 + 2*x^25*y*z0^3 + x^25*z0^4 + x^26*y*z0 + x^26*z0^2 + 2*x^24*y*z0^3 + 2*x^24*z0^4 - x^27 - 2*x^25*y*z0 - x^25*z0^2 - x^23*z0^4 + 2*x^26 - 2*x^24*y*z0 - 2*x^24*z0^2 - x^22*y*z0^3 - 2*x^22*z0^4 + 2*x^25 - x^23*y*z0 + x^23*z0^2 - x^21*z0^4 + x^22*y*z0 + x^22*z0^2 - x^20*y*z0^3 + x^20*z0^4 + x^23 + 2*x^21*y*z0 + 2*x^21*z0^2 + 2*x^19*y*z0^3 + x^22 + 2*x^20*y*z0 - x^20*z0^2 - 2*x^18*y*z0^3 - x^18*z0^4 - x^19*y*z0 + 2*x^19*z0^2 + x^17*y*z0^3 + 2*x^17*z0^4 - 2*x^20 + 2*x^16*y*z0^3 + x^16*z0^4 + x^17*y*z0 - x^15*y*z0^3 - x^15*z0^4 - x^14*y*z0^3 + x^17 - 2*x^15*y*z0 + 2*x^13*y*z0^3 + 2*x^13*z0^4 - x^16 + 2*x^14*y*z0 - 2*x^14*z0^2 - 2*x^12*y*z0^3 + 2*x^12*z0^4 + x^15 + x^13*z0^2 + 2*x^11*y*z0^3 + 2*x^11*z0^4 + x^14 - x^12*z0^2 - x^10*y*z0^3 - 2*x^11*y*z0 - x^11*z0^2 - x^9*y*z0^3 - x^9*z0^4 + 2*x^12 - 2*x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^11 + x^9*y*z0 + 2*x^9*z0^2 + x^7*y*z0^3 - x^7*z0^4 - 2*x^10 + 2*x^8*y*z0 - x^6*z0^4 - 2*x^9 + 2*x^7*y*z0 + 2*x^5*y*z0^3 + x^5*z0^4 + 2*x^8 + x^6*y*z0 - 2*x^4*y*z0^3 + 2*x^4*z0^4 + x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*y*z0^3 - x^3*z0^4 + 2*x^6 + 2*x^4*y*z0 - 2*x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 - 2*x^3*z0^2 + x*y*z0^3 - 2*x^2*y*z0 - x^3 + 2*x^2)/y) * dx, - ((-2*x^61*z0^3 + x^60*z0^3 + 2*x^58*y^2*z0^3 + 2*x^61*z0 - x^59*z0^3 - x^57*y^2*z0^3 + x^60*z0 - 2*x^58*y^2*z0 - 2*x^58*z0^3 + x^56*y^2*z0^3 + 2*x^59*z0 - x^57*y^2*z0 + 2*x^57*z0^3 - x^55*y^2*z0^3 - 2*x^58*z0 - 2*x^56*y^2*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 - x^57*z0 + 2*x^55*z0^3 - 2*x^56*z0 - 2*x^54*z0^3 + 2*x^55*z0 - x^53*z0^3 + x^54*z0 - 2*x^52*z0^3 + 2*x^53*z0 + 2*x^51*z0^3 - 2*x^52*z0 + x^50*z0^3 - x^51*z0 + 2*x^49*z0^3 - 2*x^50*z0 - 2*x^48*z0^3 + 2*x^49*z0 - x^47*z0^3 + x^48*z0 - 2*x^46*z0^3 + 2*x^47*z0 + 2*x^45*z0^3 - 2*x^46*z0 + x^44*z0^3 - x^45*z0 + 2*x^43*z0^3 - 2*x^44*z0 - 2*x^42*z0^3 + 2*x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 + x^42*z0 - x^40*y*z0^2 - x^40*z0^3 - 2*x^38*y*z0^4 - x^41*z0 + 2*x^39*y*z0^2 - x^39*z0^3 + 2*x^37*y*z0^4 + x^40*y + 2*x^40*z0 + x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 + x^39*y + x^39*z0 + x^37*y*z0^2 + 2*x^37*z0^3 - x^35*y*z0^4 - x^38*y - x^38*z0 - 2*x^36*z0^3 - x^34*y*z0^4 + 2*x^37*y - x^37*z0 + 2*x^35*y*z0^2 - 2*x^35*z0^3 - 2*x^33*y*z0^4 + 2*x^36*y - x^34*y*z0^2 - 2*x^34*z0^3 + x^32*y*z0^4 - 2*x^35*y - 2*x^35*z0 - x^33*y*z0^2 - x^33*z0^3 + x^31*y*z0^4 + x^34*y + 2*x^34*z0 + 2*x^32*y*z0^2 - 2*x^30*y*z0^4 + x^33*y + x^33*z0 - 2*x^31*y*z0^2 - x^31*z0^3 + x^29*y*z0^4 - x^30*y*z0^2 - x^30*z0^3 + 2*x^28*y*z0^4 + x^31*y - 2*x^31*z0 - x^27*y*z0^4 + x^30*y + 2*x^30*z0 - x^28*z0^3 - x^26*y*z0^4 - x^29*y - x^29*z0 + x^25*y*z0^4 - x^28*y + x^26*y*z0^2 + x^26*z0^3 - x^24*y*z0^4 + 2*x^27*y + 2*x^25*y*z0^2 - 2*x^25*z0^3 - x^23*y*z0^4 + x^26*y + x^24*y*z0^2 + x^24*z0^3 + 2*x^25*y - x^23*y*z0^2 + 2*x^23*z0^3 - x^21*y*z0^4 + x^24*y + x^24*z0 + 2*x^22*y*z0^2 + x^22*z0^3 + x^20*y*z0^4 - 2*x^23*y + 2*x^21*y*z0^2 - x^21*z0^3 + x^19*y*z0^4 + 2*x^22*y + x^20*y*z0^2 + 2*x^20*z0^3 + x^21*y - x^21*z0 - 2*x^19*y*z0^2 + 2*x^19*z0^3 - 2*x^20*z0 + 2*x^18*y*z0^2 - 2*x^18*z0^3 - x^16*y*z0^4 - 2*x^19*z0 - 2*x^17*y*z0^2 + 2*x^17*z0^3 + 2*x^15*y*z0^4 + 2*x^18*z0 + x^16*y*z0^2 + 2*x^14*y*z0^4 + x^17*y + x^17*z0 + 2*x^15*y*z0^2 + 2*x^15*z0^3 + 2*x^13*y*z0^4 - x^16*z0 - x^14*z0^3 - x^12*y*z0^4 - 2*x^15*z0 - x^13*y*z0^2 - x^11*y*z0^4 + 2*x^14*y + 2*x^14*z0 + x^12*y*z0^2 + x^12*z0^3 + x^10*y*z0^4 - 2*x^13*y - 2*x^13*z0 + 2*x^11*y*z0^2 + x^9*y*z0^4 - x^12*z0 + 2*x^10*y*z0^2 - 2*x^10*z0^3 - x^8*y*z0^4 - x^11*y + 2*x^11*z0 - 2*x^9*z0^3 + 2*x^7*y*z0^4 - x^10*z0 + 2*x^8*y*z0^2 + x^8*z0^3 - 2*x^9*y - x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 - x^5*y*z0^4 - x^8*y - x^6*y*z0^2 - 2*x^6*z0^3 - x^4*y*z0^4 + 2*x^7*y - x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - 2*x^6*y + x^4*y*z0^2 - x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y - x^5*z0 + x^3*z0^3 + x*y*z0^4 - 2*x^4*y + x^2*y*z0^2 - 2*x^3*z0 - x^2*y + x^2*z0)/y) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 + 2*x^61*z0^2 - 2*x^59*z0^4 + 2*x^60*z0^2 - 2*x^58*y^2*z0^2 - x^58*z0^4 + 2*x^56*y^2*z0^4 - x^61 - 2*x^57*y^2*z0^2 + 2*x^60 + x^58*y^2 - 2*x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 - 2*x^57*z0^2 + x^55*z0^4 + x^58 - 2*x^57 + 2*x^55*z0^2 - 2*x^53*z0^4 + 2*x^54*z0^2 - x^52*z0^4 - x^55 + 2*x^54 - 2*x^52*z0^2 + 2*x^50*z0^4 - 2*x^51*z0^2 + x^49*z0^4 + x^52 - 2*x^51 + 2*x^49*z0^2 - 2*x^47*z0^4 + 2*x^48*z0^2 - x^46*z0^4 - x^49 + 2*x^48 - 2*x^46*z0^2 + 2*x^44*z0^4 - 2*x^45*z0^2 + x^43*z0^4 + x^46 - 2*x^45 + 2*x^43*z0^2 + x^41*z0^4 + 2*x^42*z0^2 - 2*x^40*y*z0^3 - x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^42 + x^40*y*z0 - 2*x^40*z0^2 - x^38*y*z0^3 + x^38*z0^4 - 2*x^41 + x^39*y*z0 + x^39*z0^2 - 2*x^37*y*z0^3 + 2*x^37*z0^4 + x^40 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + 2*x^37*y*z0 + 2*x^37*z0^2 - x^35*y*z0^3 + x^35*z0^4 + 2*x^38 - x^36*y*z0 - x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^34*z0^4 - x^37 - 2*x^35*y*z0 - x^33*y*z0^3 + 2*x^33*z0^4 + x^36 - x^34*y*z0 + 2*x^34*z0^2 + x^32*y*z0^3 + 2*x^35 - x^33*y*z0 - x^33*z0^2 + x^31*y*z0^3 - x^31*z0^4 + 2*x^34 - 2*x^32*z0^2 - x^30*y*z0^3 + x^30*z0^4 + 2*x^33 + x^31*y*z0 + x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - 2*x^32 + 2*x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 - x^29*y*z0 - 2*x^29*z0^2 + x^27*y*z0^3 + 2*x^27*z0^4 + x^30 - 2*x^28*z0^2 + 2*x^29 - 2*x^27*y*z0 + 2*x^27*z0^2 - 2*x^25*y*z0^3 - 2*x^25*z0^4 + 2*x^28 - x^26*y*z0 - x^26*z0^2 - x^24*y*z0^3 - 2*x^24*z0^4 + 2*x^27 + 2*x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + 2*x^24*y*z0 + x^22*z0^4 + x^21*y*z0^3 - 2*x^21*z0^4 - x^24 + 2*x^22*y*z0 - 2*x^20*y*z0^3 - x^23 + 2*x^21*y*z0 - 2*x^21*z0^2 - x^19*y*z0^3 + x^19*z0^4 + 2*x^22 + x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 - 2*x^18*z0^4 - 2*x^21 - 2*x^19*y*z0 - 2*x^19*z0^2 + x^17*y*z0^3 - 2*x^17*z0^4 - 2*x^20 + 2*x^18*y*z0 + x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^16*z0^4 - 2*x^17*y*z0 + 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^15*z0^4 + 2*x^18 + x^16*y*z0 + x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 - 2*x^17 - 2*x^15*y*z0 + 2*x^15*z0^2 + x^13*z0^4 - 2*x^16 - 2*x^14*z0^2 - x^12*z0^4 - x^13*z0^2 + x^11*z0^4 + 2*x^14 - 2*x^12*z0^2 + 2*x^10*z0^4 - 2*x^13 - x^11*z0^2 - 2*x^9*y*z0^3 - x^9*z0^4 + x^10*y*z0 + x^8*y*z0^3 + x^8*z0^4 + x^11 + x^9*y*z0 + x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 - 2*x^8*y*z0 + 2*x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 - x^9 - 2*x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + 2*x^8 + 2*x^6*z0^2 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*y*z0 - x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 + x^6 - x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 + x^5 - 2*x^3*y*z0 + x^3*z0^2 + x^2*y*z0 + x^2*z0^2 + x*y^2)/y) * dx, - ((-2*x^61*z0^3 - x^60*z0^3 + 2*x^58*y^2*z0^3 - x^61*z0 - x^59*z0^3 + x^57*y^2*z0^3 + x^58*y^2*z0 - x^58*z0^3 + x^56*y^2*z0^3 - 2*x^59*z0 - x^57*z0^3 - 2*x^55*y^2*z0^3 + x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 + x^55*z0^3 + 2*x^56*z0 + x^54*z0^3 - x^55*z0 - x^53*z0^3 - x^52*z0^3 - 2*x^53*z0 - x^51*z0^3 + x^52*z0 + x^50*z0^3 + x^49*z0^3 + 2*x^50*z0 + x^48*z0^3 - x^49*z0 - x^47*z0^3 - x^46*z0^3 - 2*x^47*z0 - x^45*z0^3 + x^46*z0 + x^44*z0^3 + x^43*z0^3 + 2*x^44*z0 + x^42*z0^3 - x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 - x^40*y*z0^2 - x^38*y*z0^4 + 2*x^41*z0 - x^39*y*z0^2 + 2*x^39*z0^3 + 2*x^37*y*z0^4 + 2*x^40*y + 2*x^40*z0 - x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 + 2*x^39*z0 + 2*x^37*y*z0^2 + x^37*z0^3 - 2*x^38*z0 - 2*x^36*y*z0^2 + 2*x^34*y*z0^4 - x^37*y + 2*x^37*z0 + x^35*y*z0^2 + x^35*z0^3 + 2*x^33*y*z0^4 - 2*x^36*y + 2*x^36*z0 + 2*x^34*y*z0^2 + 2*x^34*z0^3 + 2*x^35*y + 2*x^33*y*z0^2 - x^33*z0^3 + 2*x^34*y - x^32*y*z0^2 - 2*x^32*z0^3 - 2*x^33*y + 2*x^33*z0 + x^31*y*z0^2 + x^31*z0^3 - x^29*y*z0^4 - x^32*y - 2*x^30*y*z0^2 - 2*x^30*z0^3 + x^28*y*z0^4 - x^31*y + x^31*z0 - x^29*y*z0^2 + x^29*z0^3 + x^27*y*z0^4 - x^30*y - x^30*z0 - x^28*z0^3 + 2*x^26*y*z0^4 - x^29*y - x^29*z0 - 2*x^27*y*z0^2 + 2*x^27*z0^3 + 2*x^25*y*z0^4 + 2*x^28*y - 2*x^28*z0 - x^26*z0^3 + x^27*y + 2*x^27*z0 + 2*x^25*y*z0^2 - 2*x^25*z0^3 - 2*x^26*z0 + x^24*y*z0^2 + 2*x^22*y*z0^4 + x^25*y + 2*x^25*z0 - 2*x^23*y*z0^2 - 2*x^23*z0^3 - 2*x^21*y*z0^4 + x^24*y + x^24*z0 + x^22*y*z0^2 - 2*x^20*y*z0^4 - 2*x^23*y + x^21*y*z0^2 - x^21*z0^3 - x^19*y*z0^4 - x^22*y + 2*x^22*z0 + 2*x^18*y*z0^4 - 2*x^21*y + x^21*z0 - x^19*y*z0^2 + 2*x^19*z0^3 + 2*x^17*y*z0^4 + 2*x^20*y - x^20*z0 - x^18*y*z0^2 - x^18*z0^3 - 2*x^16*y*z0^4 + 2*x^19*z0 + 2*x^17*y*z0^2 - 2*x^17*z0^3 - x^15*y*z0^4 - 2*x^18*y - x^18*z0 + x^16*y*z0^2 + x^14*y*z0^4 - x^17*y + 2*x^17*z0 - x^15*z0^3 - 2*x^13*y*z0^4 - x^16*y - 2*x^16*z0 - 2*x^14*y*z0^2 - x^14*z0^3 + 2*x^12*y*z0^4 - 2*x^15*z0 + x^13*y*z0^2 - 2*x^14*y + 2*x^14*z0 - 2*x^12*y*z0^2 + x^10*y*z0^4 + x^13*y + x^11*y*z0^2 + x^9*y*z0^4 - x^12*z0 + x^10*y*z0^2 + 2*x^10*z0^3 + 2*x^8*y*z0^4 + x^11*y - 2*x^11*z0 + 2*x^9*y*z0^2 + x^7*y*z0^4 - 2*x^10*y - 2*x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*y - 2*x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 + x^8*y + x^8*z0 + x^6*y*z0^2 - 2*x^4*y*z0^4 + 2*x^7*y - 2*x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 - 2*x^6*y + x^4*y*z0^2 - 2*x^4*z0^3 + 2*x^2*y*z0^4 + x^5*y + 2*x^5*z0 - 2*x^3*y*z0^2 - x^3*z0^3 + x^4*y + 2*x^4*z0 - 2*x^2*y*z0^2 + x^2*z0^3 + 2*x^3*y - x^3*z0 + x*y^2*z0 + x^2*y - x^2*z0)/y) * dx, - ((2*x^61*z0^4 - 2*x^60*z0^4 - 2*x^58*y^2*z0^4 - 2*x^61*z0^2 - x^59*z0^4 + 2*x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 - x^57*y^2*z0^2 + 2*x^57*z0^4 - x^60 + 2*x^58*z0^2 + x^56*z0^4 + x^57*y^2 - x^57*z0^2 + 2*x^55*z0^4 - 2*x^54*z0^4 + x^57 - 2*x^55*z0^2 - x^53*z0^4 + x^54*z0^2 - 2*x^52*z0^4 + 2*x^51*z0^4 - x^54 + 2*x^52*z0^2 + x^50*z0^4 - x^51*z0^2 + 2*x^49*z0^4 - 2*x^48*z0^4 + x^51 - 2*x^49*z0^2 - x^47*z0^4 + x^48*z0^2 - 2*x^46*z0^4 + 2*x^45*z0^4 - x^48 + 2*x^46*z0^2 + x^44*z0^4 - x^45*z0^2 + 2*x^43*z0^4 - 2*x^42*z0^4 + x^45 - 2*x^43*z0^2 + x^41*z0^4 + x^42*z0^2 + x^40*y*z0^3 + x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - x^42 - x^40*y*z0 - 2*x^40*z0^2 - x^38*z0^4 + 2*x^41 - 2*x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 - 2*x^37*z0^4 - x^40 + 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - 2*x^35*y*z0^3 - 2*x^35*z0^4 + 2*x^38 + x^36*y*z0 - x^36*z0^2 + x^34*y*z0^3 - x^37 - x^35*y*z0 - 2*x^35*z0^2 + 2*x^33*y*z0^3 - x^34*y*z0 + x^32*y*z0^3 + 2*x^35 - 2*x^33*z0^2 - 2*x^31*y*z0^3 - 2*x^31*z0^4 + 2*x^34 + 2*x^32*z0^2 + 2*x^30*y*z0^3 - x^30*z0^4 - x^33 + 2*x^31*y*z0 - 2*x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 + 2*x^28*y*z0^3 + 2*x^28*z0^4 - x^29*y*z0 - x^29*z0^2 + 2*x^27*y*z0^3 - 2*x^27*z0^4 - 2*x^30 - x^28*y*z0 + 2*x^26*y*z0^3 + 2*x^26*z0^4 + 2*x^27*y*z0 + x^27*z0^2 + x^25*y*z0^3 + 2*x^28 - 2*x^26*y*z0 + x^26*z0^2 + 2*x^24*y*z0^3 + x^24*z0^4 + 2*x^27 + x^25*y*z0 - 2*x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 + 2*x^26 - 2*x^24*y*z0 + 2*x^24*z0^2 + 2*x^22*y*z0^3 - x^22*z0^4 + 2*x^25 + x^23*y*z0 - 2*x^23*z0^2 - x^21*y*z0^3 - 2*x^22*y*z0 - x^22*z0^2 - x^20*y*z0^3 + 2*x^20*z0^4 + 2*x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 - x^19*z0^4 - x^20*y*z0 + x^20*z0^2 + x^18*y*z0^3 + 2*x^18*z0^4 - 2*x^21 - 2*x^19*y*z0 - x^17*y*z0^3 + 2*x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^19 + 2*x^17*y*z0 + 2*x^17*z0^2 - x^15*y*z0^3 - 2*x^18 + 2*x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 + x^17 - x^15*y*z0 - x^13*y*z0^3 - x^13*z0^4 + x^16 - 2*x^14*y*z0 + x^12*y*z0^3 + x^15 - 2*x^13*y*z0 - 2*x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 - x^10*y*z0^3 - x^10*z0^4 - x^11*y*z0 + 2*x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^12 - x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 + 2*x^7*y*z0^3 + x^7*z0^4 + 2*x^10 + 2*x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 - x^7*y*z0 + 2*x^7*z0^2 + 2*x^5*z0^4 - x^8 + 2*x^6*y*z0 + x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 + 2*x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 - 2*x^2*z0^4 + x^3*y*z0 - x^3*z0^2 + x*y^2*z0^2 + x^2*z0^2 + x^3 - x^2)/y) * dx, - ((-2*x^61*z0^3 + 2*x^58*y^2*z0^3 - 2*x^61*z0 - x^59*z0^3 + x^60*z0 + 2*x^58*y^2*z0 + x^58*z0^3 + x^56*y^2*z0^3 - 2*x^59*z0 - x^57*y^2*z0 + x^55*y^2*z0^3 + 2*x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 - x^57*z0 - x^55*z0^3 + 2*x^56*z0 - 2*x^55*z0 - x^53*z0^3 + x^54*z0 + x^52*z0^3 - 2*x^53*z0 + 2*x^52*z0 + x^50*z0^3 - x^51*z0 - x^49*z0^3 + 2*x^50*z0 - 2*x^49*z0 - x^47*z0^3 + x^48*z0 + x^46*z0^3 - 2*x^47*z0 + 2*x^46*z0 + x^44*z0^3 - x^45*z0 - x^43*z0^3 + 2*x^44*z0 - 2*x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 + x^42*z0 - x^40*y*z0^2 + x^40*z0^3 + x^41*z0 - 2*x^39*y*z0^2 - 2*x^39*z0^3 - x^37*y*z0^4 - x^40*y - 2*x^40*z0 + x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 - 2*x^39*y + 2*x^39*z0 + x^37*y*z0^2 - 2*x^38*y + x^38*z0 - x^36*z0^3 + x^34*y*z0^4 - 2*x^37*y + 2*x^37*z0 + 2*x^35*y*z0^2 - x^35*z0^3 - x^33*y*z0^4 - x^36*y + 2*x^36*z0 - 2*x^34*y*z0^2 - x^34*z0^3 + 2*x^32*y*z0^4 - 2*x^35*y + x^35*z0 + x^33*z0^3 + x^31*y*z0^4 - x^34*z0 + x^32*z0^3 + 2*x^30*y*z0^4 + x^33*y - 2*x^33*z0 + x^31*z0^3 + x^29*y*z0^4 - x^32*y + x^32*z0 - x^30*z0^3 - 2*x^31*y + x^31*z0 + x^29*y*z0^2 - 2*x^27*y*z0^4 + 2*x^30*y + 2*x^30*z0 + x^28*y*z0^2 - x^28*z0^3 - 2*x^26*y*z0^4 + 2*x^29*z0 + x^28*y - x^28*z0 + x^26*y*z0^2 - x^26*z0^3 - 2*x^24*y*z0^4 + 2*x^27*y + x^27*z0 + x^25*y*z0^2 + 2*x^25*z0^3 + x^23*y*z0^4 + x^26*y - x^26*z0 - 2*x^24*y*z0^2 - x^25*y + 2*x^23*y*z0^2 + 2*x^23*z0^3 + x^24*y - x^24*z0 - 2*x^22*y*z0^2 - x^22*z0^3 - 2*x^20*y*z0^4 - x^23*z0 + x^21*y*z0^2 - x^21*z0^3 - 2*x^19*y*z0^4 + 2*x^22*y - x^22*z0 + x^20*z0^3 + x^18*y*z0^4 + 2*x^21*y - 2*x^21*z0 + x^19*y*z0^2 + x^19*z0^3 + x^17*y*z0^4 + x^20*y + 2*x^20*z0 + x^18*z0^3 - 2*x^16*y*z0^4 - x^19*y + x^17*y*z0^2 + x^17*z0^3 + x^15*y*z0^4 + x^18*y + 2*x^18*z0 - 2*x^16*z0^3 + x^14*y*z0^4 + 2*x^15*y*z0^2 - 2*x^15*z0^3 - 2*x^16*y - x^14*z0^3 - 2*x^12*y*z0^4 + x^15*y + x^13*y*z0^2 + 2*x^11*y*z0^4 - 2*x^14*z0 + x^12*y*z0^2 - x^12*z0^3 - x^13*y - x^13*z0 + 2*x^11*y*z0^2 - 2*x^11*z0^3 - 2*x^9*y*z0^4 + x^10*y*z0^2 + x^10*z0^3 - x^8*y*z0^4 + x^11*y - x^11*z0 + 2*x^9*y*z0^2 + 2*x^7*y*z0^4 + 2*x^10*y + 2*x^10*z0 - x^8*z0^3 + x^6*y*z0^4 - x^9*z0 + x^7*y*z0^2 + x^7*z0^3 - x^5*y*z0^4 + 2*x^8*y + x^8*z0 - 2*x^6*y*z0^2 + 2*x^6*z0^3 - x^4*y*z0^4 - x^7*y - 2*x^5*y*z0^2 - x^5*z0^3 - x^3*y*z0^4 + 2*x^6*z0 - 2*x^4*y*z0^2 + x^5*y - 2*x^3*z0^3 + x*y^2*z0^3 - 2*x^4*y + x^4*z0 - x^2*y*z0^2 + 2*x^2*z0^3 + x^3*y + 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-x^60*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^56*y^2*z0^4 - x^57*y^2*z0^2 + x^57*z0^4 - 2*x^60 + 2*x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 - x^57*z0^2 - x^54*z0^4 + 2*x^57 - 2*x^55*z0^2 + 2*x^53*z0^4 + x^54*z0^2 + x^51*z0^4 - 2*x^54 + 2*x^52*z0^2 - 2*x^50*z0^4 - x^51*z0^2 - x^48*z0^4 + 2*x^51 - 2*x^49*z0^2 + 2*x^47*z0^4 + x^48*z0^2 + x^45*z0^4 - 2*x^48 + 2*x^46*z0^2 - 2*x^44*z0^4 - x^45*z0^2 - x^42*z0^4 + 2*x^45 - 2*x^43*z0^2 + 2*x^41*z0^4 + x^42*z0^2 - x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - 2*x^42 - x^40*y*z0 + x^40*z0^2 + x^38*y*z0^3 + 2*x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 - x^40 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 - x^35*z0^4 - x^38 + 2*x^36*y*z0 - x^36*z0^2 + x^34*y*z0^3 + 2*x^34*z0^4 + x^37 - 2*x^35*y*z0 + x^35*z0^2 - x^33*y*z0^3 - 2*x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 + x^34*z0^2 - 2*x^32*y*z0^3 - x^35 + 2*x^33*y*z0 + 2*x^33*z0^2 + x^31*y*z0^3 + x^31*z0^4 - 2*x^34 + x^32*z0^2 - x^30*y*z0^3 + 2*x^30*z0^4 + x^33 - x^31*y*z0 - x^31*z0^2 + x^29*z0^4 + x^30*y*z0 - 2*x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^29*y*z0 + x^29*z0^2 + x^30 + 2*x^28*y*z0 - x^28*z0^2 + x^26*y*z0^3 - 2*x^26*z0^4 - x^27*y*z0 - 2*x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 - x^28 + 2*x^24*y*z0^3 - 2*x^24*z0^4 - x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + x^24*y*z0 - x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^25 - x^23*y*z0 + x^23*z0^2 - x^21*y*z0^3 + x^21*z0^4 + 2*x^24 + x^22*y*z0 - x^20*y*z0^3 + x^20*z0^4 - x^23 - x^21*y*z0 + x^21*z0^2 - x^19*y*z0^3 - x^19*z0^4 - 2*x^22 - x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 + x^18*z0^4 + x^21 - x^19*y*z0 + 2*x^20 - x^18*y*z0 - x^18*z0^2 + 2*x^16*y*z0^3 - 2*x^16*z0^4 + x^19 + x^17*y*z0 - x^15*y*z0^3 - 2*x^15*z0^4 + x^18 + 2*x^16*y*z0 + 2*x^16*z0^2 - 2*x^14*z0^4 + 2*x^15*y*z0 - 2*x^15*z0^2 - 2*x^13*y*z0^3 - 2*x^13*z0^4 - x^16 + x^14*z0^2 + x^12*y*z0^3 + 2*x^12*z0^4 + 2*x^13*y*z0 - 2*x^13*z0^2 - x^11*y*z0^3 - 2*x^11*z0^4 + x^14 + x^12*y*z0 - x^10*y*z0^3 - 2*x^10*z0^4 - 2*x^13 - 2*x^11*y*z0 + 2*x^11*z0^2 + x^12 + x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^11 + x^9*z0^2 - x^7*y*z0^3 + x^7*z0^4 - x^8*y*z0 - x^8*z0^2 + x^6*y*z0^3 - 2*x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 + x^4*y*z0^3 - x^4*z0^4 - 2*x^5*y*z0 - x^3*y*z0^3 + x^3*z0^4 + x*y^2*z0^4 + 2*x^6 - 2*x^4*y*z0 - x^4*z0^2 + 2*x^2*z0^4 + 2*x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^5 + x^2*y^2 + x^2)/y) * dx, - ((-x^5*z0 + x^2*y^2*z0 + x^2*z0)/y) * dx, - ((-x^5*z0^2 + x^2*y^2*z0^2 + x^2*z0^2)/y) * dx, - ((-x^5*z0^3 + x^2*y^2*z0^3 + x^2*z0^3)/y) * dx, - ((-x^5*z0^4 + x^2*y^2*z0^4 + x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^6 + x^3*y^2 + x^3)/y) * dx, - ((-x^6*z0 + x^3*y^2*z0 + x^3*z0)/y) * dx, - ((-x^6*z0^2 + x^3*y^2*z0^2 + x^3*z0^2)/y) * dx, - ((-x^6*z0^3 + x^3*y^2*z0^3 + x^3*z0^3)/y) * dx, - ((-x^6*z0^4 + x^3*y^2*z0^4 + x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 + x^58*y^2*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 - 2*x^60*z0^2 + 2*x^58*y^2*z0^2 + x^58*z0^4 - 2*x^56*y^2*z0^4 + x^61 + 2*x^57*y^2*z0^2 - 2*x^60 - x^58*y^2 + 2*x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 + 2*x^57*z0^2 - x^55*z0^4 - x^58 + 2*x^57 - 2*x^55*z0^2 + 2*x^53*z0^4 - 2*x^54*z0^2 + x^52*z0^4 + x^55 - 2*x^54 + 2*x^52*z0^2 - 2*x^50*z0^4 + 2*x^51*z0^2 - x^49*z0^4 - x^52 + 2*x^51 - 2*x^49*z0^2 + 2*x^47*z0^4 - 2*x^48*z0^2 + x^46*z0^4 + x^49 - 2*x^48 + 2*x^46*z0^2 - 2*x^44*z0^4 + 2*x^45*z0^2 - x^43*z0^4 - x^46 + 2*x^45 - 2*x^43*z0^2 - x^41*z0^4 - 2*x^42*z0^2 + 2*x^40*y*z0^3 + x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - 2*x^42 - x^40*y*z0 + 2*x^40*z0^2 + x^38*y*z0^3 - x^38*z0^4 + 2*x^41 - x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 - x^40 + 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - 2*x^37*y*z0 - 2*x^37*z0^2 + x^35*y*z0^3 - x^35*z0^4 - 2*x^38 + x^36*y*z0 + x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 + x^37 + 2*x^35*y*z0 + x^33*y*z0^3 - 2*x^33*z0^4 - x^36 + x^34*y*z0 - 2*x^34*z0^2 - x^32*y*z0^3 - 2*x^35 + x^33*y*z0 + x^33*z0^2 - x^31*y*z0^3 + x^31*z0^4 - 2*x^34 + 2*x^32*z0^2 + x^30*y*z0^3 - x^30*z0^4 - 2*x^33 - x^31*y*z0 - x^31*z0^2 - x^29*y*z0^3 - x^29*z0^4 + 2*x^32 - 2*x^28*y*z0^3 + 2*x^28*z0^4 - 2*x^31 + x^29*y*z0 + 2*x^29*z0^2 - x^27*y*z0^3 - 2*x^27*z0^4 - x^30 + 2*x^28*z0^2 - 2*x^29 + 2*x^27*y*z0 - 2*x^27*z0^2 + 2*x^25*y*z0^3 + 2*x^25*z0^4 - 2*x^28 + x^26*y*z0 + x^26*z0^2 + x^24*y*z0^3 + 2*x^24*z0^4 - 2*x^27 - 2*x^25*z0^2 + x^23*y*z0^3 - x^23*z0^4 + 2*x^26 - 2*x^24*y*z0 - x^22*z0^4 - x^21*y*z0^3 + 2*x^21*z0^4 + x^24 - 2*x^22*y*z0 + 2*x^20*y*z0^3 + x^23 - 2*x^21*y*z0 + 2*x^21*z0^2 + x^19*y*z0^3 - x^19*z0^4 - 2*x^22 - x^20*y*z0 - 2*x^20*z0^2 - x^18*y*z0^3 + 2*x^18*z0^4 + 2*x^21 + 2*x^19*y*z0 + 2*x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 + 2*x^20 - 2*x^18*y*z0 - x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^16*z0^4 + 2*x^17*y*z0 - 2*x^17*z0^2 - x^15*y*z0^3 - 2*x^15*z0^4 - 2*x^18 - x^16*y*z0 - x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 + 2*x^17 + 2*x^15*y*z0 - 2*x^15*z0^2 - x^13*z0^4 + 2*x^16 + 2*x^14*z0^2 + x^12*z0^4 + x^13*z0^2 - x^11*z0^4 - 2*x^14 + 2*x^12*z0^2 - 2*x^10*z0^4 + 2*x^13 + x^11*z0^2 + 2*x^9*y*z0^3 + x^9*z0^4 - x^10*y*z0 - x^8*y*z0^3 - x^8*z0^4 - x^11 - x^9*y*z0 - x^7*y*z0^3 - 2*x^7*z0^4 + 2*x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 + 2*x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 - 2*x^8 - 2*x^6*z0^2 + 2*x^4*z0^4 + x^7 + 2*x^5*y*z0 + x^5*z0^2 + 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 + x^4*y^2 + x^4*y*z0 + x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 - x^5 + 2*x^3*y*z0 - x^3*z0^2 - x^2*y*z0 - x^2*z0^2)/y) * dx, - ((2*x^61*z0^3 + x^60*z0^3 - 2*x^58*y^2*z0^3 + x^61*z0 + x^59*z0^3 - x^57*y^2*z0^3 - x^58*y^2*z0 + x^58*z0^3 - x^56*y^2*z0^3 + 2*x^59*z0 + x^57*z0^3 + 2*x^55*y^2*z0^3 - x^58*z0 - 2*x^56*y^2*z0 - x^56*z0^3 - 2*x^54*y^2*z0^3 - x^55*z0^3 - 2*x^56*z0 - x^54*z0^3 + x^55*z0 + x^53*z0^3 + x^52*z0^3 + 2*x^53*z0 + x^51*z0^3 - x^52*z0 - x^50*z0^3 - x^49*z0^3 - 2*x^50*z0 - x^48*z0^3 + x^49*z0 + x^47*z0^3 + x^46*z0^3 + 2*x^47*z0 + x^45*z0^3 - x^46*z0 - x^44*z0^3 - x^43*z0^3 - 2*x^44*z0 - x^42*z0^3 + x^43*z0 - 2*x^41*z0^3 + 2*x^39*y*z0^4 + x^40*y*z0^2 + x^38*y*z0^4 - 2*x^41*z0 + x^39*y*z0^2 - 2*x^39*z0^3 - 2*x^37*y*z0^4 - 2*x^40*y - 2*x^40*z0 + x^38*y*z0^2 - x^38*z0^3 - 2*x^36*y*z0^4 - 2*x^39*z0 - 2*x^37*y*z0^2 - x^37*z0^3 + 2*x^38*z0 + 2*x^36*y*z0^2 - 2*x^34*y*z0^4 + x^37*y - 2*x^37*z0 - x^35*y*z0^2 - x^35*z0^3 - 2*x^33*y*z0^4 + 2*x^36*y - 2*x^36*z0 - 2*x^34*y*z0^2 - 2*x^34*z0^3 - 2*x^35*y - 2*x^33*y*z0^2 + x^33*z0^3 - 2*x^34*y + x^32*y*z0^2 + 2*x^32*z0^3 + 2*x^33*y - 2*x^33*z0 - x^31*y*z0^2 - x^31*z0^3 + x^29*y*z0^4 + x^32*y + 2*x^30*y*z0^2 + 2*x^30*z0^3 - x^28*y*z0^4 + x^31*y - x^31*z0 + x^29*y*z0^2 - x^29*z0^3 - x^27*y*z0^4 + x^30*y + x^30*z0 + x^28*z0^3 - 2*x^26*y*z0^4 + x^29*y + x^29*z0 + 2*x^27*y*z0^2 - 2*x^27*z0^3 - 2*x^25*y*z0^4 - 2*x^28*y + 2*x^28*z0 + x^26*z0^3 - x^27*y - 2*x^27*z0 - 2*x^25*y*z0^2 + 2*x^25*z0^3 + 2*x^26*z0 - x^24*y*z0^2 - 2*x^22*y*z0^4 - x^25*y - 2*x^25*z0 + 2*x^23*y*z0^2 + 2*x^23*z0^3 + 2*x^21*y*z0^4 - x^24*y - x^24*z0 - x^22*y*z0^2 + 2*x^20*y*z0^4 + 2*x^23*y - x^21*y*z0^2 + x^21*z0^3 + x^19*y*z0^4 + x^22*y - 2*x^22*z0 - 2*x^18*y*z0^4 + 2*x^21*y - x^21*z0 + x^19*y*z0^2 - 2*x^19*z0^3 - 2*x^17*y*z0^4 - 2*x^20*y + x^20*z0 + x^18*y*z0^2 + x^18*z0^3 + 2*x^16*y*z0^4 - 2*x^19*z0 - 2*x^17*y*z0^2 + 2*x^17*z0^3 + x^15*y*z0^4 + 2*x^18*y + x^18*z0 - x^16*y*z0^2 - x^14*y*z0^4 + x^17*y - 2*x^17*z0 + x^15*z0^3 + 2*x^13*y*z0^4 + x^16*y + 2*x^16*z0 + 2*x^14*y*z0^2 + x^14*z0^3 - 2*x^12*y*z0^4 + 2*x^15*z0 - x^13*y*z0^2 + 2*x^14*y - 2*x^14*z0 + 2*x^12*y*z0^2 - x^10*y*z0^4 - x^13*y - x^11*y*z0^2 - x^9*y*z0^4 + x^12*z0 - x^10*y*z0^2 - 2*x^10*z0^3 - 2*x^8*y*z0^4 - x^11*y + 2*x^11*z0 - 2*x^9*y*z0^2 - x^7*y*z0^4 + 2*x^10*y + 2*x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 - 2*x^6*y*z0^4 - x^9*y + 2*x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + x^5*y*z0^4 - x^8*y - x^8*z0 - x^6*y*z0^2 + 2*x^4*y*z0^4 - 2*x^7*y + x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 - 2*x^3*y*z0^4 + 2*x^6*y + x^4*y^2*z0 - x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^2*y*z0^4 - x^5*y - 2*x^5*z0 + 2*x^3*y*z0^2 + x^3*z0^3 - x^4*y - 2*x^4*z0 + 2*x^2*y*z0^2 - x^2*z0^3 - 2*x^3*y + x^3*z0 - x^2*y + x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + 2*x^60*z0^4 + 2*x^58*y^2*z0^4 + 2*x^61*z0^2 + x^59*z0^4 - 2*x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^58*z0^4 - x^56*y^2*z0^4 + x^57*y^2*z0^2 - 2*x^57*z0^4 + x^60 - 2*x^58*z0^2 - x^56*z0^4 - x^57*y^2 + x^57*z0^2 - 2*x^55*z0^4 + 2*x^54*z0^4 - x^57 + 2*x^55*z0^2 + x^53*z0^4 - x^54*z0^2 + 2*x^52*z0^4 - 2*x^51*z0^4 + x^54 - 2*x^52*z0^2 - x^50*z0^4 + x^51*z0^2 - 2*x^49*z0^4 + 2*x^48*z0^4 - x^51 + 2*x^49*z0^2 + x^47*z0^4 - x^48*z0^2 + 2*x^46*z0^4 - 2*x^45*z0^4 + x^48 - 2*x^46*z0^2 - x^44*z0^4 + x^45*z0^2 - 2*x^43*z0^4 + 2*x^42*z0^4 - x^45 + 2*x^43*z0^2 - x^41*z0^4 - x^42*z0^2 - x^40*y*z0^3 - x^40*z0^4 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 + x^42 + x^40*y*z0 + 2*x^40*z0^2 + x^38*z0^4 - 2*x^41 + 2*x^39*y*z0 - x^39*z0^2 + x^37*y*z0^3 + 2*x^37*z0^4 + x^40 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - x^37*y*z0 + 2*x^35*y*z0^3 + 2*x^35*z0^4 - 2*x^38 - x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 + x^37 + x^35*y*z0 + 2*x^35*z0^2 - 2*x^33*y*z0^3 + x^34*y*z0 - x^32*y*z0^3 - 2*x^35 + 2*x^33*z0^2 + 2*x^31*y*z0^3 + 2*x^31*z0^4 - 2*x^34 - 2*x^32*z0^2 - 2*x^30*y*z0^3 + x^30*z0^4 + x^33 - 2*x^31*y*z0 + 2*x^31*z0^2 - x^29*y*z0^3 - x^29*z0^4 + 2*x^32 + 2*x^30*y*z0 - 2*x^28*y*z0^3 - 2*x^28*z0^4 + x^29*y*z0 + x^29*z0^2 - 2*x^27*y*z0^3 + 2*x^27*z0^4 + 2*x^30 + x^28*y*z0 - 2*x^26*y*z0^3 - 2*x^26*z0^4 - 2*x^27*y*z0 - x^27*z0^2 - x^25*y*z0^3 - 2*x^28 + 2*x^26*y*z0 - x^26*z0^2 - 2*x^24*y*z0^3 - x^24*z0^4 - 2*x^27 - x^25*y*z0 + 2*x^25*z0^2 + x^23*y*z0^3 - x^23*z0^4 - 2*x^26 + 2*x^24*y*z0 - 2*x^24*z0^2 - 2*x^22*y*z0^3 + x^22*z0^4 - 2*x^25 - x^23*y*z0 + 2*x^23*z0^2 + x^21*y*z0^3 + 2*x^22*y*z0 + x^22*z0^2 + x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^21*y*z0 + x^21*z0^2 + x^19*y*z0^3 + x^19*z0^4 + x^20*y*z0 - x^20*z0^2 - x^18*y*z0^3 - 2*x^18*z0^4 + 2*x^21 + 2*x^19*y*z0 + x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^19 - 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^18 - 2*x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 - x^17 + x^15*y*z0 + x^13*y*z0^3 + x^13*z0^4 - x^16 + 2*x^14*y*z0 - x^12*y*z0^3 - x^15 + 2*x^13*y*z0 + 2*x^13*z0^2 - x^11*y*z0^3 - x^11*z0^4 + x^10*y*z0^3 + x^10*z0^4 + x^11*y*z0 - 2*x^9*y*z0^3 + 2*x^9*z0^4 - 2*x^12 + x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^7*y*z0^3 - x^7*z0^4 - 2*x^10 - 2*x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - 2*x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 + x^4*y^2*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^3*y*z0^3 - 2*x^3*z0^4 + x^6 - 2*x^4*y*z0 + 2*x^4*z0^2 + x^2*y*z0^3 + 2*x^2*z0^4 - x^3*y*z0 + x^3*z0^2 - x^2*z0^2 - x^3 + x^2)/y) * dx, - ((2*x^61*z0^3 - 2*x^58*y^2*z0^3 + 2*x^61*z0 + x^59*z0^3 - x^60*z0 - 2*x^58*y^2*z0 - x^58*z0^3 - x^56*y^2*z0^3 + 2*x^59*z0 + x^57*y^2*z0 - x^55*y^2*z0^3 - 2*x^58*z0 - 2*x^56*y^2*z0 - x^56*z0^3 + x^57*z0 + x^55*z0^3 - 2*x^56*z0 + 2*x^55*z0 + x^53*z0^3 - x^54*z0 - x^52*z0^3 + 2*x^53*z0 - 2*x^52*z0 - x^50*z0^3 + x^51*z0 + x^49*z0^3 - 2*x^50*z0 + 2*x^49*z0 + x^47*z0^3 - x^48*z0 - x^46*z0^3 + 2*x^47*z0 - 2*x^46*z0 - x^44*z0^3 + x^45*z0 + x^43*z0^3 - 2*x^44*z0 + 2*x^43*z0 - 2*x^41*z0^3 + 2*x^39*y*z0^4 - x^42*z0 + x^40*y*z0^2 - x^40*z0^3 - x^41*z0 + 2*x^39*y*z0^2 + 2*x^39*z0^3 + x^37*y*z0^4 + x^40*y + 2*x^40*z0 - x^38*y*z0^2 - x^38*z0^3 - 2*x^36*y*z0^4 + 2*x^39*y - 2*x^39*z0 - x^37*y*z0^2 + 2*x^38*y - x^38*z0 + x^36*z0^3 - x^34*y*z0^4 + 2*x^37*y - 2*x^37*z0 - 2*x^35*y*z0^2 + x^35*z0^3 + x^33*y*z0^4 + x^36*y - 2*x^36*z0 + 2*x^34*y*z0^2 + x^34*z0^3 - 2*x^32*y*z0^4 + 2*x^35*y - x^35*z0 - x^33*z0^3 - x^31*y*z0^4 + x^34*z0 - x^32*z0^3 - 2*x^30*y*z0^4 - x^33*y + 2*x^33*z0 - x^31*z0^3 - x^29*y*z0^4 + x^32*y - x^32*z0 + x^30*z0^3 + 2*x^31*y - x^31*z0 - x^29*y*z0^2 + 2*x^27*y*z0^4 - 2*x^30*y - 2*x^30*z0 - x^28*y*z0^2 + x^28*z0^3 + 2*x^26*y*z0^4 - 2*x^29*z0 - x^28*y + x^28*z0 - x^26*y*z0^2 + x^26*z0^3 + 2*x^24*y*z0^4 - 2*x^27*y - x^27*z0 - x^25*y*z0^2 - 2*x^25*z0^3 - x^23*y*z0^4 - x^26*y + x^26*z0 + 2*x^24*y*z0^2 + x^25*y - 2*x^23*y*z0^2 - 2*x^23*z0^3 - x^24*y + x^24*z0 + 2*x^22*y*z0^2 + x^22*z0^3 + 2*x^20*y*z0^4 + x^23*z0 - x^21*y*z0^2 + x^21*z0^3 + 2*x^19*y*z0^4 - 2*x^22*y + x^22*z0 - x^20*z0^3 - x^18*y*z0^4 - 2*x^21*y + 2*x^21*z0 - x^19*y*z0^2 - x^19*z0^3 - x^17*y*z0^4 - x^20*y - 2*x^20*z0 - x^18*z0^3 + 2*x^16*y*z0^4 + x^19*y - x^17*y*z0^2 - x^17*z0^3 - x^15*y*z0^4 - x^18*y - 2*x^18*z0 + 2*x^16*z0^3 - x^14*y*z0^4 - 2*x^15*y*z0^2 + 2*x^15*z0^3 + 2*x^16*y + x^14*z0^3 + 2*x^12*y*z0^4 - x^15*y - x^13*y*z0^2 - 2*x^11*y*z0^4 + 2*x^14*z0 - x^12*y*z0^2 + x^12*z0^3 + x^13*y + x^13*z0 - 2*x^11*y*z0^2 + 2*x^11*z0^3 + 2*x^9*y*z0^4 - x^10*y*z0^2 - x^10*z0^3 + x^8*y*z0^4 - x^11*y + x^11*z0 - 2*x^9*y*z0^2 - 2*x^7*y*z0^4 - 2*x^10*y - 2*x^10*z0 + x^8*z0^3 - x^6*y*z0^4 + x^9*z0 - x^7*y*z0^2 - 2*x^7*z0^3 + x^5*y*z0^4 - 2*x^8*y - x^8*z0 + 2*x^6*y*z0^2 - 2*x^6*z0^3 + x^4*y^2*z0^3 + x^4*y*z0^4 + x^7*y + 2*x^5*y*z0^2 + x^5*z0^3 + x^3*y*z0^4 - 2*x^6*z0 + 2*x^4*y*z0^2 - x^5*y + 2*x^3*z0^3 + 2*x^4*y - x^4*z0 + x^2*y*z0^2 - 2*x^2*z0^3 - x^3*y - 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((x^60*z0^4 + 2*x^61*z0^2 - 2*x^59*z0^4 - x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^56*y^2*z0^4 + x^57*y^2*z0^2 - x^57*z0^4 + 2*x^60 - 2*x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 + x^57*z0^2 + x^54*z0^4 - 2*x^57 + 2*x^55*z0^2 - 2*x^53*z0^4 - x^54*z0^2 - x^51*z0^4 + 2*x^54 - 2*x^52*z0^2 + 2*x^50*z0^4 + x^51*z0^2 + x^48*z0^4 - 2*x^51 + 2*x^49*z0^2 - 2*x^47*z0^4 - x^48*z0^2 - x^45*z0^4 + 2*x^48 - 2*x^46*z0^2 + 2*x^44*z0^4 + x^45*z0^2 + x^42*z0^4 - 2*x^45 + 2*x^43*z0^2 - 2*x^41*z0^4 - x^42*z0^2 + x^40*z0^4 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 + 2*x^42 + x^40*y*z0 - x^40*z0^2 - x^38*y*z0^3 - 2*x^39*y*z0 - x^39*z0^2 + x^37*y*z0^3 + x^40 - x^38*z0^2 + x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - x^37*y*z0 + 2*x^37*z0^2 + 2*x^35*y*z0^3 + x^35*z0^4 + x^38 - 2*x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 - 2*x^34*z0^4 - x^37 + 2*x^35*y*z0 - x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 - 2*x^36 + 2*x^34*y*z0 - x^34*z0^2 + 2*x^32*y*z0^3 + x^35 - 2*x^33*y*z0 - 2*x^33*z0^2 - x^31*y*z0^3 - x^31*z0^4 + 2*x^34 - x^32*z0^2 + x^30*y*z0^3 - 2*x^30*z0^4 - x^33 + x^31*y*z0 + x^31*z0^2 - x^29*z0^4 - x^30*y*z0 + 2*x^28*y*z0^3 - 2*x^28*z0^4 - 2*x^29*y*z0 - x^29*z0^2 - x^30 - 2*x^28*y*z0 + x^28*z0^2 - x^26*y*z0^3 + 2*x^26*z0^4 + x^27*y*z0 + 2*x^27*z0^2 - x^25*y*z0^3 + x^25*z0^4 + x^28 - 2*x^24*y*z0^3 + 2*x^24*z0^4 + x^23*y*z0^3 - x^23*z0^4 + 2*x^26 - x^24*y*z0 + x^24*z0^2 + 2*x^22*y*z0^3 - 2*x^25 + x^23*y*z0 - x^23*z0^2 + x^21*y*z0^3 - x^21*z0^4 - 2*x^24 - x^22*y*z0 + x^20*y*z0^3 - x^20*z0^4 + x^23 + x^21*y*z0 - x^21*z0^2 + x^19*y*z0^3 + x^19*z0^4 + 2*x^22 + x^20*y*z0 - 2*x^20*z0^2 - x^18*y*z0^3 - x^18*z0^4 - x^21 + x^19*y*z0 - 2*x^20 + x^18*y*z0 + x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 - x^19 - x^17*y*z0 + x^15*y*z0^3 + 2*x^15*z0^4 - x^18 - 2*x^16*y*z0 - 2*x^16*z0^2 + 2*x^14*z0^4 - 2*x^15*y*z0 + 2*x^15*z0^2 + 2*x^13*y*z0^3 + 2*x^13*z0^4 + x^16 - x^14*z0^2 - x^12*y*z0^3 - 2*x^12*z0^4 - 2*x^13*y*z0 + 2*x^13*z0^2 + x^11*y*z0^3 + 2*x^11*z0^4 - x^14 - x^12*y*z0 + x^10*y*z0^3 + 2*x^10*z0^4 + 2*x^13 + 2*x^11*y*z0 - 2*x^11*z0^2 - x^12 - x^8*y*z0^3 + 2*x^8*z0^4 + 2*x^11 - x^9*z0^2 + x^7*y*z0^3 - 2*x^7*z0^4 + x^8*y*z0 + x^8*z0^2 - x^6*y*z0^3 + 2*x^6*z0^4 + x^4*y^2*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 - x^4*y*z0^3 + x^4*z0^4 + 2*x^5*y*z0 + x^3*y*z0^3 - x^3*z0^4 - 2*x^6 + 2*x^4*y*z0 + x^4*z0^2 - 2*x^2*z0^4 - 2*x^3*y*z0 - 2*x^3*z0^2 + 2*x^2*y*z0)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^8 + x^5*y^2 + x^5 - x^2)/y) * dx, - ((-x^8*z0 + x^5*y^2*z0 + x^5*z0 - x^2*z0)/y) * dx, - ((-x^8*z0^2 + x^5*y^2*z0^2 + x^5*z0^2 - x^2*z0^2)/y) * dx, - ((-x^8*z0^3 + x^5*y^2*z0^3 + x^5*z0^3 - x^2*z0^3)/y) * dx, - ((-x^8*z0^4 + x^5*y^2*z0^4 + x^5*z0^4 - x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^9 + x^6*y^2 + x^6 - x^3)/y) * dx, - ((-x^9*z0 + x^6*y^2*z0 + x^6*z0 - x^3*z0)/y) * dx, - ((-x^9*z0^2 + x^6*y^2*z0^2 + x^6*z0^2 - x^3*z0^2)/y) * dx, - ((-x^9*z0^3 + x^6*y^2*z0^3 + x^6*z0^3 - x^3*z0^3)/y) * dx, - ((-x^9*z0^4 + x^6*y^2*z0^4 + x^6*z0^4 - x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 + 2*x^61*z0^2 - 2*x^59*z0^4 + 2*x^60*z0^2 - 2*x^58*y^2*z0^2 - x^58*z0^4 + 2*x^56*y^2*z0^4 - x^61 - 2*x^57*y^2*z0^2 + 2*x^60 + x^58*y^2 - 2*x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 - 2*x^57*z0^2 + x^55*z0^4 + x^58 - 2*x^57 + 2*x^55*z0^2 - 2*x^53*z0^4 + 2*x^54*z0^2 - x^52*z0^4 - x^55 + 2*x^54 - 2*x^52*z0^2 + 2*x^50*z0^4 - 2*x^51*z0^2 + x^49*z0^4 + x^52 - 2*x^51 + 2*x^49*z0^2 - 2*x^47*z0^4 + 2*x^48*z0^2 - x^46*z0^4 - x^49 + 2*x^48 - 2*x^46*z0^2 + 2*x^44*z0^4 - 2*x^45*z0^2 + x^43*z0^4 + x^46 - 2*x^45 + 2*x^43*z0^2 + x^41*z0^4 + 2*x^42*z0^2 - 2*x^40*y*z0^3 - x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^42 + x^40*y*z0 - 2*x^40*z0^2 - x^38*y*z0^3 + x^38*z0^4 - 2*x^41 + x^39*y*z0 + x^39*z0^2 - 2*x^37*y*z0^3 + 2*x^37*z0^4 + x^40 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + 2*x^37*y*z0 + 2*x^37*z0^2 - x^35*y*z0^3 + x^35*z0^4 + 2*x^38 - x^36*y*z0 - x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^34*z0^4 - x^37 - 2*x^35*y*z0 - x^33*y*z0^3 + 2*x^33*z0^4 + x^36 - x^34*y*z0 + 2*x^34*z0^2 + x^32*y*z0^3 + 2*x^35 - x^33*y*z0 - x^33*z0^2 + x^31*y*z0^3 - x^31*z0^4 + 2*x^34 - 2*x^32*z0^2 - x^30*y*z0^3 + x^30*z0^4 + 2*x^33 + x^31*y*z0 + x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - 2*x^32 + 2*x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 - x^29*y*z0 - 2*x^29*z0^2 + x^27*y*z0^3 + 2*x^27*z0^4 + x^30 - 2*x^28*z0^2 + 2*x^29 - 2*x^27*y*z0 + 2*x^27*z0^2 - 2*x^25*y*z0^3 - 2*x^25*z0^4 + 2*x^28 - x^26*y*z0 - x^26*z0^2 - x^24*y*z0^3 - 2*x^24*z0^4 + 2*x^27 + 2*x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + 2*x^24*y*z0 + x^22*z0^4 + x^21*y*z0^3 - 2*x^21*z0^4 - x^24 + 2*x^22*y*z0 - 2*x^20*y*z0^3 - x^23 + 2*x^21*y*z0 - 2*x^21*z0^2 - x^19*y*z0^3 + x^19*z0^4 + 2*x^22 + x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 - 2*x^18*z0^4 - 2*x^21 - 2*x^19*y*z0 - 2*x^19*z0^2 + x^17*y*z0^3 - 2*x^17*z0^4 - 2*x^20 + 2*x^18*y*z0 + x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^16*z0^4 - 2*x^17*y*z0 + 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^15*z0^4 + 2*x^18 + x^16*y*z0 + x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 - 2*x^17 - 2*x^15*y*z0 + 2*x^15*z0^2 + x^13*z0^4 - 2*x^16 - 2*x^14*z0^2 - x^12*z0^4 - x^13*z0^2 + x^11*z0^4 + 2*x^14 - 2*x^12*z0^2 + 2*x^10*z0^4 - 2*x^13 - x^11*z0^2 - 2*x^9*y*z0^3 - x^9*z0^4 + x^10*y*z0 + x^8*y*z0^3 + x^8*z0^4 + x^11 + x^9*y*z0 + x^7*y*z0^3 + 2*x^7*z0^4 + 2*x^10 - 2*x^8*y*z0 + 2*x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 - x^9 + x^7*y^2 - 2*x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + 2*x^8 + 2*x^6*z0^2 - 2*x^4*z0^4 - x^7 - 2*x^5*y*z0 - x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 + x^6 - x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 + x^5 - 2*x^3*y*z0 + x^3*z0^2 + x^2*y*z0 + x^2*z0^2)/y) * dx, - ((-2*x^61*z0^3 - x^60*z0^3 + 2*x^58*y^2*z0^3 - x^61*z0 - x^59*z0^3 + x^57*y^2*z0^3 + x^58*y^2*z0 - x^58*z0^3 + x^56*y^2*z0^3 - 2*x^59*z0 - x^57*z0^3 - 2*x^55*y^2*z0^3 + x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 + x^55*z0^3 + 2*x^56*z0 + x^54*z0^3 - x^55*z0 - x^53*z0^3 - x^52*z0^3 - 2*x^53*z0 - x^51*z0^3 + x^52*z0 + x^50*z0^3 + x^49*z0^3 + 2*x^50*z0 + x^48*z0^3 - x^49*z0 - x^47*z0^3 - x^46*z0^3 - 2*x^47*z0 - x^45*z0^3 + x^46*z0 + x^44*z0^3 + x^43*z0^3 + 2*x^44*z0 + x^42*z0^3 - x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 - x^40*y*z0^2 - x^38*y*z0^4 + 2*x^41*z0 - x^39*y*z0^2 + 2*x^39*z0^3 + 2*x^37*y*z0^4 + 2*x^40*y + 2*x^40*z0 - x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 + 2*x^39*z0 + 2*x^37*y*z0^2 + x^37*z0^3 - 2*x^38*z0 - 2*x^36*y*z0^2 + 2*x^34*y*z0^4 - x^37*y + 2*x^37*z0 + x^35*y*z0^2 + x^35*z0^3 + 2*x^33*y*z0^4 - 2*x^36*y + 2*x^36*z0 + 2*x^34*y*z0^2 + 2*x^34*z0^3 + 2*x^35*y + 2*x^33*y*z0^2 - x^33*z0^3 + 2*x^34*y - x^32*y*z0^2 - 2*x^32*z0^3 - 2*x^33*y + 2*x^33*z0 + x^31*y*z0^2 + x^31*z0^3 - x^29*y*z0^4 - x^32*y - 2*x^30*y*z0^2 - 2*x^30*z0^3 + x^28*y*z0^4 - x^31*y + x^31*z0 - x^29*y*z0^2 + x^29*z0^3 + x^27*y*z0^4 - x^30*y - x^30*z0 - x^28*z0^3 + 2*x^26*y*z0^4 - x^29*y - x^29*z0 - 2*x^27*y*z0^2 + 2*x^27*z0^3 + 2*x^25*y*z0^4 + 2*x^28*y - 2*x^28*z0 - x^26*z0^3 + x^27*y + 2*x^27*z0 + 2*x^25*y*z0^2 - 2*x^25*z0^3 - 2*x^26*z0 + x^24*y*z0^2 + 2*x^22*y*z0^4 + x^25*y + 2*x^25*z0 - 2*x^23*y*z0^2 - 2*x^23*z0^3 - 2*x^21*y*z0^4 + x^24*y + x^24*z0 + x^22*y*z0^2 - 2*x^20*y*z0^4 - 2*x^23*y + x^21*y*z0^2 - x^21*z0^3 - x^19*y*z0^4 - x^22*y + 2*x^22*z0 + 2*x^18*y*z0^4 - 2*x^21*y + x^21*z0 - x^19*y*z0^2 + 2*x^19*z0^3 + 2*x^17*y*z0^4 + 2*x^20*y - x^20*z0 - x^18*y*z0^2 - x^18*z0^3 - 2*x^16*y*z0^4 + 2*x^19*z0 + 2*x^17*y*z0^2 - 2*x^17*z0^3 - x^15*y*z0^4 - 2*x^18*y - x^18*z0 + x^16*y*z0^2 + x^14*y*z0^4 - x^17*y + 2*x^17*z0 - x^15*z0^3 - 2*x^13*y*z0^4 - x^16*y - 2*x^16*z0 - 2*x^14*y*z0^2 - x^14*z0^3 + 2*x^12*y*z0^4 - 2*x^15*z0 + x^13*y*z0^2 - 2*x^14*y + 2*x^14*z0 - 2*x^12*y*z0^2 + x^10*y*z0^4 + x^13*y + x^11*y*z0^2 + x^9*y*z0^4 - x^12*z0 + x^10*y*z0^2 + 2*x^10*z0^3 + 2*x^8*y*z0^4 + x^11*y - 2*x^11*z0 + 2*x^9*y*z0^2 + x^7*y*z0^4 - 2*x^10*y + 2*x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*y - 2*x^9*z0 + x^7*y^2*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 + x^8*y + x^8*z0 + x^6*y*z0^2 - 2*x^4*y*z0^4 + 2*x^7*y - x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 - 2*x^6*y + x^4*y*z0^2 - 2*x^4*z0^3 + 2*x^2*y*z0^4 + x^5*y + 2*x^5*z0 - 2*x^3*y*z0^2 - x^3*z0^3 + x^4*y + 2*x^4*z0 - 2*x^2*y*z0^2 + x^2*z0^3 + 2*x^3*y - x^3*z0 + x^2*y - x^2*z0)/y) * dx, - ((2*x^61*z0^4 - 2*x^60*z0^4 - 2*x^58*y^2*z0^4 - 2*x^61*z0^2 - x^59*z0^4 + 2*x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 - x^57*y^2*z0^2 + 2*x^57*z0^4 - x^60 + 2*x^58*z0^2 + x^56*z0^4 + x^57*y^2 - x^57*z0^2 + 2*x^55*z0^4 - 2*x^54*z0^4 + x^57 - 2*x^55*z0^2 - x^53*z0^4 + x^54*z0^2 - 2*x^52*z0^4 + 2*x^51*z0^4 - x^54 + 2*x^52*z0^2 + x^50*z0^4 - x^51*z0^2 + 2*x^49*z0^4 - 2*x^48*z0^4 + x^51 - 2*x^49*z0^2 - x^47*z0^4 + x^48*z0^2 - 2*x^46*z0^4 + 2*x^45*z0^4 - x^48 + 2*x^46*z0^2 + x^44*z0^4 - x^45*z0^2 + 2*x^43*z0^4 - 2*x^42*z0^4 + x^45 - 2*x^43*z0^2 + x^41*z0^4 + x^42*z0^2 + x^40*y*z0^3 + x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - x^42 - x^40*y*z0 - 2*x^40*z0^2 - x^38*z0^4 + 2*x^41 - 2*x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 - 2*x^37*z0^4 - x^40 + 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - 2*x^35*y*z0^3 - 2*x^35*z0^4 + 2*x^38 + x^36*y*z0 - x^36*z0^2 + x^34*y*z0^3 - x^37 - x^35*y*z0 - 2*x^35*z0^2 + 2*x^33*y*z0^3 - x^34*y*z0 + x^32*y*z0^3 + 2*x^35 - 2*x^33*z0^2 - 2*x^31*y*z0^3 - 2*x^31*z0^4 + 2*x^34 + 2*x^32*z0^2 + 2*x^30*y*z0^3 - x^30*z0^4 - x^33 + 2*x^31*y*z0 - 2*x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 + 2*x^28*y*z0^3 + 2*x^28*z0^4 - x^29*y*z0 - x^29*z0^2 + 2*x^27*y*z0^3 - 2*x^27*z0^4 - 2*x^30 - x^28*y*z0 + 2*x^26*y*z0^3 + 2*x^26*z0^4 + 2*x^27*y*z0 + x^27*z0^2 + x^25*y*z0^3 + 2*x^28 - 2*x^26*y*z0 + x^26*z0^2 + 2*x^24*y*z0^3 + x^24*z0^4 + 2*x^27 + x^25*y*z0 - 2*x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 + 2*x^26 - 2*x^24*y*z0 + 2*x^24*z0^2 + 2*x^22*y*z0^3 - x^22*z0^4 + 2*x^25 + x^23*y*z0 - 2*x^23*z0^2 - x^21*y*z0^3 - 2*x^22*y*z0 - x^22*z0^2 - x^20*y*z0^3 + 2*x^20*z0^4 + 2*x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 - x^19*z0^4 - x^20*y*z0 + x^20*z0^2 + x^18*y*z0^3 + 2*x^18*z0^4 - 2*x^21 - 2*x^19*y*z0 - x^17*y*z0^3 + 2*x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^19 + 2*x^17*y*z0 + 2*x^17*z0^2 - x^15*y*z0^3 - 2*x^18 + 2*x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 + x^17 - x^15*y*z0 - x^13*y*z0^3 - x^13*z0^4 + x^16 - 2*x^14*y*z0 + x^12*y*z0^3 + x^15 - 2*x^13*y*z0 - 2*x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 - x^10*y*z0^3 - x^10*z0^4 - x^11*y*z0 + 2*x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^12 - x^10*y*z0 + 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^7*y^2*z0^2 + 2*x^7*y*z0^3 + x^7*z0^4 + 2*x^10 + 2*x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*z0^4 - x^8 + 2*x^6*y*z0 + x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 + 2*x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 - 2*x^2*z0^4 + x^3*y*z0 - x^3*z0^2 + x^2*z0^2 + x^3 - x^2)/y) * dx, - ((-2*x^61*z0^3 + 2*x^58*y^2*z0^3 - 2*x^61*z0 - x^59*z0^3 + x^60*z0 + 2*x^58*y^2*z0 + x^58*z0^3 + x^56*y^2*z0^3 - 2*x^59*z0 - x^57*y^2*z0 + x^55*y^2*z0^3 + 2*x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 - x^57*z0 - x^55*z0^3 + 2*x^56*z0 - 2*x^55*z0 - x^53*z0^3 + x^54*z0 + x^52*z0^3 - 2*x^53*z0 + 2*x^52*z0 + x^50*z0^3 - x^51*z0 - x^49*z0^3 + 2*x^50*z0 - 2*x^49*z0 - x^47*z0^3 + x^48*z0 + x^46*z0^3 - 2*x^47*z0 + 2*x^46*z0 + x^44*z0^3 - x^45*z0 - x^43*z0^3 + 2*x^44*z0 - 2*x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 + x^42*z0 - x^40*y*z0^2 + x^40*z0^3 + x^41*z0 - 2*x^39*y*z0^2 - 2*x^39*z0^3 - x^37*y*z0^4 - x^40*y - 2*x^40*z0 + x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 - 2*x^39*y + 2*x^39*z0 + x^37*y*z0^2 - 2*x^38*y + x^38*z0 - x^36*z0^3 + x^34*y*z0^4 - 2*x^37*y + 2*x^37*z0 + 2*x^35*y*z0^2 - x^35*z0^3 - x^33*y*z0^4 - x^36*y + 2*x^36*z0 - 2*x^34*y*z0^2 - x^34*z0^3 + 2*x^32*y*z0^4 - 2*x^35*y + x^35*z0 + x^33*z0^3 + x^31*y*z0^4 - x^34*z0 + x^32*z0^3 + 2*x^30*y*z0^4 + x^33*y - 2*x^33*z0 + x^31*z0^3 + x^29*y*z0^4 - x^32*y + x^32*z0 - x^30*z0^3 - 2*x^31*y + x^31*z0 + x^29*y*z0^2 - 2*x^27*y*z0^4 + 2*x^30*y + 2*x^30*z0 + x^28*y*z0^2 - x^28*z0^3 - 2*x^26*y*z0^4 + 2*x^29*z0 + x^28*y - x^28*z0 + x^26*y*z0^2 - x^26*z0^3 - 2*x^24*y*z0^4 + 2*x^27*y + x^27*z0 + x^25*y*z0^2 + 2*x^25*z0^3 + x^23*y*z0^4 + x^26*y - x^26*z0 - 2*x^24*y*z0^2 - x^25*y + 2*x^23*y*z0^2 + 2*x^23*z0^3 + x^24*y - x^24*z0 - 2*x^22*y*z0^2 - x^22*z0^3 - 2*x^20*y*z0^4 - x^23*z0 + x^21*y*z0^2 - x^21*z0^3 - 2*x^19*y*z0^4 + 2*x^22*y - x^22*z0 + x^20*z0^3 + x^18*y*z0^4 + 2*x^21*y - 2*x^21*z0 + x^19*y*z0^2 + x^19*z0^3 + x^17*y*z0^4 + x^20*y + 2*x^20*z0 + x^18*z0^3 - 2*x^16*y*z0^4 - x^19*y + x^17*y*z0^2 + x^17*z0^3 + x^15*y*z0^4 + x^18*y + 2*x^18*z0 - 2*x^16*z0^3 + x^14*y*z0^4 + 2*x^15*y*z0^2 - 2*x^15*z0^3 - 2*x^16*y - x^14*z0^3 - 2*x^12*y*z0^4 + x^15*y + x^13*y*z0^2 + 2*x^11*y*z0^4 - 2*x^14*z0 + x^12*y*z0^2 - x^12*z0^3 - x^13*y - x^13*z0 + 2*x^11*y*z0^2 - 2*x^11*z0^3 - 2*x^9*y*z0^4 + x^10*y*z0^2 - x^8*y*z0^4 + x^11*y - x^11*z0 + 2*x^9*y*z0^2 + x^7*y^2*z0^3 + 2*x^7*y*z0^4 + 2*x^10*y + 2*x^10*z0 - x^8*z0^3 + x^6*y*z0^4 - x^9*z0 + x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 + 2*x^8*y + x^8*z0 - 2*x^6*y*z0^2 + 2*x^6*z0^3 - x^4*y*z0^4 - x^7*y - 2*x^5*y*z0^2 - x^5*z0^3 - x^3*y*z0^4 + 2*x^6*z0 - 2*x^4*y*z0^2 + x^5*y - 2*x^3*z0^3 - 2*x^4*y + x^4*z0 - x^2*y*z0^2 + 2*x^2*z0^3 + x^3*y + 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-x^60*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^56*y^2*z0^4 - x^57*y^2*z0^2 + x^57*z0^4 - 2*x^60 + 2*x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 - x^57*z0^2 - x^54*z0^4 + 2*x^57 - 2*x^55*z0^2 + 2*x^53*z0^4 + x^54*z0^2 + x^51*z0^4 - 2*x^54 + 2*x^52*z0^2 - 2*x^50*z0^4 - x^51*z0^2 - x^48*z0^4 + 2*x^51 - 2*x^49*z0^2 + 2*x^47*z0^4 + x^48*z0^2 + x^45*z0^4 - 2*x^48 + 2*x^46*z0^2 - 2*x^44*z0^4 - x^45*z0^2 - x^42*z0^4 + 2*x^45 - 2*x^43*z0^2 + 2*x^41*z0^4 + x^42*z0^2 - x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - 2*x^42 - x^40*y*z0 + x^40*z0^2 + x^38*y*z0^3 + 2*x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 - x^40 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 - x^35*z0^4 - x^38 + 2*x^36*y*z0 - x^36*z0^2 + x^34*y*z0^3 + 2*x^34*z0^4 + x^37 - 2*x^35*y*z0 + x^35*z0^2 - x^33*y*z0^3 - 2*x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 + x^34*z0^2 - 2*x^32*y*z0^3 - x^35 + 2*x^33*y*z0 + 2*x^33*z0^2 + x^31*y*z0^3 + x^31*z0^4 - 2*x^34 + x^32*z0^2 - x^30*y*z0^3 + 2*x^30*z0^4 + x^33 - x^31*y*z0 - x^31*z0^2 + x^29*z0^4 + x^30*y*z0 - 2*x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^29*y*z0 + x^29*z0^2 + x^30 + 2*x^28*y*z0 - x^28*z0^2 + x^26*y*z0^3 - 2*x^26*z0^4 - x^27*y*z0 - 2*x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 - x^28 + 2*x^24*y*z0^3 - 2*x^24*z0^4 - x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + x^24*y*z0 - x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^25 - x^23*y*z0 + x^23*z0^2 - x^21*y*z0^3 + x^21*z0^4 + 2*x^24 + x^22*y*z0 - x^20*y*z0^3 + x^20*z0^4 - x^23 - x^21*y*z0 + x^21*z0^2 - x^19*y*z0^3 - x^19*z0^4 - 2*x^22 - x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 + x^18*z0^4 + x^21 - x^19*y*z0 + 2*x^20 - x^18*y*z0 - x^18*z0^2 + 2*x^16*y*z0^3 - 2*x^16*z0^4 + x^19 + x^17*y*z0 - x^15*y*z0^3 - 2*x^15*z0^4 + x^18 + 2*x^16*y*z0 + 2*x^16*z0^2 - 2*x^14*z0^4 + 2*x^15*y*z0 - 2*x^15*z0^2 - 2*x^13*y*z0^3 - 2*x^13*z0^4 - x^16 + x^14*z0^2 + x^12*y*z0^3 + 2*x^12*z0^4 + 2*x^13*y*z0 - 2*x^13*z0^2 - x^11*y*z0^3 - 2*x^11*z0^4 + x^14 + x^12*y*z0 - x^10*y*z0^3 + 2*x^10*z0^4 - 2*x^13 - 2*x^11*y*z0 + 2*x^11*z0^2 + x^7*y^2*z0^4 + x^12 + x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^11 + x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 - x^8*y*z0 - x^8*z0^2 + x^6*y*z0^3 - 2*x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 + x^4*y*z0^3 - x^4*z0^4 - 2*x^5*y*z0 - x^3*y*z0^3 + x^3*z0^4 + 2*x^6 - 2*x^4*y*z0 - x^4*z0^2 + 2*x^2*z0^4 + 2*x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^11 + x^8*y^2 + x^8 - x^5 + x^2)/y) * dx, - ((-x^11*z0 + x^8*y^2*z0 + x^8*z0 - x^5*z0 + x^2*z0)/y) * dx, - ((-x^11*z0^2 + x^8*y^2*z0^2 + x^8*z0^2 - x^5*z0^2 + x^2*z0^2)/y) * dx, - ((-x^11*z0^3 + x^8*y^2*z0^3 + x^8*z0^3 - x^5*z0^3 + x^2*z0^3)/y) * dx, - ((-x^11*z0^4 + x^8*y^2*z0^4 + x^8*z0^4 - x^5*z0^4 + x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^12 + x^9*y^2 + x^9 - x^6 + x^3)/y) * dx, - ((-x^12*z0 + x^9*y^2*z0 + x^9*z0 - x^6*z0 + x^3*z0)/y) * dx, - ((-x^12*z0^2 + x^9*y^2*z0^2 + x^9*z0^2 - x^6*z0^2 + x^3*z0^2)/y) * dx, - ((-x^12*z0^3 + x^9*y^2*z0^3 + x^9*z0^3 - x^6*z0^3 + x^3*z0^3)/y) * dx, - ((-x^12*z0^4 + x^9*y^2*z0^4 + x^9*z0^4 - x^6*z0^4 + x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 + x^58*y^2*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 - 2*x^60*z0^2 + 2*x^58*y^2*z0^2 + x^58*z0^4 - 2*x^56*y^2*z0^4 + x^61 + 2*x^57*y^2*z0^2 - 2*x^60 - x^58*y^2 + 2*x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 + 2*x^57*z0^2 - x^55*z0^4 - x^58 + 2*x^57 - 2*x^55*z0^2 + 2*x^53*z0^4 - 2*x^54*z0^2 + x^52*z0^4 + x^55 - 2*x^54 + 2*x^52*z0^2 - 2*x^50*z0^4 + 2*x^51*z0^2 - x^49*z0^4 - x^52 + 2*x^51 - 2*x^49*z0^2 + 2*x^47*z0^4 - 2*x^48*z0^2 + x^46*z0^4 + x^49 - 2*x^48 + 2*x^46*z0^2 - 2*x^44*z0^4 + 2*x^45*z0^2 - x^43*z0^4 - x^46 + 2*x^45 - 2*x^43*z0^2 - x^41*z0^4 - 2*x^42*z0^2 + 2*x^40*y*z0^3 + x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - 2*x^42 - x^40*y*z0 + 2*x^40*z0^2 + x^38*y*z0^3 - x^38*z0^4 + 2*x^41 - x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 - x^40 + 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - 2*x^37*y*z0 - 2*x^37*z0^2 + x^35*y*z0^3 - x^35*z0^4 - 2*x^38 + x^36*y*z0 + x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 + x^37 + 2*x^35*y*z0 + x^33*y*z0^3 - 2*x^33*z0^4 - x^36 + x^34*y*z0 - 2*x^34*z0^2 - x^32*y*z0^3 - 2*x^35 + x^33*y*z0 + x^33*z0^2 - x^31*y*z0^3 + x^31*z0^4 - 2*x^34 + 2*x^32*z0^2 + x^30*y*z0^3 - x^30*z0^4 - 2*x^33 - x^31*y*z0 - x^31*z0^2 - x^29*y*z0^3 - x^29*z0^4 + 2*x^32 - 2*x^28*y*z0^3 + 2*x^28*z0^4 - 2*x^31 + x^29*y*z0 + 2*x^29*z0^2 - x^27*y*z0^3 - 2*x^27*z0^4 - x^30 + 2*x^28*z0^2 - 2*x^29 + 2*x^27*y*z0 - 2*x^27*z0^2 + 2*x^25*y*z0^3 + 2*x^25*z0^4 - 2*x^28 + x^26*y*z0 + x^26*z0^2 + x^24*y*z0^3 + 2*x^24*z0^4 - 2*x^27 - 2*x^25*z0^2 + x^23*y*z0^3 - x^23*z0^4 + 2*x^26 - 2*x^24*y*z0 - x^22*z0^4 - x^21*y*z0^3 + 2*x^21*z0^4 + x^24 - 2*x^22*y*z0 + 2*x^20*y*z0^3 + x^23 - 2*x^21*y*z0 + 2*x^21*z0^2 + x^19*y*z0^3 - x^19*z0^4 - 2*x^22 - x^20*y*z0 - 2*x^20*z0^2 - x^18*y*z0^3 + 2*x^18*z0^4 + 2*x^21 + 2*x^19*y*z0 + 2*x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 + 2*x^20 - 2*x^18*y*z0 - x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^16*z0^4 + 2*x^17*y*z0 - 2*x^17*z0^2 - x^15*y*z0^3 - 2*x^15*z0^4 - 2*x^18 - x^16*y*z0 - x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 + 2*x^17 + 2*x^15*y*z0 - 2*x^15*z0^2 - x^13*z0^4 + 2*x^16 + 2*x^14*z0^2 + x^12*z0^4 + x^13*z0^2 - x^11*z0^4 - 2*x^14 + 2*x^12*z0^2 - 2*x^10*z0^4 + x^13 + x^11*z0^2 + 2*x^9*y*z0^3 + x^9*z0^4 + x^10*y^2 - x^10*y*z0 - x^8*y*z0^3 - x^8*z0^4 - x^11 - x^9*y*z0 - x^7*y*z0^3 - 2*x^7*z0^4 - 2*x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 + 2*x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 - 2*x^8 - 2*x^6*z0^2 + 2*x^4*z0^4 + x^7 + 2*x^5*y*z0 + x^5*z0^2 + 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 + x^4*y*z0 + x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 - x^5 + 2*x^3*y*z0 - x^3*z0^2 - x^2*y*z0 - x^2*z0^2)/y) * dx, - ((2*x^61*z0^3 + x^60*z0^3 - 2*x^58*y^2*z0^3 + x^61*z0 + x^59*z0^3 - x^57*y^2*z0^3 - x^58*y^2*z0 + x^58*z0^3 - x^56*y^2*z0^3 + 2*x^59*z0 + x^57*z0^3 + 2*x^55*y^2*z0^3 - x^58*z0 - 2*x^56*y^2*z0 - x^56*z0^3 - 2*x^54*y^2*z0^3 - x^55*z0^3 - 2*x^56*z0 - x^54*z0^3 + x^55*z0 + x^53*z0^3 + x^52*z0^3 + 2*x^53*z0 + x^51*z0^3 - x^52*z0 - x^50*z0^3 - x^49*z0^3 - 2*x^50*z0 - x^48*z0^3 + x^49*z0 + x^47*z0^3 + x^46*z0^3 + 2*x^47*z0 + x^45*z0^3 - x^46*z0 - x^44*z0^3 - x^43*z0^3 - 2*x^44*z0 - x^42*z0^3 + x^43*z0 - 2*x^41*z0^3 + 2*x^39*y*z0^4 + x^40*y*z0^2 + x^38*y*z0^4 - 2*x^41*z0 + x^39*y*z0^2 - 2*x^39*z0^3 - 2*x^37*y*z0^4 - 2*x^40*y - 2*x^40*z0 + x^38*y*z0^2 - x^38*z0^3 - 2*x^36*y*z0^4 - 2*x^39*z0 - 2*x^37*y*z0^2 - x^37*z0^3 + 2*x^38*z0 + 2*x^36*y*z0^2 - 2*x^34*y*z0^4 + x^37*y - 2*x^37*z0 - x^35*y*z0^2 - x^35*z0^3 - 2*x^33*y*z0^4 + 2*x^36*y - 2*x^36*z0 - 2*x^34*y*z0^2 - 2*x^34*z0^3 - 2*x^35*y - 2*x^33*y*z0^2 + x^33*z0^3 - 2*x^34*y + x^32*y*z0^2 + 2*x^32*z0^3 + 2*x^33*y - 2*x^33*z0 - x^31*y*z0^2 - x^31*z0^3 + x^29*y*z0^4 + x^32*y + 2*x^30*y*z0^2 + 2*x^30*z0^3 - x^28*y*z0^4 + x^31*y - x^31*z0 + x^29*y*z0^2 - x^29*z0^3 - x^27*y*z0^4 + x^30*y + x^30*z0 + x^28*z0^3 - 2*x^26*y*z0^4 + x^29*y + x^29*z0 + 2*x^27*y*z0^2 - 2*x^27*z0^3 - 2*x^25*y*z0^4 - 2*x^28*y + 2*x^28*z0 + x^26*z0^3 - x^27*y - 2*x^27*z0 - 2*x^25*y*z0^2 + 2*x^25*z0^3 + 2*x^26*z0 - x^24*y*z0^2 - 2*x^22*y*z0^4 - x^25*y - 2*x^25*z0 + 2*x^23*y*z0^2 + 2*x^23*z0^3 + 2*x^21*y*z0^4 - x^24*y - x^24*z0 - x^22*y*z0^2 + 2*x^20*y*z0^4 + 2*x^23*y - x^21*y*z0^2 + x^21*z0^3 + x^19*y*z0^4 + x^22*y - 2*x^22*z0 - 2*x^18*y*z0^4 + 2*x^21*y - x^21*z0 + x^19*y*z0^2 - 2*x^19*z0^3 - 2*x^17*y*z0^4 - 2*x^20*y + x^20*z0 + x^18*y*z0^2 + x^18*z0^3 + 2*x^16*y*z0^4 - 2*x^19*z0 - 2*x^17*y*z0^2 + 2*x^17*z0^3 + x^15*y*z0^4 + 2*x^18*y + x^18*z0 - x^16*y*z0^2 - x^14*y*z0^4 + x^17*y - 2*x^17*z0 + x^15*z0^3 + 2*x^13*y*z0^4 + x^16*y + 2*x^16*z0 + 2*x^14*y*z0^2 + x^14*z0^3 - 2*x^12*y*z0^4 + 2*x^15*z0 - x^13*y*z0^2 + 2*x^14*y - 2*x^14*z0 + 2*x^12*y*z0^2 - x^10*y*z0^4 - x^13*y - x^13*z0 - x^11*y*z0^2 - x^9*y*z0^4 + x^12*z0 + x^10*y^2*z0 - x^10*y*z0^2 - 2*x^10*z0^3 - 2*x^8*y*z0^4 - x^11*y + 2*x^11*z0 - 2*x^9*y*z0^2 - x^7*y*z0^4 + 2*x^10*y - 2*x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 - 2*x^6*y*z0^4 - x^9*y + 2*x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + x^5*y*z0^4 - x^8*y - x^8*z0 - x^6*y*z0^2 + 2*x^4*y*z0^4 - 2*x^7*y + x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 - 2*x^3*y*z0^4 + 2*x^6*y - x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^2*y*z0^4 - x^5*y - 2*x^5*z0 + 2*x^3*y*z0^2 + x^3*z0^3 - x^4*y - 2*x^4*z0 + 2*x^2*y*z0^2 - x^2*z0^3 - 2*x^3*y + x^3*z0 - x^2*y + x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + 2*x^60*z0^4 + 2*x^58*y^2*z0^4 + 2*x^61*z0^2 + x^59*z0^4 - 2*x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^58*z0^4 - x^56*y^2*z0^4 + x^57*y^2*z0^2 - 2*x^57*z0^4 + x^60 - 2*x^58*z0^2 - x^56*z0^4 - x^57*y^2 + x^57*z0^2 - 2*x^55*z0^4 + 2*x^54*z0^4 - x^57 + 2*x^55*z0^2 + x^53*z0^4 - x^54*z0^2 + 2*x^52*z0^4 - 2*x^51*z0^4 + x^54 - 2*x^52*z0^2 - x^50*z0^4 + x^51*z0^2 - 2*x^49*z0^4 + 2*x^48*z0^4 - x^51 + 2*x^49*z0^2 + x^47*z0^4 - x^48*z0^2 + 2*x^46*z0^4 - 2*x^45*z0^4 + x^48 - 2*x^46*z0^2 - x^44*z0^4 + x^45*z0^2 - 2*x^43*z0^4 + 2*x^42*z0^4 - x^45 + 2*x^43*z0^2 - x^41*z0^4 - x^42*z0^2 - x^40*y*z0^3 - x^40*z0^4 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 + x^42 + x^40*y*z0 + 2*x^40*z0^2 + x^38*z0^4 - 2*x^41 + 2*x^39*y*z0 - x^39*z0^2 + x^37*y*z0^3 + 2*x^37*z0^4 + x^40 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - x^37*y*z0 + 2*x^35*y*z0^3 + 2*x^35*z0^4 - 2*x^38 - x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 + x^37 + x^35*y*z0 + 2*x^35*z0^2 - 2*x^33*y*z0^3 + x^34*y*z0 - x^32*y*z0^3 - 2*x^35 + 2*x^33*z0^2 + 2*x^31*y*z0^3 + 2*x^31*z0^4 - 2*x^34 - 2*x^32*z0^2 - 2*x^30*y*z0^3 + x^30*z0^4 + x^33 - 2*x^31*y*z0 + 2*x^31*z0^2 - x^29*y*z0^3 - x^29*z0^4 + 2*x^32 + 2*x^30*y*z0 - 2*x^28*y*z0^3 - 2*x^28*z0^4 + x^29*y*z0 + x^29*z0^2 - 2*x^27*y*z0^3 + 2*x^27*z0^4 + 2*x^30 + x^28*y*z0 - 2*x^26*y*z0^3 - 2*x^26*z0^4 - 2*x^27*y*z0 - x^27*z0^2 - x^25*y*z0^3 - 2*x^28 + 2*x^26*y*z0 - x^26*z0^2 - 2*x^24*y*z0^3 - x^24*z0^4 - 2*x^27 - x^25*y*z0 + 2*x^25*z0^2 + x^23*y*z0^3 - x^23*z0^4 - 2*x^26 + 2*x^24*y*z0 - 2*x^24*z0^2 - 2*x^22*y*z0^3 + x^22*z0^4 - 2*x^25 - x^23*y*z0 + 2*x^23*z0^2 + x^21*y*z0^3 + 2*x^22*y*z0 + x^22*z0^2 + x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^21*y*z0 + x^21*z0^2 + x^19*y*z0^3 + x^19*z0^4 + x^20*y*z0 - x^20*z0^2 - x^18*y*z0^3 - 2*x^18*z0^4 + 2*x^21 + 2*x^19*y*z0 + x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^19 - 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^18 - 2*x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 - x^17 + x^15*y*z0 + x^13*y*z0^3 + x^13*z0^4 - x^16 + 2*x^14*y*z0 - x^12*y*z0^3 - x^15 + 2*x^13*y*z0 + x^13*z0^2 - x^11*y*z0^3 - x^11*z0^4 + x^10*y^2*z0^2 + x^10*y*z0^3 + x^10*z0^4 + x^11*y*z0 - 2*x^9*y*z0^3 + 2*x^9*z0^4 - 2*x^12 + x^10*y*z0 - 2*x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^7*y*z0^3 - x^7*z0^4 - 2*x^10 - 2*x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - 2*x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^3*y*z0^3 - 2*x^3*z0^4 + x^6 - 2*x^4*y*z0 + 2*x^4*z0^2 + x^2*y*z0^3 + 2*x^2*z0^4 - x^3*y*z0 + x^3*z0^2 - x^2*z0^2 - x^3 + x^2)/y) * dx, - ((2*x^61*z0^3 - 2*x^58*y^2*z0^3 + 2*x^61*z0 + x^59*z0^3 - x^60*z0 - 2*x^58*y^2*z0 - x^58*z0^3 - x^56*y^2*z0^3 + 2*x^59*z0 + x^57*y^2*z0 - x^55*y^2*z0^3 - 2*x^58*z0 - 2*x^56*y^2*z0 - x^56*z0^3 + x^57*z0 + x^55*z0^3 - 2*x^56*z0 + 2*x^55*z0 + x^53*z0^3 - x^54*z0 - x^52*z0^3 + 2*x^53*z0 - 2*x^52*z0 - x^50*z0^3 + x^51*z0 + x^49*z0^3 - 2*x^50*z0 + 2*x^49*z0 + x^47*z0^3 - x^48*z0 - x^46*z0^3 + 2*x^47*z0 - 2*x^46*z0 - x^44*z0^3 + x^45*z0 + x^43*z0^3 - 2*x^44*z0 + 2*x^43*z0 - 2*x^41*z0^3 + 2*x^39*y*z0^4 - x^42*z0 + x^40*y*z0^2 - x^40*z0^3 - x^41*z0 + 2*x^39*y*z0^2 + 2*x^39*z0^3 + x^37*y*z0^4 + x^40*y + 2*x^40*z0 - x^38*y*z0^2 - x^38*z0^3 - 2*x^36*y*z0^4 + 2*x^39*y - 2*x^39*z0 - x^37*y*z0^2 + 2*x^38*y - x^38*z0 + x^36*z0^3 - x^34*y*z0^4 + 2*x^37*y - 2*x^37*z0 - 2*x^35*y*z0^2 + x^35*z0^3 + x^33*y*z0^4 + x^36*y - 2*x^36*z0 + 2*x^34*y*z0^2 + x^34*z0^3 - 2*x^32*y*z0^4 + 2*x^35*y - x^35*z0 - x^33*z0^3 - x^31*y*z0^4 + x^34*z0 - x^32*z0^3 - 2*x^30*y*z0^4 - x^33*y + 2*x^33*z0 - x^31*z0^3 - x^29*y*z0^4 + x^32*y - x^32*z0 + x^30*z0^3 + 2*x^31*y - x^31*z0 - x^29*y*z0^2 + 2*x^27*y*z0^4 - 2*x^30*y - 2*x^30*z0 - x^28*y*z0^2 + x^28*z0^3 + 2*x^26*y*z0^4 - 2*x^29*z0 - x^28*y + x^28*z0 - x^26*y*z0^2 + x^26*z0^3 + 2*x^24*y*z0^4 - 2*x^27*y - x^27*z0 - x^25*y*z0^2 - 2*x^25*z0^3 - x^23*y*z0^4 - x^26*y + x^26*z0 + 2*x^24*y*z0^2 + x^25*y - 2*x^23*y*z0^2 - 2*x^23*z0^3 - x^24*y + x^24*z0 + 2*x^22*y*z0^2 + x^22*z0^3 + 2*x^20*y*z0^4 + x^23*z0 - x^21*y*z0^2 + x^21*z0^3 + 2*x^19*y*z0^4 - 2*x^22*y + x^22*z0 - x^20*z0^3 - x^18*y*z0^4 - 2*x^21*y + 2*x^21*z0 - x^19*y*z0^2 - x^19*z0^3 - x^17*y*z0^4 - x^20*y - 2*x^20*z0 - x^18*z0^3 + 2*x^16*y*z0^4 + x^19*y - x^17*y*z0^2 - x^17*z0^3 - x^15*y*z0^4 - x^18*y - 2*x^18*z0 + 2*x^16*z0^3 - x^14*y*z0^4 - 2*x^15*y*z0^2 + 2*x^15*z0^3 + 2*x^16*y + x^14*z0^3 + 2*x^12*y*z0^4 - x^15*y - x^13*y*z0^2 - x^13*z0^3 - 2*x^11*y*z0^4 + 2*x^14*z0 - x^12*y*z0^2 + x^12*z0^3 + x^10*y^2*z0^3 + x^13*y + x^13*z0 - 2*x^11*y*z0^2 + 2*x^11*z0^3 + 2*x^9*y*z0^4 - x^10*y*z0^2 + x^8*y*z0^4 - x^11*y + x^11*z0 - 2*x^9*y*z0^2 - 2*x^7*y*z0^4 - 2*x^10*y - 2*x^10*z0 + x^8*z0^3 - x^6*y*z0^4 + x^9*z0 - x^7*y*z0^2 - 2*x^7*z0^3 + x^5*y*z0^4 - 2*x^8*y - x^8*z0 + 2*x^6*y*z0^2 - 2*x^6*z0^3 + x^4*y*z0^4 + x^7*y + 2*x^5*y*z0^2 + x^5*z0^3 + x^3*y*z0^4 - 2*x^6*z0 + 2*x^4*y*z0^2 - x^5*y + 2*x^3*z0^3 + 2*x^4*y - x^4*z0 + x^2*y*z0^2 - 2*x^2*z0^3 - x^3*y - 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((x^60*z0^4 + 2*x^61*z0^2 - 2*x^59*z0^4 - x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^56*y^2*z0^4 + x^57*y^2*z0^2 - x^57*z0^4 + 2*x^60 - 2*x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 + x^57*z0^2 + x^54*z0^4 - 2*x^57 + 2*x^55*z0^2 - 2*x^53*z0^4 - x^54*z0^2 - x^51*z0^4 + 2*x^54 - 2*x^52*z0^2 + 2*x^50*z0^4 + x^51*z0^2 + x^48*z0^4 - 2*x^51 + 2*x^49*z0^2 - 2*x^47*z0^4 - x^48*z0^2 - x^45*z0^4 + 2*x^48 - 2*x^46*z0^2 + 2*x^44*z0^4 + x^45*z0^2 + x^42*z0^4 - 2*x^45 + 2*x^43*z0^2 - 2*x^41*z0^4 - x^42*z0^2 + x^40*z0^4 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 + 2*x^42 + x^40*y*z0 - x^40*z0^2 - x^38*y*z0^3 - 2*x^39*y*z0 - x^39*z0^2 + x^37*y*z0^3 + x^40 - x^38*z0^2 + x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - x^37*y*z0 + 2*x^37*z0^2 + 2*x^35*y*z0^3 + x^35*z0^4 + x^38 - 2*x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 - 2*x^34*z0^4 - x^37 + 2*x^35*y*z0 - x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 - 2*x^36 + 2*x^34*y*z0 - x^34*z0^2 + 2*x^32*y*z0^3 + x^35 - 2*x^33*y*z0 - 2*x^33*z0^2 - x^31*y*z0^3 - x^31*z0^4 + 2*x^34 - x^32*z0^2 + x^30*y*z0^3 - 2*x^30*z0^4 - x^33 + x^31*y*z0 + x^31*z0^2 - x^29*z0^4 - x^30*y*z0 + 2*x^28*y*z0^3 - 2*x^28*z0^4 - 2*x^29*y*z0 - x^29*z0^2 - x^30 - 2*x^28*y*z0 + x^28*z0^2 - x^26*y*z0^3 + 2*x^26*z0^4 + x^27*y*z0 + 2*x^27*z0^2 - x^25*y*z0^3 + x^25*z0^4 + x^28 - 2*x^24*y*z0^3 + 2*x^24*z0^4 + x^23*y*z0^3 - x^23*z0^4 + 2*x^26 - x^24*y*z0 + x^24*z0^2 + 2*x^22*y*z0^3 - 2*x^25 + x^23*y*z0 - x^23*z0^2 + x^21*y*z0^3 - x^21*z0^4 - 2*x^24 - x^22*y*z0 + x^20*y*z0^3 - x^20*z0^4 + x^23 + x^21*y*z0 - x^21*z0^2 + x^19*y*z0^3 + x^19*z0^4 + 2*x^22 + x^20*y*z0 - 2*x^20*z0^2 - x^18*y*z0^3 - x^18*z0^4 - x^21 + x^19*y*z0 - 2*x^20 + x^18*y*z0 + x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 - x^19 - x^17*y*z0 + x^15*y*z0^3 + 2*x^15*z0^4 - x^18 - 2*x^16*y*z0 - 2*x^16*z0^2 + 2*x^14*z0^4 - 2*x^15*y*z0 + 2*x^15*z0^2 + 2*x^13*y*z0^3 + x^13*z0^4 + x^16 - x^14*z0^2 - x^12*y*z0^3 - 2*x^12*z0^4 + x^10*y^2*z0^4 - 2*x^13*y*z0 + 2*x^13*z0^2 + x^11*y*z0^3 + 2*x^11*z0^4 - x^14 - x^12*y*z0 + x^10*y*z0^3 - 2*x^10*z0^4 + 2*x^13 + 2*x^11*y*z0 - 2*x^11*z0^2 - x^12 - x^8*y*z0^3 + 2*x^8*z0^4 + 2*x^11 - x^9*z0^2 + x^7*y*z0^3 - 2*x^7*z0^4 + x^8*y*z0 + x^8*z0^2 - x^6*y*z0^3 + 2*x^6*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 - x^4*y*z0^3 + x^4*z0^4 + 2*x^5*y*z0 + x^3*y*z0^3 - x^3*z0^4 - 2*x^6 + 2*x^4*y*z0 + x^4*z0^2 - 2*x^2*z0^4 - 2*x^3*y*z0 - 2*x^3*z0^2 + 2*x^2*y*z0)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^14 + x^11*y^2 + x^11 - x^8 + x^5 - x^2)/y) * dx, - ((-x^14*z0 + x^11*y^2*z0 + x^11*z0 - x^8*z0 + x^5*z0 - x^2*z0)/y) * dx, - ((-x^14*z0^2 + x^11*y^2*z0^2 + x^11*z0^2 - x^8*z0^2 + x^5*z0^2 - x^2*z0^2)/y) * dx, - ((-x^14*z0^3 + x^11*y^2*z0^3 + x^11*z0^3 - x^8*z0^3 + x^5*z0^3 - x^2*z0^3)/y) * dx, - ((-x^14*z0^4 + x^11*y^2*z0^4 + x^11*z0^4 - x^8*z0^4 + x^5*z0^4 - x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^15 + x^12*y^2 + x^12 - x^9 + x^6 - x^3)/y) * dx, - ((-x^15*z0 + x^12*y^2*z0 + x^12*z0 - x^9*z0 + x^6*z0 - x^3*z0)/y) * dx, - ((-x^15*z0^2 + x^12*y^2*z0^2 + x^12*z0^2 - x^9*z0^2 + x^6*z0^2 - x^3*z0^2)/y) * dx, - ((-x^15*z0^3 + x^12*y^2*z0^3 + x^12*z0^3 - x^9*z0^3 + x^6*z0^3 - x^3*z0^3)/y) * dx, - ((-x^15*z0^4 + x^12*y^2*z0^4 + x^12*z0^4 - x^9*z0^4 + x^6*z0^4 - x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 + 2*x^61*z0^2 - 2*x^59*z0^4 + 2*x^60*z0^2 - 2*x^58*y^2*z0^2 - x^58*z0^4 + 2*x^56*y^2*z0^4 - x^61 - 2*x^57*y^2*z0^2 + 2*x^60 + x^58*y^2 - 2*x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 - 2*x^57*z0^2 + x^55*z0^4 + x^58 - 2*x^57 + 2*x^55*z0^2 - 2*x^53*z0^4 + 2*x^54*z0^2 - x^52*z0^4 - x^55 + 2*x^54 - 2*x^52*z0^2 + 2*x^50*z0^4 - 2*x^51*z0^2 + x^49*z0^4 + x^52 - 2*x^51 + 2*x^49*z0^2 - 2*x^47*z0^4 + 2*x^48*z0^2 - x^46*z0^4 - x^49 + 2*x^48 - 2*x^46*z0^2 + 2*x^44*z0^4 - 2*x^45*z0^2 + x^43*z0^4 + x^46 - 2*x^45 + 2*x^43*z0^2 + x^41*z0^4 + 2*x^42*z0^2 - 2*x^40*y*z0^3 - x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^42 + x^40*y*z0 - 2*x^40*z0^2 - x^38*y*z0^3 + x^38*z0^4 - 2*x^41 + x^39*y*z0 + x^39*z0^2 - 2*x^37*y*z0^3 + 2*x^37*z0^4 + x^40 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + 2*x^37*y*z0 + 2*x^37*z0^2 - x^35*y*z0^3 + x^35*z0^4 + 2*x^38 - x^36*y*z0 - x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^34*z0^4 - x^37 - 2*x^35*y*z0 - x^33*y*z0^3 + 2*x^33*z0^4 + x^36 - x^34*y*z0 + 2*x^34*z0^2 + x^32*y*z0^3 + 2*x^35 - x^33*y*z0 - x^33*z0^2 + x^31*y*z0^3 - x^31*z0^4 + 2*x^34 - 2*x^32*z0^2 - x^30*y*z0^3 + x^30*z0^4 + 2*x^33 + x^31*y*z0 + x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - 2*x^32 + 2*x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 - x^29*y*z0 - 2*x^29*z0^2 + x^27*y*z0^3 + 2*x^27*z0^4 + x^30 - 2*x^28*z0^2 + 2*x^29 - 2*x^27*y*z0 + 2*x^27*z0^2 - 2*x^25*y*z0^3 - 2*x^25*z0^4 + 2*x^28 - x^26*y*z0 - x^26*z0^2 - x^24*y*z0^3 - 2*x^24*z0^4 + 2*x^27 + 2*x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + 2*x^24*y*z0 + x^22*z0^4 + x^21*y*z0^3 - 2*x^21*z0^4 - x^24 + 2*x^22*y*z0 - 2*x^20*y*z0^3 - x^23 + 2*x^21*y*z0 - 2*x^21*z0^2 - x^19*y*z0^3 + x^19*z0^4 + 2*x^22 + x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 - 2*x^18*z0^4 - 2*x^21 - 2*x^19*y*z0 - 2*x^19*z0^2 + x^17*y*z0^3 - 2*x^17*z0^4 - 2*x^20 + 2*x^18*y*z0 + x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^16*z0^4 - 2*x^17*y*z0 + 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^15*z0^4 + 2*x^18 + x^16*y*z0 + x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 - 2*x^17 - 2*x^15*y*z0 + 2*x^15*z0^2 + x^13*z0^4 + 2*x^16 - 2*x^14*z0^2 - x^12*z0^4 + x^13*y^2 - x^13*z0^2 + x^11*z0^4 + 2*x^14 - 2*x^12*z0^2 + 2*x^10*z0^4 - x^13 - x^11*z0^2 - 2*x^9*y*z0^3 - x^9*z0^4 + x^10*y*z0 + x^8*y*z0^3 + x^8*z0^4 + x^11 + x^9*y*z0 + x^7*y*z0^3 + 2*x^7*z0^4 + 2*x^10 - 2*x^8*y*z0 + 2*x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 - x^9 - 2*x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + 2*x^8 + 2*x^6*z0^2 - 2*x^4*z0^4 - x^7 - 2*x^5*y*z0 - x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 + x^6 - x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 + x^5 - 2*x^3*y*z0 + x^3*z0^2 + x^2*y*z0 + x^2*z0^2)/y) * dx, - ((-2*x^61*z0^3 - x^60*z0^3 + 2*x^58*y^2*z0^3 - x^61*z0 - x^59*z0^3 + x^57*y^2*z0^3 + x^58*y^2*z0 - x^58*z0^3 + x^56*y^2*z0^3 - 2*x^59*z0 - x^57*z0^3 - 2*x^55*y^2*z0^3 + x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 + x^55*z0^3 + 2*x^56*z0 + x^54*z0^3 - x^55*z0 - x^53*z0^3 - x^52*z0^3 - 2*x^53*z0 - x^51*z0^3 + x^52*z0 + x^50*z0^3 + x^49*z0^3 + 2*x^50*z0 + x^48*z0^3 - x^49*z0 - x^47*z0^3 - x^46*z0^3 - 2*x^47*z0 - x^45*z0^3 + x^46*z0 + x^44*z0^3 + x^43*z0^3 + 2*x^44*z0 + x^42*z0^3 - x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 - x^40*y*z0^2 - x^38*y*z0^4 + 2*x^41*z0 - x^39*y*z0^2 + 2*x^39*z0^3 + 2*x^37*y*z0^4 + 2*x^40*y + 2*x^40*z0 - x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 + 2*x^39*z0 + 2*x^37*y*z0^2 + x^37*z0^3 - 2*x^38*z0 - 2*x^36*y*z0^2 + 2*x^34*y*z0^4 - x^37*y + 2*x^37*z0 + x^35*y*z0^2 + x^35*z0^3 + 2*x^33*y*z0^4 - 2*x^36*y + 2*x^36*z0 + 2*x^34*y*z0^2 + 2*x^34*z0^3 + 2*x^35*y + 2*x^33*y*z0^2 - x^33*z0^3 + 2*x^34*y - x^32*y*z0^2 - 2*x^32*z0^3 - 2*x^33*y + 2*x^33*z0 + x^31*y*z0^2 + x^31*z0^3 - x^29*y*z0^4 - x^32*y - 2*x^30*y*z0^2 - 2*x^30*z0^3 + x^28*y*z0^4 - x^31*y + x^31*z0 - x^29*y*z0^2 + x^29*z0^3 + x^27*y*z0^4 - x^30*y - x^30*z0 - x^28*z0^3 + 2*x^26*y*z0^4 - x^29*y - x^29*z0 - 2*x^27*y*z0^2 + 2*x^27*z0^3 + 2*x^25*y*z0^4 + 2*x^28*y - 2*x^28*z0 - x^26*z0^3 + x^27*y + 2*x^27*z0 + 2*x^25*y*z0^2 - 2*x^25*z0^3 - 2*x^26*z0 + x^24*y*z0^2 + 2*x^22*y*z0^4 + x^25*y + 2*x^25*z0 - 2*x^23*y*z0^2 - 2*x^23*z0^3 - 2*x^21*y*z0^4 + x^24*y + x^24*z0 + x^22*y*z0^2 - 2*x^20*y*z0^4 - 2*x^23*y + x^21*y*z0^2 - x^21*z0^3 - x^19*y*z0^4 - x^22*y + 2*x^22*z0 + 2*x^18*y*z0^4 - 2*x^21*y + x^21*z0 - x^19*y*z0^2 + 2*x^19*z0^3 + 2*x^17*y*z0^4 + 2*x^20*y - x^20*z0 - x^18*y*z0^2 - x^18*z0^3 - 2*x^16*y*z0^4 + 2*x^19*z0 + 2*x^17*y*z0^2 - 2*x^17*z0^3 - x^15*y*z0^4 - 2*x^18*y - x^18*z0 + x^16*y*z0^2 + x^14*y*z0^4 - x^17*y + 2*x^17*z0 - x^15*z0^3 - 2*x^13*y*z0^4 - x^16*y + 2*x^16*z0 - 2*x^14*y*z0^2 - x^14*z0^3 + 2*x^12*y*z0^4 - 2*x^15*z0 + x^13*y^2*z0 + x^13*y*z0^2 - 2*x^14*y + 2*x^14*z0 - 2*x^12*y*z0^2 + x^10*y*z0^4 + x^13*y + x^13*z0 + x^11*y*z0^2 + x^9*y*z0^4 - x^12*z0 + x^10*y*z0^2 + 2*x^10*z0^3 + 2*x^8*y*z0^4 + x^11*y - 2*x^11*z0 + 2*x^9*y*z0^2 + x^7*y*z0^4 - 2*x^10*y + 2*x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*y - 2*x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 + x^8*y + x^8*z0 + x^6*y*z0^2 - 2*x^4*y*z0^4 + 2*x^7*y - x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 - 2*x^6*y + x^4*y*z0^2 - 2*x^4*z0^3 + 2*x^2*y*z0^4 + x^5*y + 2*x^5*z0 - 2*x^3*y*z0^2 - x^3*z0^3 + x^4*y + 2*x^4*z0 - 2*x^2*y*z0^2 + x^2*z0^3 + 2*x^3*y - x^3*z0 + x^2*y - x^2*z0)/y) * dx, - ((2*x^61*z0^4 - 2*x^60*z0^4 - 2*x^58*y^2*z0^4 - 2*x^61*z0^2 - x^59*z0^4 + 2*x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 - x^57*y^2*z0^2 + 2*x^57*z0^4 - x^60 + 2*x^58*z0^2 + x^56*z0^4 + x^57*y^2 - x^57*z0^2 + 2*x^55*z0^4 - 2*x^54*z0^4 + x^57 - 2*x^55*z0^2 - x^53*z0^4 + x^54*z0^2 - 2*x^52*z0^4 + 2*x^51*z0^4 - x^54 + 2*x^52*z0^2 + x^50*z0^4 - x^51*z0^2 + 2*x^49*z0^4 - 2*x^48*z0^4 + x^51 - 2*x^49*z0^2 - x^47*z0^4 + x^48*z0^2 - 2*x^46*z0^4 + 2*x^45*z0^4 - x^48 + 2*x^46*z0^2 + x^44*z0^4 - x^45*z0^2 + 2*x^43*z0^4 - 2*x^42*z0^4 + x^45 - 2*x^43*z0^2 + x^41*z0^4 + x^42*z0^2 + x^40*y*z0^3 + x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - x^42 - x^40*y*z0 - 2*x^40*z0^2 - x^38*z0^4 + 2*x^41 - 2*x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 - 2*x^37*z0^4 - x^40 + 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - 2*x^35*y*z0^3 - 2*x^35*z0^4 + 2*x^38 + x^36*y*z0 - x^36*z0^2 + x^34*y*z0^3 - x^37 - x^35*y*z0 - 2*x^35*z0^2 + 2*x^33*y*z0^3 - x^34*y*z0 + x^32*y*z0^3 + 2*x^35 - 2*x^33*z0^2 - 2*x^31*y*z0^3 - 2*x^31*z0^4 + 2*x^34 + 2*x^32*z0^2 + 2*x^30*y*z0^3 - x^30*z0^4 - x^33 + 2*x^31*y*z0 - 2*x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 + 2*x^28*y*z0^3 + 2*x^28*z0^4 - x^29*y*z0 - x^29*z0^2 + 2*x^27*y*z0^3 - 2*x^27*z0^4 - 2*x^30 - x^28*y*z0 + 2*x^26*y*z0^3 + 2*x^26*z0^4 + 2*x^27*y*z0 + x^27*z0^2 + x^25*y*z0^3 + 2*x^28 - 2*x^26*y*z0 + x^26*z0^2 + 2*x^24*y*z0^3 + x^24*z0^4 + 2*x^27 + x^25*y*z0 - 2*x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 + 2*x^26 - 2*x^24*y*z0 + 2*x^24*z0^2 + 2*x^22*y*z0^3 - x^22*z0^4 + 2*x^25 + x^23*y*z0 - 2*x^23*z0^2 - x^21*y*z0^3 - 2*x^22*y*z0 - x^22*z0^2 - x^20*y*z0^3 + 2*x^20*z0^4 + 2*x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 - x^19*z0^4 - x^20*y*z0 + x^20*z0^2 + x^18*y*z0^3 + 2*x^18*z0^4 - 2*x^21 - 2*x^19*y*z0 - x^17*y*z0^3 + 2*x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^19 + 2*x^17*y*z0 + 2*x^17*z0^2 - x^15*y*z0^3 - 2*x^18 + x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 + x^17 - x^15*y*z0 + x^13*y^2*z0^2 - x^13*y*z0^3 - x^13*z0^4 + x^16 - 2*x^14*y*z0 + x^12*y*z0^3 + x^15 - 2*x^13*y*z0 - x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 - x^10*y*z0^3 - x^10*z0^4 - x^11*y*z0 + 2*x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^12 - x^10*y*z0 + 2*x^8*y*z0^3 + 2*x^8*z0^4 + 2*x^7*y*z0^3 + x^7*z0^4 + 2*x^10 + 2*x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*z0^4 - x^8 + 2*x^6*y*z0 + x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 + 2*x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 - 2*x^2*z0^4 + x^3*y*z0 - x^3*z0^2 + x^2*z0^2 + x^3 - x^2)/y) * dx, - ((-2*x^61*z0^3 + 2*x^58*y^2*z0^3 - 2*x^61*z0 - x^59*z0^3 + x^60*z0 + 2*x^58*y^2*z0 + x^58*z0^3 + x^56*y^2*z0^3 - 2*x^59*z0 - x^57*y^2*z0 + x^55*y^2*z0^3 + 2*x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 - x^57*z0 - x^55*z0^3 + 2*x^56*z0 - 2*x^55*z0 - x^53*z0^3 + x^54*z0 + x^52*z0^3 - 2*x^53*z0 + 2*x^52*z0 + x^50*z0^3 - x^51*z0 - x^49*z0^3 + 2*x^50*z0 - 2*x^49*z0 - x^47*z0^3 + x^48*z0 + x^46*z0^3 - 2*x^47*z0 + 2*x^46*z0 + x^44*z0^3 - x^45*z0 - x^43*z0^3 + 2*x^44*z0 - 2*x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 + x^42*z0 - x^40*y*z0^2 + x^40*z0^3 + x^41*z0 - 2*x^39*y*z0^2 - 2*x^39*z0^3 - x^37*y*z0^4 - x^40*y - 2*x^40*z0 + x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 - 2*x^39*y + 2*x^39*z0 + x^37*y*z0^2 - 2*x^38*y + x^38*z0 - x^36*z0^3 + x^34*y*z0^4 - 2*x^37*y + 2*x^37*z0 + 2*x^35*y*z0^2 - x^35*z0^3 - x^33*y*z0^4 - x^36*y + 2*x^36*z0 - 2*x^34*y*z0^2 - x^34*z0^3 + 2*x^32*y*z0^4 - 2*x^35*y + x^35*z0 + x^33*z0^3 + x^31*y*z0^4 - x^34*z0 + x^32*z0^3 + 2*x^30*y*z0^4 + x^33*y - 2*x^33*z0 + x^31*z0^3 + x^29*y*z0^4 - x^32*y + x^32*z0 - x^30*z0^3 - 2*x^31*y + x^31*z0 + x^29*y*z0^2 - 2*x^27*y*z0^4 + 2*x^30*y + 2*x^30*z0 + x^28*y*z0^2 - x^28*z0^3 - 2*x^26*y*z0^4 + 2*x^29*z0 + x^28*y - x^28*z0 + x^26*y*z0^2 - x^26*z0^3 - 2*x^24*y*z0^4 + 2*x^27*y + x^27*z0 + x^25*y*z0^2 + 2*x^25*z0^3 + x^23*y*z0^4 + x^26*y - x^26*z0 - 2*x^24*y*z0^2 - x^25*y + 2*x^23*y*z0^2 + 2*x^23*z0^3 + x^24*y - x^24*z0 - 2*x^22*y*z0^2 - x^22*z0^3 - 2*x^20*y*z0^4 - x^23*z0 + x^21*y*z0^2 - x^21*z0^3 - 2*x^19*y*z0^4 + 2*x^22*y - x^22*z0 + x^20*z0^3 + x^18*y*z0^4 + 2*x^21*y - 2*x^21*z0 + x^19*y*z0^2 + x^19*z0^3 + x^17*y*z0^4 + x^20*y + 2*x^20*z0 + x^18*z0^3 - 2*x^16*y*z0^4 - x^19*y + x^17*y*z0^2 + x^17*z0^3 + x^15*y*z0^4 + x^18*y + 2*x^18*z0 + 2*x^16*z0^3 + x^14*y*z0^4 + 2*x^15*y*z0^2 - 2*x^15*z0^3 + x^13*y^2*z0^3 - 2*x^16*y - x^14*z0^3 - 2*x^12*y*z0^4 + x^15*y + x^13*y*z0^2 + x^13*z0^3 + 2*x^11*y*z0^4 - 2*x^14*z0 + x^12*y*z0^2 - x^12*z0^3 - x^13*y - x^13*z0 + 2*x^11*y*z0^2 - 2*x^11*z0^3 - 2*x^9*y*z0^4 + x^10*y*z0^2 - x^8*y*z0^4 + x^11*y - x^11*z0 + 2*x^9*y*z0^2 + 2*x^7*y*z0^4 + 2*x^10*y + 2*x^10*z0 - x^8*z0^3 + x^6*y*z0^4 - x^9*z0 + x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 + 2*x^8*y + x^8*z0 - 2*x^6*y*z0^2 + 2*x^6*z0^3 - x^4*y*z0^4 - x^7*y - 2*x^5*y*z0^2 - x^5*z0^3 - x^3*y*z0^4 + 2*x^6*z0 - 2*x^4*y*z0^2 + x^5*y - 2*x^3*z0^3 - 2*x^4*y + x^4*z0 - x^2*y*z0^2 + 2*x^2*z0^3 + x^3*y + 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-x^60*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^56*y^2*z0^4 - x^57*y^2*z0^2 + x^57*z0^4 - 2*x^60 + 2*x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 - x^57*z0^2 - x^54*z0^4 + 2*x^57 - 2*x^55*z0^2 + 2*x^53*z0^4 + x^54*z0^2 + x^51*z0^4 - 2*x^54 + 2*x^52*z0^2 - 2*x^50*z0^4 - x^51*z0^2 - x^48*z0^4 + 2*x^51 - 2*x^49*z0^2 + 2*x^47*z0^4 + x^48*z0^2 + x^45*z0^4 - 2*x^48 + 2*x^46*z0^2 - 2*x^44*z0^4 - x^45*z0^2 - x^42*z0^4 + 2*x^45 - 2*x^43*z0^2 + 2*x^41*z0^4 + x^42*z0^2 - x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - 2*x^42 - x^40*y*z0 + x^40*z0^2 + x^38*y*z0^3 + 2*x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 - x^40 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 - x^35*z0^4 - x^38 + 2*x^36*y*z0 - x^36*z0^2 + x^34*y*z0^3 + 2*x^34*z0^4 + x^37 - 2*x^35*y*z0 + x^35*z0^2 - x^33*y*z0^3 - 2*x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 + x^34*z0^2 - 2*x^32*y*z0^3 - x^35 + 2*x^33*y*z0 + 2*x^33*z0^2 + x^31*y*z0^3 + x^31*z0^4 - 2*x^34 + x^32*z0^2 - x^30*y*z0^3 + 2*x^30*z0^4 + x^33 - x^31*y*z0 - x^31*z0^2 + x^29*z0^4 + x^30*y*z0 - 2*x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^29*y*z0 + x^29*z0^2 + x^30 + 2*x^28*y*z0 - x^28*z0^2 + x^26*y*z0^3 - 2*x^26*z0^4 - x^27*y*z0 - 2*x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 - x^28 + 2*x^24*y*z0^3 - 2*x^24*z0^4 - x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + x^24*y*z0 - x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^25 - x^23*y*z0 + x^23*z0^2 - x^21*y*z0^3 + x^21*z0^4 + 2*x^24 + x^22*y*z0 - x^20*y*z0^3 + x^20*z0^4 - x^23 - x^21*y*z0 + x^21*z0^2 - x^19*y*z0^3 - x^19*z0^4 - 2*x^22 - x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 + x^18*z0^4 + x^21 - x^19*y*z0 + 2*x^20 - x^18*y*z0 - x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^16*z0^4 + x^19 + x^17*y*z0 - x^15*y*z0^3 - 2*x^15*z0^4 + x^13*y^2*z0^4 + x^18 + 2*x^16*y*z0 + 2*x^16*z0^2 - 2*x^14*z0^4 + 2*x^15*y*z0 - 2*x^15*z0^2 - 2*x^13*y*z0^3 - x^13*z0^4 - x^16 + x^14*z0^2 + x^12*y*z0^3 + 2*x^12*z0^4 + 2*x^13*y*z0 - 2*x^13*z0^2 - x^11*y*z0^3 - 2*x^11*z0^4 + x^14 + x^12*y*z0 - x^10*y*z0^3 + 2*x^10*z0^4 - 2*x^13 - 2*x^11*y*z0 + 2*x^11*z0^2 + x^12 + x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^11 + x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 - x^8*y*z0 - x^8*z0^2 + x^6*y*z0^3 - 2*x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 + x^4*y*z0^3 - x^4*z0^4 - 2*x^5*y*z0 - x^3*y*z0^3 + x^3*z0^4 + 2*x^6 - 2*x^4*y*z0 - x^4*z0^2 + 2*x^2*z0^4 + 2*x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^17 + x^14*y^2 + x^14 - x^11 + x^8 - x^5 + x^2)/y) * dx, - ((-x^17*z0 + x^14*y^2*z0 + x^14*z0 - x^11*z0 + x^8*z0 - x^5*z0 + x^2*z0)/y) * dx, - ((-x^17*z0^2 + x^14*y^2*z0^2 + x^14*z0^2 - x^11*z0^2 + x^8*z0^2 - x^5*z0^2 + x^2*z0^2)/y) * dx, - ((-x^17*z0^3 + x^14*y^2*z0^3 + x^14*z0^3 - x^11*z0^3 + x^8*z0^3 - x^5*z0^3 + x^2*z0^3)/y) * dx, - ((-x^17*z0^4 + x^14*y^2*z0^4 + x^14*z0^4 - x^11*z0^4 + x^8*z0^4 - x^5*z0^4 + x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^18 + x^15*y^2 + x^15 - x^12 + x^9 - x^6 + x^3)/y) * dx, - ((-x^18*z0 + x^15*y^2*z0 + x^15*z0 - x^12*z0 + x^9*z0 - x^6*z0 + x^3*z0)/y) * dx, - ((-x^18*z0^2 + x^15*y^2*z0^2 + x^15*z0^2 - x^12*z0^2 + x^9*z0^2 - x^6*z0^2 + x^3*z0^2)/y) * dx, - ((-x^18*z0^3 + x^15*y^2*z0^3 + x^15*z0^3 - x^12*z0^3 + x^9*z0^3 - x^6*z0^3 + x^3*z0^3)/y) * dx, - ((-x^18*z0^4 + x^15*y^2*z0^4 + x^15*z0^4 - x^12*z0^4 + x^9*z0^4 - x^6*z0^4 + x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 + x^58*y^2*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 - 2*x^60*z0^2 + 2*x^58*y^2*z0^2 + x^58*z0^4 - 2*x^56*y^2*z0^4 + x^61 + 2*x^57*y^2*z0^2 - 2*x^60 - x^58*y^2 + 2*x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 + 2*x^57*z0^2 - x^55*z0^4 - x^58 + 2*x^57 - 2*x^55*z0^2 + 2*x^53*z0^4 - 2*x^54*z0^2 + x^52*z0^4 + x^55 - 2*x^54 + 2*x^52*z0^2 - 2*x^50*z0^4 + 2*x^51*z0^2 - x^49*z0^4 - x^52 + 2*x^51 - 2*x^49*z0^2 + 2*x^47*z0^4 - 2*x^48*z0^2 + x^46*z0^4 + x^49 - 2*x^48 + 2*x^46*z0^2 - 2*x^44*z0^4 + 2*x^45*z0^2 - x^43*z0^4 - x^46 + 2*x^45 - 2*x^43*z0^2 - x^41*z0^4 - 2*x^42*z0^2 + 2*x^40*y*z0^3 + x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - 2*x^42 - x^40*y*z0 + 2*x^40*z0^2 + x^38*y*z0^3 - x^38*z0^4 + 2*x^41 - x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 - x^40 + 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - 2*x^37*y*z0 - 2*x^37*z0^2 + x^35*y*z0^3 - x^35*z0^4 - 2*x^38 + x^36*y*z0 + x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 + x^37 + 2*x^35*y*z0 + x^33*y*z0^3 - 2*x^33*z0^4 - x^36 + x^34*y*z0 - 2*x^34*z0^2 - x^32*y*z0^3 - 2*x^35 + x^33*y*z0 + x^33*z0^2 - x^31*y*z0^3 + x^31*z0^4 - 2*x^34 + 2*x^32*z0^2 + x^30*y*z0^3 - x^30*z0^4 - 2*x^33 - x^31*y*z0 - x^31*z0^2 - x^29*y*z0^3 - x^29*z0^4 + 2*x^32 - 2*x^28*y*z0^3 + 2*x^28*z0^4 - 2*x^31 + x^29*y*z0 + 2*x^29*z0^2 - x^27*y*z0^3 - 2*x^27*z0^4 - x^30 + 2*x^28*z0^2 - 2*x^29 + 2*x^27*y*z0 - 2*x^27*z0^2 + 2*x^25*y*z0^3 + 2*x^25*z0^4 - 2*x^28 + x^26*y*z0 + x^26*z0^2 + x^24*y*z0^3 + 2*x^24*z0^4 - 2*x^27 - 2*x^25*z0^2 + x^23*y*z0^3 - x^23*z0^4 + 2*x^26 - 2*x^24*y*z0 - x^22*z0^4 - x^21*y*z0^3 + 2*x^21*z0^4 + x^24 - 2*x^22*y*z0 + 2*x^20*y*z0^3 + x^23 - 2*x^21*y*z0 + 2*x^21*z0^2 + x^19*y*z0^3 - x^19*z0^4 - 2*x^22 - x^20*y*z0 - 2*x^20*z0^2 - x^18*y*z0^3 + 2*x^18*z0^4 + 2*x^21 + 2*x^19*y*z0 + 2*x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 + 2*x^20 - 2*x^18*y*z0 - x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^16*z0^4 - x^19 + 2*x^17*y*z0 - 2*x^17*z0^2 - x^15*y*z0^3 - 2*x^15*z0^4 - 2*x^18 + x^16*y^2 - x^16*y*z0 - x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 + 2*x^17 + 2*x^15*y*z0 - 2*x^15*z0^2 - x^13*z0^4 - 2*x^16 + 2*x^14*z0^2 + x^12*z0^4 + x^13*z0^2 - x^11*z0^4 - 2*x^14 + 2*x^12*z0^2 - 2*x^10*z0^4 + x^13 + x^11*z0^2 + 2*x^9*y*z0^3 + x^9*z0^4 - x^10*y*z0 - x^8*y*z0^3 - x^8*z0^4 - x^11 - x^9*y*z0 - x^7*y*z0^3 - 2*x^7*z0^4 - 2*x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 + 2*x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 - 2*x^8 - 2*x^6*z0^2 + 2*x^4*z0^4 + x^7 + 2*x^5*y*z0 + x^5*z0^2 + 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 + x^4*y*z0 + x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 - x^5 + 2*x^3*y*z0 - x^3*z0^2 - x^2*y*z0 - x^2*z0^2)/y) * dx, - ((2*x^61*z0^3 + x^60*z0^3 - 2*x^58*y^2*z0^3 + x^61*z0 + x^59*z0^3 - x^57*y^2*z0^3 - x^58*y^2*z0 + x^58*z0^3 - x^56*y^2*z0^3 + 2*x^59*z0 + x^57*z0^3 + 2*x^55*y^2*z0^3 - x^58*z0 - 2*x^56*y^2*z0 - x^56*z0^3 - 2*x^54*y^2*z0^3 - x^55*z0^3 - 2*x^56*z0 - x^54*z0^3 + x^55*z0 + x^53*z0^3 + x^52*z0^3 + 2*x^53*z0 + x^51*z0^3 - x^52*z0 - x^50*z0^3 - x^49*z0^3 - 2*x^50*z0 - x^48*z0^3 + x^49*z0 + x^47*z0^3 + x^46*z0^3 + 2*x^47*z0 + x^45*z0^3 - x^46*z0 - x^44*z0^3 - x^43*z0^3 - 2*x^44*z0 - x^42*z0^3 + x^43*z0 - 2*x^41*z0^3 + 2*x^39*y*z0^4 + x^40*y*z0^2 + x^38*y*z0^4 - 2*x^41*z0 + x^39*y*z0^2 - 2*x^39*z0^3 - 2*x^37*y*z0^4 - 2*x^40*y - 2*x^40*z0 + x^38*y*z0^2 - x^38*z0^3 - 2*x^36*y*z0^4 - 2*x^39*z0 - 2*x^37*y*z0^2 - x^37*z0^3 + 2*x^38*z0 + 2*x^36*y*z0^2 - 2*x^34*y*z0^4 + x^37*y - 2*x^37*z0 - x^35*y*z0^2 - x^35*z0^3 - 2*x^33*y*z0^4 + 2*x^36*y - 2*x^36*z0 - 2*x^34*y*z0^2 - 2*x^34*z0^3 - 2*x^35*y - 2*x^33*y*z0^2 + x^33*z0^3 - 2*x^34*y + x^32*y*z0^2 + 2*x^32*z0^3 + 2*x^33*y - 2*x^33*z0 - x^31*y*z0^2 - x^31*z0^3 + x^29*y*z0^4 + x^32*y + 2*x^30*y*z0^2 + 2*x^30*z0^3 - x^28*y*z0^4 + x^31*y - x^31*z0 + x^29*y*z0^2 - x^29*z0^3 - x^27*y*z0^4 + x^30*y + x^30*z0 + x^28*z0^3 - 2*x^26*y*z0^4 + x^29*y + x^29*z0 + 2*x^27*y*z0^2 - 2*x^27*z0^3 - 2*x^25*y*z0^4 - 2*x^28*y + 2*x^28*z0 + x^26*z0^3 - x^27*y - 2*x^27*z0 - 2*x^25*y*z0^2 + 2*x^25*z0^3 + 2*x^26*z0 - x^24*y*z0^2 - 2*x^22*y*z0^4 - x^25*y - 2*x^25*z0 + 2*x^23*y*z0^2 + 2*x^23*z0^3 + 2*x^21*y*z0^4 - x^24*y - x^24*z0 - x^22*y*z0^2 + 2*x^20*y*z0^4 + 2*x^23*y - x^21*y*z0^2 + x^21*z0^3 + x^19*y*z0^4 + x^22*y - 2*x^22*z0 - 2*x^18*y*z0^4 + 2*x^21*y - x^21*z0 + x^19*y*z0^2 - 2*x^19*z0^3 - 2*x^17*y*z0^4 - 2*x^20*y + x^20*z0 + x^18*y*z0^2 + x^18*z0^3 + 2*x^16*y*z0^4 + 2*x^19*z0 - 2*x^17*y*z0^2 + 2*x^17*z0^3 + x^15*y*z0^4 + 2*x^18*y + x^18*z0 + x^16*y^2*z0 - x^16*y*z0^2 - x^14*y*z0^4 + x^17*y - 2*x^17*z0 + x^15*z0^3 + 2*x^13*y*z0^4 + x^16*y - 2*x^16*z0 + 2*x^14*y*z0^2 + x^14*z0^3 - 2*x^12*y*z0^4 + 2*x^15*z0 - x^13*y*z0^2 + 2*x^14*y - 2*x^14*z0 + 2*x^12*y*z0^2 - x^10*y*z0^4 - x^13*y - x^13*z0 - x^11*y*z0^2 - x^9*y*z0^4 + x^12*z0 - x^10*y*z0^2 - 2*x^10*z0^3 - 2*x^8*y*z0^4 - x^11*y + 2*x^11*z0 - 2*x^9*y*z0^2 - x^7*y*z0^4 + 2*x^10*y - 2*x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 - 2*x^6*y*z0^4 - x^9*y + 2*x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + x^5*y*z0^4 - x^8*y - x^8*z0 - x^6*y*z0^2 + 2*x^4*y*z0^4 - 2*x^7*y + x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 - 2*x^3*y*z0^4 + 2*x^6*y - x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^2*y*z0^4 - x^5*y - 2*x^5*z0 + 2*x^3*y*z0^2 + x^3*z0^3 - x^4*y - 2*x^4*z0 + 2*x^2*y*z0^2 - x^2*z0^3 - 2*x^3*y + x^3*z0 - x^2*y + x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + 2*x^60*z0^4 + 2*x^58*y^2*z0^4 + 2*x^61*z0^2 + x^59*z0^4 - 2*x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^58*z0^4 - x^56*y^2*z0^4 + x^57*y^2*z0^2 - 2*x^57*z0^4 + x^60 - 2*x^58*z0^2 - x^56*z0^4 - x^57*y^2 + x^57*z0^2 - 2*x^55*z0^4 + 2*x^54*z0^4 - x^57 + 2*x^55*z0^2 + x^53*z0^4 - x^54*z0^2 + 2*x^52*z0^4 - 2*x^51*z0^4 + x^54 - 2*x^52*z0^2 - x^50*z0^4 + x^51*z0^2 - 2*x^49*z0^4 + 2*x^48*z0^4 - x^51 + 2*x^49*z0^2 + x^47*z0^4 - x^48*z0^2 + 2*x^46*z0^4 - 2*x^45*z0^4 + x^48 - 2*x^46*z0^2 - x^44*z0^4 + x^45*z0^2 - 2*x^43*z0^4 + 2*x^42*z0^4 - x^45 + 2*x^43*z0^2 - x^41*z0^4 - x^42*z0^2 - x^40*y*z0^3 - x^40*z0^4 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 + x^42 + x^40*y*z0 + 2*x^40*z0^2 + x^38*z0^4 - 2*x^41 + 2*x^39*y*z0 - x^39*z0^2 + x^37*y*z0^3 + 2*x^37*z0^4 + x^40 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - x^37*y*z0 + 2*x^35*y*z0^3 + 2*x^35*z0^4 - 2*x^38 - x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 + x^37 + x^35*y*z0 + 2*x^35*z0^2 - 2*x^33*y*z0^3 + x^34*y*z0 - x^32*y*z0^3 - 2*x^35 + 2*x^33*z0^2 + 2*x^31*y*z0^3 + 2*x^31*z0^4 - 2*x^34 - 2*x^32*z0^2 - 2*x^30*y*z0^3 + x^30*z0^4 + x^33 - 2*x^31*y*z0 + 2*x^31*z0^2 - x^29*y*z0^3 - x^29*z0^4 + 2*x^32 + 2*x^30*y*z0 - 2*x^28*y*z0^3 - 2*x^28*z0^4 + x^29*y*z0 + x^29*z0^2 - 2*x^27*y*z0^3 + 2*x^27*z0^4 + 2*x^30 + x^28*y*z0 - 2*x^26*y*z0^3 - 2*x^26*z0^4 - 2*x^27*y*z0 - x^27*z0^2 - x^25*y*z0^3 - 2*x^28 + 2*x^26*y*z0 - x^26*z0^2 - 2*x^24*y*z0^3 - x^24*z0^4 - 2*x^27 - x^25*y*z0 + 2*x^25*z0^2 + x^23*y*z0^3 - x^23*z0^4 - 2*x^26 + 2*x^24*y*z0 - 2*x^24*z0^2 - 2*x^22*y*z0^3 + x^22*z0^4 - 2*x^25 - x^23*y*z0 + 2*x^23*z0^2 + x^21*y*z0^3 + 2*x^22*y*z0 + x^22*z0^2 + x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^21*y*z0 + x^21*z0^2 + x^19*y*z0^3 + x^19*z0^4 + x^20*y*z0 - x^20*z0^2 - x^18*y*z0^3 - 2*x^18*z0^4 + 2*x^21 + 2*x^19*y*z0 - x^19*z0^2 + x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^18*z0^2 + x^16*y^2*z0^2 + 2*x^16*y*z0^3 + 2*x^19 - 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^18 - x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 - x^17 + x^15*y*z0 + x^13*y*z0^3 + x^13*z0^4 - x^16 + 2*x^14*y*z0 - x^12*y*z0^3 - x^15 + 2*x^13*y*z0 + x^13*z0^2 - x^11*y*z0^3 - x^11*z0^4 + x^10*y*z0^3 + x^10*z0^4 + x^11*y*z0 - 2*x^9*y*z0^3 + 2*x^9*z0^4 - 2*x^12 + x^10*y*z0 - 2*x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^7*y*z0^3 - x^7*z0^4 - 2*x^10 - 2*x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - 2*x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^3*y*z0^3 - 2*x^3*z0^4 + x^6 - 2*x^4*y*z0 + 2*x^4*z0^2 + x^2*y*z0^3 + 2*x^2*z0^4 - x^3*y*z0 + x^3*z0^2 - x^2*z0^2 - x^3 + x^2)/y) * dx, - ((2*x^61*z0^3 - 2*x^58*y^2*z0^3 + 2*x^61*z0 + x^59*z0^3 - x^60*z0 - 2*x^58*y^2*z0 - x^58*z0^3 - x^56*y^2*z0^3 + 2*x^59*z0 + x^57*y^2*z0 - x^55*y^2*z0^3 - 2*x^58*z0 - 2*x^56*y^2*z0 - x^56*z0^3 + x^57*z0 + x^55*z0^3 - 2*x^56*z0 + 2*x^55*z0 + x^53*z0^3 - x^54*z0 - x^52*z0^3 + 2*x^53*z0 - 2*x^52*z0 - x^50*z0^3 + x^51*z0 + x^49*z0^3 - 2*x^50*z0 + 2*x^49*z0 + x^47*z0^3 - x^48*z0 - x^46*z0^3 + 2*x^47*z0 - 2*x^46*z0 - x^44*z0^3 + x^45*z0 + x^43*z0^3 - 2*x^44*z0 + 2*x^43*z0 - 2*x^41*z0^3 + 2*x^39*y*z0^4 - x^42*z0 + x^40*y*z0^2 - x^40*z0^3 - x^41*z0 + 2*x^39*y*z0^2 + 2*x^39*z0^3 + x^37*y*z0^4 + x^40*y + 2*x^40*z0 - x^38*y*z0^2 - x^38*z0^3 - 2*x^36*y*z0^4 + 2*x^39*y - 2*x^39*z0 - x^37*y*z0^2 + 2*x^38*y - x^38*z0 + x^36*z0^3 - x^34*y*z0^4 + 2*x^37*y - 2*x^37*z0 - 2*x^35*y*z0^2 + x^35*z0^3 + x^33*y*z0^4 + x^36*y - 2*x^36*z0 + 2*x^34*y*z0^2 + x^34*z0^3 - 2*x^32*y*z0^4 + 2*x^35*y - x^35*z0 - x^33*z0^3 - x^31*y*z0^4 + x^34*z0 - x^32*z0^3 - 2*x^30*y*z0^4 - x^33*y + 2*x^33*z0 - x^31*z0^3 - x^29*y*z0^4 + x^32*y - x^32*z0 + x^30*z0^3 + 2*x^31*y - x^31*z0 - x^29*y*z0^2 + 2*x^27*y*z0^4 - 2*x^30*y - 2*x^30*z0 - x^28*y*z0^2 + x^28*z0^3 + 2*x^26*y*z0^4 - 2*x^29*z0 - x^28*y + x^28*z0 - x^26*y*z0^2 + x^26*z0^3 + 2*x^24*y*z0^4 - 2*x^27*y - x^27*z0 - x^25*y*z0^2 - 2*x^25*z0^3 - x^23*y*z0^4 - x^26*y + x^26*z0 + 2*x^24*y*z0^2 + x^25*y - 2*x^23*y*z0^2 - 2*x^23*z0^3 - x^24*y + x^24*z0 + 2*x^22*y*z0^2 + x^22*z0^3 + 2*x^20*y*z0^4 + x^23*z0 - x^21*y*z0^2 + x^21*z0^3 + 2*x^19*y*z0^4 - 2*x^22*y + x^22*z0 - x^20*z0^3 - x^18*y*z0^4 - 2*x^21*y + 2*x^21*z0 - x^19*y*z0^2 - 2*x^19*z0^3 - x^17*y*z0^4 - x^20*y - 2*x^20*z0 - x^18*z0^3 + x^16*y^2*z0^3 + 2*x^16*y*z0^4 + x^19*y - x^17*y*z0^2 - x^17*z0^3 - x^15*y*z0^4 - x^18*y - 2*x^18*z0 - 2*x^16*z0^3 - x^14*y*z0^4 - 2*x^15*y*z0^2 + 2*x^15*z0^3 + 2*x^16*y + x^14*z0^3 + 2*x^12*y*z0^4 - x^15*y - x^13*y*z0^2 - x^13*z0^3 - 2*x^11*y*z0^4 + 2*x^14*z0 - x^12*y*z0^2 + x^12*z0^3 + x^13*y + x^13*z0 - 2*x^11*y*z0^2 + 2*x^11*z0^3 + 2*x^9*y*z0^4 - x^10*y*z0^2 + x^8*y*z0^4 - x^11*y + x^11*z0 - 2*x^9*y*z0^2 - 2*x^7*y*z0^4 - 2*x^10*y - 2*x^10*z0 + x^8*z0^3 - x^6*y*z0^4 + x^9*z0 - x^7*y*z0^2 - 2*x^7*z0^3 + x^5*y*z0^4 - 2*x^8*y - x^8*z0 + 2*x^6*y*z0^2 - 2*x^6*z0^3 + x^4*y*z0^4 + x^7*y + 2*x^5*y*z0^2 + x^5*z0^3 + x^3*y*z0^4 - 2*x^6*z0 + 2*x^4*y*z0^2 - x^5*y + 2*x^3*z0^3 + 2*x^4*y - x^4*z0 + x^2*y*z0^2 - 2*x^2*z0^3 - x^3*y - 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((x^60*z0^4 + 2*x^61*z0^2 - 2*x^59*z0^4 - x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^56*y^2*z0^4 + x^57*y^2*z0^2 - x^57*z0^4 + 2*x^60 - 2*x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 + x^57*z0^2 + x^54*z0^4 - 2*x^57 + 2*x^55*z0^2 - 2*x^53*z0^4 - x^54*z0^2 - x^51*z0^4 + 2*x^54 - 2*x^52*z0^2 + 2*x^50*z0^4 + x^51*z0^2 + x^48*z0^4 - 2*x^51 + 2*x^49*z0^2 - 2*x^47*z0^4 - x^48*z0^2 - x^45*z0^4 + 2*x^48 - 2*x^46*z0^2 + 2*x^44*z0^4 + x^45*z0^2 + x^42*z0^4 - 2*x^45 + 2*x^43*z0^2 - 2*x^41*z0^4 - x^42*z0^2 + x^40*z0^4 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 + 2*x^42 + x^40*y*z0 - x^40*z0^2 - x^38*y*z0^3 - 2*x^39*y*z0 - x^39*z0^2 + x^37*y*z0^3 + x^40 - x^38*z0^2 + x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - x^37*y*z0 + 2*x^37*z0^2 + 2*x^35*y*z0^3 + x^35*z0^4 + x^38 - 2*x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 - 2*x^34*z0^4 - x^37 + 2*x^35*y*z0 - x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 - 2*x^36 + 2*x^34*y*z0 - x^34*z0^2 + 2*x^32*y*z0^3 + x^35 - 2*x^33*y*z0 - 2*x^33*z0^2 - x^31*y*z0^3 - x^31*z0^4 + 2*x^34 - x^32*z0^2 + x^30*y*z0^3 - 2*x^30*z0^4 - x^33 + x^31*y*z0 + x^31*z0^2 - x^29*z0^4 - x^30*y*z0 + 2*x^28*y*z0^3 - 2*x^28*z0^4 - 2*x^29*y*z0 - x^29*z0^2 - x^30 - 2*x^28*y*z0 + x^28*z0^2 - x^26*y*z0^3 + 2*x^26*z0^4 + x^27*y*z0 + 2*x^27*z0^2 - x^25*y*z0^3 + x^25*z0^4 + x^28 - 2*x^24*y*z0^3 + 2*x^24*z0^4 + x^23*y*z0^3 - x^23*z0^4 + 2*x^26 - x^24*y*z0 + x^24*z0^2 + 2*x^22*y*z0^3 - 2*x^25 + x^23*y*z0 - x^23*z0^2 + x^21*y*z0^3 - x^21*z0^4 - 2*x^24 - x^22*y*z0 + x^20*y*z0^3 - x^20*z0^4 + x^23 + x^21*y*z0 - x^21*z0^2 + x^19*y*z0^3 + 2*x^22 + x^20*y*z0 - 2*x^20*z0^2 - x^18*y*z0^3 - x^18*z0^4 + x^16*y^2*z0^4 - x^21 + x^19*y*z0 - 2*x^20 + x^18*y*z0 + x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^16*z0^4 - x^19 - x^17*y*z0 + x^15*y*z0^3 + 2*x^15*z0^4 - x^18 - 2*x^16*y*z0 - 2*x^16*z0^2 + 2*x^14*z0^4 - 2*x^15*y*z0 + 2*x^15*z0^2 + 2*x^13*y*z0^3 + x^13*z0^4 + x^16 - x^14*z0^2 - x^12*y*z0^3 - 2*x^12*z0^4 - 2*x^13*y*z0 + 2*x^13*z0^2 + x^11*y*z0^3 + 2*x^11*z0^4 - x^14 - x^12*y*z0 + x^10*y*z0^3 - 2*x^10*z0^4 + 2*x^13 + 2*x^11*y*z0 - 2*x^11*z0^2 - x^12 - x^8*y*z0^3 + 2*x^8*z0^4 + 2*x^11 - x^9*z0^2 + x^7*y*z0^3 - 2*x^7*z0^4 + x^8*y*z0 + x^8*z0^2 - x^6*y*z0^3 + 2*x^6*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 - x^4*y*z0^3 + x^4*z0^4 + 2*x^5*y*z0 + x^3*y*z0^3 - x^3*z0^4 - 2*x^6 + 2*x^4*y*z0 + x^4*z0^2 - 2*x^2*z0^4 - 2*x^3*y*z0 - 2*x^3*z0^2 + 2*x^2*y*z0)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^20 + x^17*y^2 + x^17 - x^14 + x^11 - x^8 + x^5 - x^2)/y) * dx, - ((-x^20*z0 + x^17*y^2*z0 + x^17*z0 - x^14*z0 + x^11*z0 - x^8*z0 + x^5*z0 - x^2*z0)/y) * dx, - ((-x^20*z0^2 + x^17*y^2*z0^2 + x^17*z0^2 - x^14*z0^2 + x^11*z0^2 - x^8*z0^2 + x^5*z0^2 - x^2*z0^2)/y) * dx, - ((-x^20*z0^3 + x^17*y^2*z0^3 + x^17*z0^3 - x^14*z0^3 + x^11*z0^3 - x^8*z0^3 + x^5*z0^3 - x^2*z0^3)/y) * dx, - ((-x^20*z0^4 + x^17*y^2*z0^4 + x^17*z0^4 - x^14*z0^4 + x^11*z0^4 - x^8*z0^4 + x^5*z0^4 - x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^21 + x^18*y^2 + x^18 - x^15 + x^12 - x^9 + x^6 - x^3)/y) * dx, - ((-x^21*z0 + x^18*y^2*z0 + x^18*z0 - x^15*z0 + x^12*z0 - x^9*z0 + x^6*z0 - x^3*z0)/y) * dx, - ((-x^21*z0^2 + x^18*y^2*z0^2 + x^18*z0^2 - x^15*z0^2 + x^12*z0^2 - x^9*z0^2 + x^6*z0^2 - x^3*z0^2)/y) * dx, - ((-x^21*z0^3 + x^18*y^2*z0^3 + x^18*z0^3 - x^15*z0^3 + x^12*z0^3 - x^9*z0^3 + x^6*z0^3 - x^3*z0^3)/y) * dx, - ((-x^21*z0^4 + x^18*y^2*z0^4 + x^18*z0^4 - x^15*z0^4 + x^12*z0^4 - x^9*z0^4 + x^6*z0^4 - x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 + 2*x^61*z0^2 - 2*x^59*z0^4 + 2*x^60*z0^2 - 2*x^58*y^2*z0^2 - x^58*z0^4 + 2*x^56*y^2*z0^4 - x^61 - 2*x^57*y^2*z0^2 + 2*x^60 + x^58*y^2 - 2*x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 - 2*x^57*z0^2 + x^55*z0^4 + x^58 - 2*x^57 + 2*x^55*z0^2 - 2*x^53*z0^4 + 2*x^54*z0^2 - x^52*z0^4 - x^55 + 2*x^54 - 2*x^52*z0^2 + 2*x^50*z0^4 - 2*x^51*z0^2 + x^49*z0^4 + x^52 - 2*x^51 + 2*x^49*z0^2 - 2*x^47*z0^4 + 2*x^48*z0^2 - x^46*z0^4 - x^49 + 2*x^48 - 2*x^46*z0^2 + 2*x^44*z0^4 - 2*x^45*z0^2 + x^43*z0^4 + x^46 - 2*x^45 + 2*x^43*z0^2 + x^41*z0^4 + 2*x^42*z0^2 - 2*x^40*y*z0^3 - x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^42 + x^40*y*z0 - 2*x^40*z0^2 - x^38*y*z0^3 + x^38*z0^4 - 2*x^41 + x^39*y*z0 + x^39*z0^2 - 2*x^37*y*z0^3 + 2*x^37*z0^4 + x^40 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + 2*x^37*y*z0 + 2*x^37*z0^2 - x^35*y*z0^3 + x^35*z0^4 + 2*x^38 - x^36*y*z0 - x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^34*z0^4 - x^37 - 2*x^35*y*z0 - x^33*y*z0^3 + 2*x^33*z0^4 + x^36 - x^34*y*z0 + 2*x^34*z0^2 + x^32*y*z0^3 + 2*x^35 - x^33*y*z0 - x^33*z0^2 + x^31*y*z0^3 - x^31*z0^4 + 2*x^34 - 2*x^32*z0^2 - x^30*y*z0^3 + x^30*z0^4 + 2*x^33 + x^31*y*z0 + x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - 2*x^32 + 2*x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 - x^29*y*z0 - 2*x^29*z0^2 + x^27*y*z0^3 + 2*x^27*z0^4 + x^30 - 2*x^28*z0^2 + 2*x^29 - 2*x^27*y*z0 + 2*x^27*z0^2 - 2*x^25*y*z0^3 - 2*x^25*z0^4 + 2*x^28 - x^26*y*z0 - x^26*z0^2 - x^24*y*z0^3 - 2*x^24*z0^4 + 2*x^27 + 2*x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + 2*x^24*y*z0 + x^22*z0^4 + x^21*y*z0^3 - 2*x^21*z0^4 - x^24 + 2*x^22*y*z0 - 2*x^20*y*z0^3 - x^23 + 2*x^21*y*z0 - 2*x^21*z0^2 - x^19*y*z0^3 + x^19*z0^4 + x^22 + x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 - 2*x^18*z0^4 - 2*x^21 + x^19*y^2 - 2*x^19*y*z0 - 2*x^19*z0^2 + x^17*y*z0^3 - 2*x^17*z0^4 - 2*x^20 + 2*x^18*y*z0 + x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^16*z0^4 + x^19 - 2*x^17*y*z0 + 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^15*z0^4 + 2*x^18 + x^16*y*z0 + x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 - 2*x^17 - 2*x^15*y*z0 + 2*x^15*z0^2 + x^13*z0^4 + 2*x^16 - 2*x^14*z0^2 - x^12*z0^4 - x^13*z0^2 + x^11*z0^4 + 2*x^14 - 2*x^12*z0^2 + 2*x^10*z0^4 - x^13 - x^11*z0^2 - 2*x^9*y*z0^3 - x^9*z0^4 + x^10*y*z0 + x^8*y*z0^3 + x^8*z0^4 + x^11 + x^9*y*z0 + x^7*y*z0^3 + 2*x^7*z0^4 + 2*x^10 - 2*x^8*y*z0 + 2*x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 - x^9 - 2*x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + 2*x^8 + 2*x^6*z0^2 - 2*x^4*z0^4 - x^7 - 2*x^5*y*z0 - x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 + x^6 - x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 + x^5 - 2*x^3*y*z0 + x^3*z0^2 + x^2*y*z0 + x^2*z0^2)/y) * dx, - ((-2*x^61*z0^3 - x^60*z0^3 + 2*x^58*y^2*z0^3 - x^61*z0 - x^59*z0^3 + x^57*y^2*z0^3 + x^58*y^2*z0 - x^58*z0^3 + x^56*y^2*z0^3 - 2*x^59*z0 - x^57*z0^3 - 2*x^55*y^2*z0^3 + x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 + x^55*z0^3 + 2*x^56*z0 + x^54*z0^3 - x^55*z0 - x^53*z0^3 - x^52*z0^3 - 2*x^53*z0 - x^51*z0^3 + x^52*z0 + x^50*z0^3 + x^49*z0^3 + 2*x^50*z0 + x^48*z0^3 - x^49*z0 - x^47*z0^3 - x^46*z0^3 - 2*x^47*z0 - x^45*z0^3 + x^46*z0 + x^44*z0^3 + x^43*z0^3 + 2*x^44*z0 + x^42*z0^3 - x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 - x^40*y*z0^2 - x^38*y*z0^4 + 2*x^41*z0 - x^39*y*z0^2 + 2*x^39*z0^3 + 2*x^37*y*z0^4 + 2*x^40*y + 2*x^40*z0 - x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 + 2*x^39*z0 + 2*x^37*y*z0^2 + x^37*z0^3 - 2*x^38*z0 - 2*x^36*y*z0^2 + 2*x^34*y*z0^4 - x^37*y + 2*x^37*z0 + x^35*y*z0^2 + x^35*z0^3 + 2*x^33*y*z0^4 - 2*x^36*y + 2*x^36*z0 + 2*x^34*y*z0^2 + 2*x^34*z0^3 + 2*x^35*y + 2*x^33*y*z0^2 - x^33*z0^3 + 2*x^34*y - x^32*y*z0^2 - 2*x^32*z0^3 - 2*x^33*y + 2*x^33*z0 + x^31*y*z0^2 + x^31*z0^3 - x^29*y*z0^4 - x^32*y - 2*x^30*y*z0^2 - 2*x^30*z0^3 + x^28*y*z0^4 - x^31*y + x^31*z0 - x^29*y*z0^2 + x^29*z0^3 + x^27*y*z0^4 - x^30*y - x^30*z0 - x^28*z0^3 + 2*x^26*y*z0^4 - x^29*y - x^29*z0 - 2*x^27*y*z0^2 + 2*x^27*z0^3 + 2*x^25*y*z0^4 + 2*x^28*y - 2*x^28*z0 - x^26*z0^3 + x^27*y + 2*x^27*z0 + 2*x^25*y*z0^2 - 2*x^25*z0^3 - 2*x^26*z0 + x^24*y*z0^2 + 2*x^22*y*z0^4 + x^25*y + 2*x^25*z0 - 2*x^23*y*z0^2 - 2*x^23*z0^3 - 2*x^21*y*z0^4 + x^24*y + x^24*z0 + x^22*y*z0^2 - 2*x^20*y*z0^4 - 2*x^23*y + x^21*y*z0^2 - x^21*z0^3 - x^19*y*z0^4 - x^22*y + x^22*z0 + 2*x^18*y*z0^4 - 2*x^21*y + x^21*z0 + x^19*y^2*z0 - x^19*y*z0^2 + 2*x^19*z0^3 + 2*x^17*y*z0^4 + 2*x^20*y - x^20*z0 - x^18*y*z0^2 - x^18*z0^3 - 2*x^16*y*z0^4 - 2*x^19*z0 + 2*x^17*y*z0^2 - 2*x^17*z0^3 - x^15*y*z0^4 - 2*x^18*y - x^18*z0 + x^16*y*z0^2 + x^14*y*z0^4 - x^17*y + 2*x^17*z0 - x^15*z0^3 - 2*x^13*y*z0^4 - x^16*y + 2*x^16*z0 - 2*x^14*y*z0^2 - x^14*z0^3 + 2*x^12*y*z0^4 - 2*x^15*z0 + x^13*y*z0^2 - 2*x^14*y + 2*x^14*z0 - 2*x^12*y*z0^2 + x^10*y*z0^4 + x^13*y + x^13*z0 + x^11*y*z0^2 + x^9*y*z0^4 - x^12*z0 + x^10*y*z0^2 + 2*x^10*z0^3 + 2*x^8*y*z0^4 + x^11*y - 2*x^11*z0 + 2*x^9*y*z0^2 + x^7*y*z0^4 - 2*x^10*y + 2*x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*y - 2*x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 + x^8*y + x^8*z0 + x^6*y*z0^2 - 2*x^4*y*z0^4 + 2*x^7*y - x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 - 2*x^6*y + x^4*y*z0^2 - 2*x^4*z0^3 + 2*x^2*y*z0^4 + x^5*y + 2*x^5*z0 - 2*x^3*y*z0^2 - x^3*z0^3 + x^4*y + 2*x^4*z0 - 2*x^2*y*z0^2 + x^2*z0^3 + 2*x^3*y - x^3*z0 + x^2*y - x^2*z0)/y) * dx, - ((2*x^61*z0^4 - 2*x^60*z0^4 - 2*x^58*y^2*z0^4 - 2*x^61*z0^2 - x^59*z0^4 + 2*x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 - x^57*y^2*z0^2 + 2*x^57*z0^4 - x^60 + 2*x^58*z0^2 + x^56*z0^4 + x^57*y^2 - x^57*z0^2 + 2*x^55*z0^4 - 2*x^54*z0^4 + x^57 - 2*x^55*z0^2 - x^53*z0^4 + x^54*z0^2 - 2*x^52*z0^4 + 2*x^51*z0^4 - x^54 + 2*x^52*z0^2 + x^50*z0^4 - x^51*z0^2 + 2*x^49*z0^4 - 2*x^48*z0^4 + x^51 - 2*x^49*z0^2 - x^47*z0^4 + x^48*z0^2 - 2*x^46*z0^4 + 2*x^45*z0^4 - x^48 + 2*x^46*z0^2 + x^44*z0^4 - x^45*z0^2 + 2*x^43*z0^4 - 2*x^42*z0^4 + x^45 - 2*x^43*z0^2 + x^41*z0^4 + x^42*z0^2 + x^40*y*z0^3 + x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - x^42 - x^40*y*z0 - 2*x^40*z0^2 - x^38*z0^4 + 2*x^41 - 2*x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 - 2*x^37*z0^4 - x^40 + 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - 2*x^35*y*z0^3 - 2*x^35*z0^4 + 2*x^38 + x^36*y*z0 - x^36*z0^2 + x^34*y*z0^3 - x^37 - x^35*y*z0 - 2*x^35*z0^2 + 2*x^33*y*z0^3 - x^34*y*z0 + x^32*y*z0^3 + 2*x^35 - 2*x^33*z0^2 - 2*x^31*y*z0^3 - 2*x^31*z0^4 + 2*x^34 + 2*x^32*z0^2 + 2*x^30*y*z0^3 - x^30*z0^4 - x^33 + 2*x^31*y*z0 - 2*x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 + 2*x^28*y*z0^3 + 2*x^28*z0^4 - x^29*y*z0 - x^29*z0^2 + 2*x^27*y*z0^3 - 2*x^27*z0^4 - 2*x^30 - x^28*y*z0 + 2*x^26*y*z0^3 + 2*x^26*z0^4 + 2*x^27*y*z0 + x^27*z0^2 + x^25*y*z0^3 + 2*x^28 - 2*x^26*y*z0 + x^26*z0^2 + 2*x^24*y*z0^3 + x^24*z0^4 + 2*x^27 + x^25*y*z0 - 2*x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 + 2*x^26 - 2*x^24*y*z0 + 2*x^24*z0^2 + 2*x^22*y*z0^3 - x^22*z0^4 + 2*x^25 + x^23*y*z0 - 2*x^23*z0^2 - x^21*y*z0^3 - 2*x^22*y*z0 - 2*x^22*z0^2 - x^20*y*z0^3 + 2*x^20*z0^4 + 2*x^21*y*z0 - x^21*z0^2 + x^19*y^2*z0^2 - x^19*y*z0^3 - x^19*z0^4 - x^20*y*z0 + x^20*z0^2 + x^18*y*z0^3 + 2*x^18*z0^4 - 2*x^21 - 2*x^19*y*z0 + x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^19 + 2*x^17*y*z0 + 2*x^17*z0^2 - x^15*y*z0^3 - 2*x^18 + x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 + x^17 - x^15*y*z0 - x^13*y*z0^3 - x^13*z0^4 + x^16 - 2*x^14*y*z0 + x^12*y*z0^3 + x^15 - 2*x^13*y*z0 - x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 - x^10*y*z0^3 - x^10*z0^4 - x^11*y*z0 + 2*x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^12 - x^10*y*z0 + 2*x^8*y*z0^3 + 2*x^8*z0^4 + 2*x^7*y*z0^3 + x^7*z0^4 + 2*x^10 + 2*x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*z0^4 - x^8 + 2*x^6*y*z0 + x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 + 2*x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 - 2*x^2*z0^4 + x^3*y*z0 - x^3*z0^2 + x^2*z0^2 + x^3 - x^2)/y) * dx, - ((-2*x^61*z0^3 + 2*x^58*y^2*z0^3 - 2*x^61*z0 - x^59*z0^3 + x^60*z0 + 2*x^58*y^2*z0 + x^58*z0^3 + x^56*y^2*z0^3 - 2*x^59*z0 - x^57*y^2*z0 + x^55*y^2*z0^3 + 2*x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 - x^57*z0 - x^55*z0^3 + 2*x^56*z0 - 2*x^55*z0 - x^53*z0^3 + x^54*z0 + x^52*z0^3 - 2*x^53*z0 + 2*x^52*z0 + x^50*z0^3 - x^51*z0 - x^49*z0^3 + 2*x^50*z0 - 2*x^49*z0 - x^47*z0^3 + x^48*z0 + x^46*z0^3 - 2*x^47*z0 + 2*x^46*z0 + x^44*z0^3 - x^45*z0 - x^43*z0^3 + 2*x^44*z0 - 2*x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 + x^42*z0 - x^40*y*z0^2 + x^40*z0^3 + x^41*z0 - 2*x^39*y*z0^2 - 2*x^39*z0^3 - x^37*y*z0^4 - x^40*y - 2*x^40*z0 + x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 - 2*x^39*y + 2*x^39*z0 + x^37*y*z0^2 - 2*x^38*y + x^38*z0 - x^36*z0^3 + x^34*y*z0^4 - 2*x^37*y + 2*x^37*z0 + 2*x^35*y*z0^2 - x^35*z0^3 - x^33*y*z0^4 - x^36*y + 2*x^36*z0 - 2*x^34*y*z0^2 - x^34*z0^3 + 2*x^32*y*z0^4 - 2*x^35*y + x^35*z0 + x^33*z0^3 + x^31*y*z0^4 - x^34*z0 + x^32*z0^3 + 2*x^30*y*z0^4 + x^33*y - 2*x^33*z0 + x^31*z0^3 + x^29*y*z0^4 - x^32*y + x^32*z0 - x^30*z0^3 - 2*x^31*y + x^31*z0 + x^29*y*z0^2 - 2*x^27*y*z0^4 + 2*x^30*y + 2*x^30*z0 + x^28*y*z0^2 - x^28*z0^3 - 2*x^26*y*z0^4 + 2*x^29*z0 + x^28*y - x^28*z0 + x^26*y*z0^2 - x^26*z0^3 - 2*x^24*y*z0^4 + 2*x^27*y + x^27*z0 + x^25*y*z0^2 + 2*x^25*z0^3 + x^23*y*z0^4 + x^26*y - x^26*z0 - 2*x^24*y*z0^2 - x^25*y + 2*x^23*y*z0^2 + 2*x^23*z0^3 + x^24*y - x^24*z0 - 2*x^22*y*z0^2 - 2*x^22*z0^3 - 2*x^20*y*z0^4 - x^23*z0 + x^21*y*z0^2 - x^21*z0^3 + x^19*y^2*z0^3 - 2*x^19*y*z0^4 + 2*x^22*y - x^22*z0 + x^20*z0^3 + x^18*y*z0^4 + 2*x^21*y - 2*x^21*z0 + x^19*y*z0^2 + 2*x^19*z0^3 + x^17*y*z0^4 + x^20*y + 2*x^20*z0 + x^18*z0^3 - 2*x^16*y*z0^4 - x^19*y + x^17*y*z0^2 + x^17*z0^3 + x^15*y*z0^4 + x^18*y + 2*x^18*z0 + 2*x^16*z0^3 + x^14*y*z0^4 + 2*x^15*y*z0^2 - 2*x^15*z0^3 - 2*x^16*y - x^14*z0^3 - 2*x^12*y*z0^4 + x^15*y + x^13*y*z0^2 + x^13*z0^3 + 2*x^11*y*z0^4 - 2*x^14*z0 + x^12*y*z0^2 - x^12*z0^3 - x^13*y - x^13*z0 + 2*x^11*y*z0^2 - 2*x^11*z0^3 - 2*x^9*y*z0^4 + x^10*y*z0^2 - x^8*y*z0^4 + x^11*y - x^11*z0 + 2*x^9*y*z0^2 + 2*x^7*y*z0^4 + 2*x^10*y + 2*x^10*z0 - x^8*z0^3 + x^6*y*z0^4 - x^9*z0 + x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 + 2*x^8*y + x^8*z0 - 2*x^6*y*z0^2 + 2*x^6*z0^3 - x^4*y*z0^4 - x^7*y - 2*x^5*y*z0^2 - x^5*z0^3 - x^3*y*z0^4 + 2*x^6*z0 - 2*x^4*y*z0^2 + x^5*y - 2*x^3*z0^3 - 2*x^4*y + x^4*z0 - x^2*y*z0^2 + 2*x^2*z0^3 + x^3*y + 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-x^60*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^56*y^2*z0^4 - x^57*y^2*z0^2 + x^57*z0^4 - 2*x^60 + 2*x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 - x^57*z0^2 - x^54*z0^4 + 2*x^57 - 2*x^55*z0^2 + 2*x^53*z0^4 + x^54*z0^2 + x^51*z0^4 - 2*x^54 + 2*x^52*z0^2 - 2*x^50*z0^4 - x^51*z0^2 - x^48*z0^4 + 2*x^51 - 2*x^49*z0^2 + 2*x^47*z0^4 + x^48*z0^2 + x^45*z0^4 - 2*x^48 + 2*x^46*z0^2 - 2*x^44*z0^4 - x^45*z0^2 - x^42*z0^4 + 2*x^45 - 2*x^43*z0^2 + 2*x^41*z0^4 + x^42*z0^2 - x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - 2*x^42 - x^40*y*z0 + x^40*z0^2 + x^38*y*z0^3 + 2*x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 - x^40 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 - x^35*z0^4 - x^38 + 2*x^36*y*z0 - x^36*z0^2 + x^34*y*z0^3 + 2*x^34*z0^4 + x^37 - 2*x^35*y*z0 + x^35*z0^2 - x^33*y*z0^3 - 2*x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 + x^34*z0^2 - 2*x^32*y*z0^3 - x^35 + 2*x^33*y*z0 + 2*x^33*z0^2 + x^31*y*z0^3 + x^31*z0^4 - 2*x^34 + x^32*z0^2 - x^30*y*z0^3 + 2*x^30*z0^4 + x^33 - x^31*y*z0 - x^31*z0^2 + x^29*z0^4 + x^30*y*z0 - 2*x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^29*y*z0 + x^29*z0^2 + x^30 + 2*x^28*y*z0 - x^28*z0^2 + x^26*y*z0^3 - 2*x^26*z0^4 - x^27*y*z0 - 2*x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 - x^28 + 2*x^24*y*z0^3 - 2*x^24*z0^4 - x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + x^24*y*z0 - x^24*z0^2 - 2*x^22*y*z0^3 - x^22*z0^4 + 2*x^25 - x^23*y*z0 + x^23*z0^2 - x^21*y*z0^3 + x^21*z0^4 + x^19*y^2*z0^4 + 2*x^24 + x^22*y*z0 - x^20*y*z0^3 + x^20*z0^4 - x^23 - x^21*y*z0 + x^21*z0^2 - x^19*y*z0^3 - 2*x^22 - x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 + x^18*z0^4 + x^21 - x^19*y*z0 + 2*x^20 - x^18*y*z0 - x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^16*z0^4 + x^19 + x^17*y*z0 - x^15*y*z0^3 - 2*x^15*z0^4 + x^18 + 2*x^16*y*z0 + 2*x^16*z0^2 - 2*x^14*z0^4 + 2*x^15*y*z0 - 2*x^15*z0^2 - 2*x^13*y*z0^3 - x^13*z0^4 - x^16 + x^14*z0^2 + x^12*y*z0^3 + 2*x^12*z0^4 + 2*x^13*y*z0 - 2*x^13*z0^2 - x^11*y*z0^3 - 2*x^11*z0^4 + x^14 + x^12*y*z0 - x^10*y*z0^3 + 2*x^10*z0^4 - 2*x^13 - 2*x^11*y*z0 + 2*x^11*z0^2 + x^12 + x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^11 + x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 - x^8*y*z0 - x^8*z0^2 + x^6*y*z0^3 - 2*x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 + x^4*y*z0^3 - x^4*z0^4 - 2*x^5*y*z0 - x^3*y*z0^3 + x^3*z0^4 + 2*x^6 - 2*x^4*y*z0 - x^4*z0^2 + 2*x^2*z0^4 + 2*x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^23 + x^20*y^2 + x^20 - x^17 + x^14 - x^11 + x^8 - x^5 + x^2)/y) * dx, - ((-x^23*z0 + x^20*y^2*z0 + x^20*z0 - x^17*z0 + x^14*z0 - x^11*z0 + x^8*z0 - x^5*z0 + x^2*z0)/y) * dx, - ((-x^23*z0^2 + x^20*y^2*z0^2 + x^20*z0^2 - x^17*z0^2 + x^14*z0^2 - x^11*z0^2 + x^8*z0^2 - x^5*z0^2 + x^2*z0^2)/y) * dx, - ((-x^23*z0^3 + x^20*y^2*z0^3 + x^20*z0^3 - x^17*z0^3 + x^14*z0^3 - x^11*z0^3 + x^8*z0^3 - x^5*z0^3 + x^2*z0^3)/y) * dx, - ((-x^23*z0^4 + x^20*y^2*z0^4 + x^20*z0^4 - x^17*z0^4 + x^14*z0^4 - x^11*z0^4 + x^8*z0^4 - x^5*z0^4 + x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^4 + x^60*z0^4 - x^58*y^2*z0^4 - x^59*z0^4 - x^57*y^2*z0^4 + 2*x^60*z0^2 - x^58*z0^4 + x^56*y^2*z0^4 + 2*x^61 - 2*x^57*y^2*z0^2 - x^57*z0^4 - 2*x^58*y^2 + x^56*z0^4 - 2*x^57*z0^2 + x^55*z0^4 - 2*x^58 + x^54*z0^4 - x^53*z0^4 + 2*x^54*z0^2 - x^52*z0^4 + 2*x^55 - x^51*z0^4 + x^50*z0^4 - 2*x^51*z0^2 + x^49*z0^4 - 2*x^52 + x^48*z0^4 - x^47*z0^4 + 2*x^48*z0^2 - x^46*z0^4 + 2*x^49 - x^45*z0^4 + x^44*z0^4 - 2*x^45*z0^2 + x^43*z0^4 - 2*x^46 + x^42*z0^4 + x^41*z0^4 + 2*x^42*z0^2 - 2*x^40*y*z0^3 + 2*x^43 - x^39*z0^4 + 2*x^40*z0^2 - x^38*z0^4 + 2*x^41 + 2*x^39*y*z0 - 2*x^39*z0^2 + x^37*y*z0^3 + 2*x^37*z0^4 + 2*x^40 + x^38*y*z0 - 2*x^36*z0^4 - 2*x^39 - x^37*y*z0 - 2*x^37*z0^2 - x^35*y*z0^3 + 2*x^38 + 2*x^36*y*z0 + 2*x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^35*y*z0 - x^35*z0^2 + x^33*y*z0^3 + x^33*z0^4 - x^36 - x^34*y*z0 - 2*x^32*y*z0^3 + x^35 + x^33*z0^2 + x^31*y*z0^3 - 2*x^31*z0^4 - 2*x^32*y*z0 - x^32*z0^2 - x^30*y*z0^3 + 2*x^30*z0^4 - 2*x^33 - 2*x^31*y*z0 - 2*x^29*y*z0^3 - 2*x^29*z0^4 + x^30*y*z0 - x^30*z0^2 - 2*x^28*y*z0^3 + x^28*z0^4 - x^31 - x^29*y*z0 - 2*x^29*z0^2 + x^27*y*z0^3 + 2*x^27*z0^4 + 2*x^30 - 2*x^28*y*z0 - x^26*y*z0^3 - x^26*z0^4 + x^27*y*z0 + x^25*z0^4 - x^28 - x^26*y*z0 - 2*x^26*z0^2 - x^24*y*z0^3 - x^24*z0^4 + 2*x^27 + x^25*y*z0 - x^25*z0^2 - 2*x^23*y*z0^3 - x^23*z0^4 + x^24*y*z0 - x^22*y*z0^3 - 2*x^22*z0^4 + x^23*y*z0 - x^23*z0^2 - x^21*y*z0^3 + x^21*z0^4 + x^24 - x^22*z0^2 + 2*x^20*y*z0^3 - 2*x^20*z0^4 + x^21*y^2 - x^21*y*z0 + 2*x^21*z0^2 + 2*x^19*y*z0^3 + x^19*z0^4 - x^22 - x^20*z0^2 + 2*x^18*z0^4 - x^21 + 2*x^19*z0^2 - 2*x^17*y*z0^3 + x^17*z0^4 - x^20 - 2*x^18*y*z0 + x^18*z0^2 + 2*x^16*y*z0^3 + x^17*z0^2 + x^15*y*z0^3 + x^15*z0^4 + 2*x^18 + 2*x^16*y*z0 - 2*x^14*z0^4 + 2*x^17 - 2*x^15*z0^2 + x^13*y*z0^3 - x^13*z0^4 + 2*x^16 + 2*x^14*y*z0 + 2*x^12*y*z0^3 + 2*x^12*z0^4 + x^15 - 2*x^13*y*z0 + x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 - 2*x^14 + x^12*y*z0 - x^12*z0^2 - 2*x^10*y*z0^3 + x^10*z0^4 - x^13 + x^11*y*z0 - 2*x^11*z0^2 - x^9*y*z0^3 + 2*x^9*z0^4 + x^12 - x^10*y*z0 - x^8*y*z0^3 - 2*x^8*z0^4 - x^11 - x^9*y*z0 + 2*x^9*z0^2 + 2*x^7*y*z0^3 + x^10 - 2*x^8*y*z0 + x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 - x^9 - 2*x^7*y*z0 - x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 + 2*x^8 - 2*x^4*y*z0^3 - x^7 + x^5*y*z0 - 2*x^3*y*z0^3 - 2*x^6 - x^4*y*z0 + 2*x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - x^3*y*z0 + x^3*z0^2 - x^2*y*z0 + 2*x^2*z0^2 - x^3 - x^2)/y) * dx, - ((-x^61*z0^3 - 2*x^60*z0^3 + x^58*y^2*z0^3 + 2*x^61*z0 + 2*x^59*z0^3 + 2*x^57*y^2*z0^3 - 2*x^58*y^2*z0 - 2*x^58*z0^3 - 2*x^56*y^2*z0^3 + 2*x^59*z0 + x^57*z0^3 - 2*x^55*y^2*z0^3 - 2*x^58*z0 - 2*x^56*y^2*z0 - 2*x^56*z0^3 + x^54*y^2*z0^3 + 2*x^55*z0^3 - 2*x^56*z0 - x^54*z0^3 + 2*x^55*z0 + 2*x^53*z0^3 - 2*x^52*z0^3 + 2*x^53*z0 + x^51*z0^3 - 2*x^52*z0 - 2*x^50*z0^3 + 2*x^49*z0^3 - 2*x^50*z0 - x^48*z0^3 + 2*x^49*z0 + 2*x^47*z0^3 - 2*x^46*z0^3 + 2*x^47*z0 + x^45*z0^3 - 2*x^46*z0 - 2*x^44*z0^3 + 2*x^43*z0^3 - 2*x^44*z0 - x^42*z0^3 + 2*x^43*z0 + x^41*z0^3 - x^39*y*z0^4 + 2*x^40*y*z0^2 - 2*x^40*z0^3 - x^38*y*z0^4 - x^41*z0 + 2*x^39*y*z0^2 - 2*x^39*z0^3 + x^40*y + 2*x^40*z0 + 2*x^38*y*z0^2 - 2*x^38*z0^3 + x^36*y*z0^4 - 2*x^39*y + 2*x^39*z0 + 2*x^37*y*z0^2 + x^37*z0^3 - x^35*y*z0^4 - x^38*z0 - 2*x^36*z0^3 + 2*x^34*y*z0^4 + 2*x^37*y + x^37*z0 + x^35*y*z0^2 - x^35*z0^3 - 2*x^33*y*z0^4 + x^36*y - x^36*z0 - 2*x^34*y*z0^2 + 2*x^32*y*z0^4 - 2*x^35*y + x^35*z0 - x^33*y*z0^2 - 2*x^34*y + 2*x^32*y*z0^2 - x^32*z0^3 - x^33*y - 2*x^31*z0^3 - x^29*y*z0^4 - x^32*y + x^32*z0 + x^30*y*z0^2 - x^31*y - x^31*z0 - x^29*y*z0^2 - x^29*z0^3 + 2*x^27*y*z0^4 + 2*x^30*y + x^30*z0 - x^28*y*z0^2 - x^28*z0^3 + x^26*y*z0^4 + 2*x^29*y + 2*x^27*y*z0^2 - x^27*z0^3 - x^25*y*z0^4 + x^28*y - 2*x^28*z0 - 2*x^26*z0^3 + 2*x^24*y*z0^4 + 2*x^27*y + x^27*z0 - x^25*y*z0^2 - x^25*z0^3 - 2*x^26*y + x^26*z0 - x^24*y*z0^2 - x^24*z0^3 + 2*x^22*y*z0^4 - x^25*y - 2*x^25*z0 - 2*x^23*y*z0^2 + 2*x^23*z0^3 - 2*x^21*y*z0^4 - 2*x^24*y + 2*x^22*z0^3 + x^20*y*z0^4 - 2*x^23*y - 2*x^23*z0 + x^21*y^2*z0 - x^21*y*z0^2 - 2*x^21*z0^3 - x^19*y*z0^4 - x^22*y + x^22*z0 - x^20*y*z0^2 + x^20*z0^3 - x^18*y*z0^4 - 2*x^21*y - 2*x^21*z0 - x^19*z0^3 + x^17*y*z0^4 + x^20*y - x^18*y*z0^2 - 2*x^16*y*z0^4 + 2*x^19*z0 + x^17*y*z0^2 - 2*x^17*z0^3 - x^15*y*z0^4 + 2*x^18*y - 2*x^16*y*z0^2 - x^16*z0^3 + 2*x^14*y*z0^4 - x^17*y - 2*x^17*z0 + x^15*y*z0^2 + x^15*z0^3 + x^13*y*z0^4 + x^14*y*z0^2 + 2*x^14*z0^3 + x^15*y + x^15*z0 - x^13*y*z0^2 - 2*x^13*z0^3 - 2*x^11*y*z0^4 + 2*x^14*y + x^14*z0 - 2*x^12*y*z0^2 - 2*x^10*y*z0^4 + 2*x^13*y - 2*x^13*z0 - 2*x^11*z0^3 - 2*x^9*y*z0^4 + 2*x^12*z0 + x^10*y*z0^2 - 2*x^8*y*z0^4 - 2*x^11*z0 + 2*x^9*y*z0^2 + 2*x^7*y*z0^4 + x^10*y + 2*x^8*y*z0^2 + 2*x^6*y*z0^4 + 2*x^9*y - 2*x^9*z0 + x^7*y*z0^2 + x^7*z0^3 + x^5*y*z0^4 + 2*x^8*y - x^8*z0 + 2*x^6*y*z0^2 + 2*x^6*z0^3 + 2*x^4*y*z0^4 - 2*x^7*y + x^7*z0 + x^5*z0^3 + 2*x^3*y*z0^4 + 2*x^6*y + 2*x^6*z0 - 2*x^4*y*z0^2 - x^5*y - 2*x^5*z0 + x^3*y*z0^2 - x^3*z0^3 - 2*x^4*z0 - x^2*z0^3 - 2*x^3*y - 2*x^3*z0 + 2*x^2*y - x^2*z0)/y) * dx, - ((x^61*z0^4 + x^60*z0^4 - x^58*y^2*z0^4 - 2*x^61*z0^2 - 2*x^59*z0^4 - x^57*y^2*z0^4 - x^60*z0^2 + 2*x^58*y^2*z0^2 - x^58*z0^4 + 2*x^56*y^2*z0^4 + x^57*y^2*z0^2 - x^57*z0^4 + x^60 + 2*x^58*z0^2 + 2*x^56*z0^4 - x^57*y^2 + x^57*z0^2 + x^55*z0^4 + x^54*z0^4 - x^57 - 2*x^55*z0^2 - 2*x^53*z0^4 - x^54*z0^2 - x^52*z0^4 - x^51*z0^4 + x^54 + 2*x^52*z0^2 + 2*x^50*z0^4 + x^51*z0^2 + x^49*z0^4 + x^48*z0^4 - x^51 - 2*x^49*z0^2 - 2*x^47*z0^4 - x^48*z0^2 - x^46*z0^4 - x^45*z0^4 + x^48 + 2*x^46*z0^2 + 2*x^44*z0^4 + x^45*z0^2 + x^43*z0^4 + x^42*z0^4 - x^45 - 2*x^43*z0^2 - x^41*z0^4 - x^42*z0^2 - 2*x^40*y*z0^3 - x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 + x^42 - x^40*y*z0 - 2*x^40*z0^2 - x^38*y*z0^3 + 2*x^38*z0^4 + x^41 - 2*x^39*z0^2 - 2*x^40 + x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 + 2*x^37*z0^2 + 2*x^35*y*z0^3 + 2*x^35*z0^4 - 2*x^38 - x^36*y*z0 + 2*x^36*z0^2 - x^34*y*z0^3 - 2*x^34*z0^4 - x^37 - 2*x^35*z0^2 - 2*x^33*y*z0^3 - 2*x^33*z0^4 + x^36 + x^34*y*z0 + 2*x^34*z0^2 + 2*x^32*y*z0^3 - 2*x^32*z0^4 + 2*x^35 + 2*x^33*y*z0 - x^33*z0^2 + x^31*y*z0^3 - 2*x^32*y*z0 + x^31*y*z0 + x^31*z0^2 + x^29*y*z0^3 - x^29*z0^4 + x^32 + 2*x^30*y*z0 + x^30*z0^2 - 2*x^31 - x^29*y*z0 + 2*x^29*z0^2 - 2*x^27*y*z0^3 + x^27*z0^4 - x^30 - 2*x^28*y*z0 - x^28*z0^2 + 2*x^26*y*z0^3 + 2*x^27*y*z0 + 2*x^25*y*z0^3 + 2*x^25*z0^4 - x^28 - x^26*y*z0 - 2*x^24*y*z0^3 + x^24*z0^4 - x^25*y*z0 + x^25*z0^2 + x^23*y*z0^3 + 2*x^24*y*z0 + x^24*z0^2 + 2*x^22*z0^4 + 2*x^25 + x^21*y^2*z0^2 - x^21*y*z0^3 + 2*x^21*z0^4 - 2*x^24 + x^22*y*z0 + x^22*z0^2 - 2*x^20*y*z0^3 - x^20*z0^4 + 2*x^21*y*z0 - 2*x^21*z0^2 + x^19*y*z0^3 + 2*x^19*z0^4 + 2*x^22 - x^20*y*z0 + x^20*z0^2 - x^18*z0^4 - x^21 + x^19*y*z0 + 2*x^19*z0^2 + 2*x^17*y*z0^3 - x^17*z0^4 - 2*x^18*y*z0 - 2*x^18*z0^2 - x^16*y*z0^3 + x^16*z0^4 + 2*x^19 + 2*x^17*y*z0 + x^17*z0^2 - 2*x^15*y*z0^3 + x^15*z0^4 + 2*x^18 - x^16*y*z0 + 2*x^16*z0^2 + 2*x^14*y*z0^3 + 2*x^14*z0^4 - x^17 - x^15*y*z0 - x^15*z0^2 - x^13*y*z0^3 - x^13*z0^4 + x^16 - x^14*z0^2 + 2*x^12*y*z0^3 - 2*x^12*z0^4 + x^15 + 2*x^13*z0^2 - x^11*z0^4 + x^14 - x^12*y*z0 + 2*x^12*z0^2 - x^10*y*z0^3 + x^10*z0^4 - 2*x^13 - 2*x^11*y*z0 + x^11*z0^2 - 2*x^9*y*z0^3 - x^9*z0^4 + 2*x^12 + x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 + 2*x^11 + x^9*y*z0 + x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 + 2*x^8*y*z0 - x^8*z0^2 + 2*x^6*y*z0^3 + x^6*z0^4 + 2*x^9 - x^7*y*z0 + x^7*z0^2 + 2*x^5*y*z0^3 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + x^4*z0^4 - x^7 - 2*x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*y*z0^3 + x^3*z0^4 + x^6 + x^4*y*z0 + 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 - x^2)/y) * dx, - ((x^61*z0^3 + x^60*z0^3 - x^58*y^2*z0^3 - x^61*z0 - 2*x^59*z0^3 - x^57*y^2*z0^3 - x^60*z0 + x^58*y^2*z0 + 2*x^58*z0^3 + 2*x^56*y^2*z0^3 + x^59*z0 + x^57*y^2*z0 + 2*x^57*z0^3 + 2*x^55*y^2*z0^3 + x^58*z0 - x^56*y^2*z0 + 2*x^56*z0^3 + 2*x^54*y^2*z0^3 + x^57*z0 - 2*x^55*z0^3 - x^56*z0 - 2*x^54*z0^3 - x^55*z0 - 2*x^53*z0^3 - x^54*z0 + 2*x^52*z0^3 + x^53*z0 + 2*x^51*z0^3 + x^52*z0 + 2*x^50*z0^3 + x^51*z0 - 2*x^49*z0^3 - x^50*z0 - 2*x^48*z0^3 - x^49*z0 - 2*x^47*z0^3 - x^48*z0 + 2*x^46*z0^3 + x^47*z0 + 2*x^45*z0^3 + x^46*z0 + 2*x^44*z0^3 + x^45*z0 - 2*x^43*z0^3 - x^44*z0 - 2*x^42*z0^3 - x^43*z0 - x^41*z0^3 + x^39*y*z0^4 - x^42*z0 - 2*x^40*y*z0^2 - 2*x^40*z0^3 - x^39*y*z0^2 - 2*x^39*z0^3 + 2*x^40*y + 2*x^40*z0 + x^38*y*z0^2 + 2*x^38*z0^3 - x^36*y*z0^4 - x^39*y - x^39*z0 - x^37*z0^3 - 2*x^35*y*z0^4 + 2*x^38*y - 2*x^38*z0 - x^36*y*z0^2 + x^36*z0^3 - x^37*y + x^37*z0 + x^35*y*z0^2 - 2*x^35*z0^3 - x^33*y*z0^4 + x^36*y - x^36*z0 - 2*x^34*y*z0^2 - x^34*z0^3 - 2*x^35*y - x^35*z0 + x^33*y*z0^2 + 2*x^33*z0^3 + x^34*y + 2*x^34*z0 + 2*x^32*y*z0^2 - 2*x^32*z0^3 - x^30*y*z0^4 - 2*x^33*z0 - 2*x^31*y*z0^2 + 2*x^29*y*z0^4 - 2*x^32*y - x^30*y*z0^2 + 2*x^28*y*z0^4 - 2*x^31*y + x^31*z0 + x^29*y*z0^2 - 2*x^29*z0^3 + 2*x^27*y*z0^4 - 2*x^30*y + 2*x^28*y*z0^2 + x^28*z0^3 + x^26*y*z0^4 + x^29*y - x^29*z0 - x^27*y*z0^2 + 2*x^27*z0^3 - 2*x^25*y*z0^4 + 2*x^28*y + x^28*z0 + 2*x^26*y*z0^2 - 2*x^26*z0^3 + 2*x^24*y*z0^4 + x^27*y + 2*x^27*z0 - x^25*y*z0^2 + x^25*z0^3 + x^26*y - 2*x^24*z0^3 + x^25*y + x^25*z0 - x^23*z0^3 + x^21*y^2*z0^3 + x^21*y*z0^4 + 2*x^24*y - x^24*z0 - x^22*y*z0^2 - 2*x^22*z0^3 - 2*x^23*z0 + 2*x^21*y*z0^2 - x^22*y + x^22*z0 - 2*x^20*y*z0^2 + 2*x^20*z0^3 + x^18*y*z0^4 + 2*x^21*y + 2*x^19*y*z0^2 + 2*x^19*z0^3 - 2*x^17*y*z0^4 - x^20*y + x^20*z0 + 2*x^18*y*z0^2 + 2*x^18*z0^3 + 2*x^16*y*z0^4 - 2*x^19*y - 2*x^19*z0 - x^17*y*z0^2 + 2*x^15*y*z0^4 + x^16*y*z0^2 + 2*x^16*z0^3 - 2*x^17*y + x^15*y*z0^2 + 2*x^15*z0^3 + 2*x^13*y*z0^4 + 2*x^16*y + x^16*z0 - x^14*y*z0^2 - 2*x^14*z0^3 - x^12*y*z0^4 - x^15*y + 2*x^13*y*z0^2 - x^13*z0^3 + x^11*y*z0^4 - x^14*z0 + x^12*y*z0^2 + 2*x^12*z0^3 + x^13*y - x^13*z0 + x^11*y*z0^2 - 2*x^9*y*z0^4 + x^12*y + x^12*z0 - x^10*z0^3 - 2*x^8*y*z0^4 + x^11*y + 2*x^11*z0 + 2*x^9*y*z0^2 + x^10*y + x^10*z0 - x^8*z0^3 - 2*x^9*y - 2*x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 - x^8*y + 2*x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^4*y*z0^4 + x^7*y - x^5*y*z0^2 + 2*x^5*z0^3 + x^3*y*z0^4 + 2*x^6*y + 2*x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 + 2*x^5*y + 2*x^5*z0 + 2*x^3*y*z0^2 + x^3*z0^3 + x^4*y - 2*x^4*z0 - x^2*y*z0^2 + 2*x^2*z0^3 - 2*x^3*y - x^2*z0)/y) * dx, - ((-x^61*z0^4 + 2*x^60*z0^4 + x^58*y^2*z0^4 - x^59*z0^4 - 2*x^57*y^2*z0^4 + 2*x^60*z0^2 + x^58*z0^4 + x^56*y^2*z0^4 - 2*x^57*y^2*z0^2 - 2*x^57*z0^4 + x^60 + x^56*z0^4 - x^57*y^2 - 2*x^57*z0^2 - x^55*z0^4 + 2*x^54*z0^4 - x^57 - x^53*z0^4 + 2*x^54*z0^2 + x^52*z0^4 - 2*x^51*z0^4 + x^54 + x^50*z0^4 - 2*x^51*z0^2 - x^49*z0^4 + 2*x^48*z0^4 - x^51 - x^47*z0^4 + 2*x^48*z0^2 + x^46*z0^4 - 2*x^45*z0^4 + x^48 + x^44*z0^4 - 2*x^45*z0^2 - x^43*z0^4 + 2*x^42*z0^4 - x^45 - 2*x^41*z0^4 + 2*x^42*z0^2 + 2*x^40*y*z0^3 - 2*x^40*z0^4 - x^39*z0^4 + x^42 - x^40*z0^2 - x^38*y*z0^3 - 2*x^38*z0^4 - x^41 - x^39*y*z0 - 2*x^39*z0^2 - x^37*y*z0^3 - x^37*z0^4 + 2*x^40 + 2*x^36*z0^4 + x^39 + x^37*y*z0 - x^37*z0^2 + 2*x^35*y*z0^3 + x^38 + x^36*y*z0 + 2*x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^34*z0^4 + 2*x^35*y*z0 + x^35*z0^2 + x^33*y*z0^3 - x^33*z0^4 - 2*x^36 - 2*x^34*y*z0 + x^34*z0^2 + 2*x^32*y*z0^3 - x^32*z0^4 + x^33*y*z0 + 2*x^33*z0^2 - x^31*y*z0^3 - 2*x^31*z0^4 - x^32*y*z0 + 2*x^30*y*z0^3 - x^30*z0^4 + 2*x^33 + x^31*y*z0 + x^29*y*z0^3 + 2*x^29*z0^4 - x^32 + 2*x^30*z0^2 - x^28*y*z0^3 - x^28*z0^4 - 2*x^31 + 2*x^29*y*z0 + 2*x^29*z0^2 + x^27*z0^4 - 2*x^28*y*z0 + x^28*z0^2 + x^26*y*z0^3 - x^26*z0^4 + 2*x^29 - 2*x^27*y*z0 + 2*x^27*z0^2 - 2*x^25*z0^4 + x^28 - x^24*y*z0^3 + 2*x^25*y*z0 - x^25*z0^2 + x^23*y*z0^3 - x^23*z0^4 + x^21*y^2*z0^4 + 2*x^26 + 2*x^24*z0^2 - 2*x^22*y*z0^3 - 2*x^22*z0^4 + x^25 - 2*x^23*y*z0 - x^23*z0^2 + x^21*y*z0^3 + 2*x^21*z0^4 + 2*x^22*y*z0 - 2*x^22*z0^2 + 2*x^20*z0^4 + x^23 + 2*x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 + x^19*z0^4 + 2*x^22 + x^20*y*z0 - x^20*z0^2 + x^18*y*z0^3 + x^18*z0^4 + 2*x^21 - x^19*z0^2 - 2*x^17*y*z0^3 - 2*x^17*z0^4 - 2*x^18*y*z0 - 2*x^18*z0^2 - x^16*y*z0^3 - 2*x^16*z0^4 + 2*x^19 - x^17*y*z0 + x^15*y*z0^3 + x^15*z0^4 + x^18 - 2*x^16*y*z0 - x^16*z0^2 - 2*x^14*y*z0^3 + x^17 - x^15*y*z0 + x^15*z0^2 + 2*x^13*z0^4 + x^16 - 2*x^14*y*z0 + x^14*z0^2 + x^12*y*z0^3 + 2*x^12*z0^4 + 2*x^15 - 2*x^13*y*z0 - x^11*y*z0^3 - 2*x^11*z0^4 + 2*x^14 - x^12*y*z0 + 2*x^12*z0^2 + 2*x^10*y*z0^3 + 2*x^10*z0^4 + 2*x^11*y*z0 - 2*x^11*z0^2 - 2*x^9*y*z0^3 - x^9*z0^4 - x^12 + 2*x^10*y*z0 + 2*x^10*z0^2 + 2*x^8*z0^4 - 2*x^9*y*z0 + x^7*y*z0^3 + x^7*z0^4 - 2*x^10 + 2*x^8*y*z0 + 2*x^8*z0^2 - x^6*y*z0^3 + 2*x^6*z0^4 - x^9 - 2*x^7*y*z0 - x^7*z0^2 + x^5*y*z0^3 - x^8 + 2*x^4*y*z0^3 - x^4*z0^4 - x^7 - x^5*y*z0 + x^5*z0^2 - x^3*y*z0^3 - x^3*z0^4 + x^6 + x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 - x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 + x^60*z0^4 + x^58*y^2*z0^4 - x^61*z0^2 - x^59*z0^4 - x^57*y^2*z0^4 - x^60*z0^2 + x^58*y^2*z0^2 + x^58*z0^4 + x^56*y^2*z0^4 + x^57*y^2*z0^2 - x^57*z0^4 + x^60 + x^58*z0^2 + x^56*z0^4 - x^57*y^2 + x^57*z0^2 - x^55*z0^4 + x^54*z0^4 - x^57 - x^55*z0^2 - x^53*z0^4 - x^54*z0^2 + x^52*z0^4 - x^51*z0^4 + x^54 + x^52*z0^2 + x^50*z0^4 + x^51*z0^2 - x^49*z0^4 + x^48*z0^4 - x^51 - x^49*z0^2 - x^47*z0^4 - x^48*z0^2 + x^46*z0^4 - x^45*z0^4 + x^48 + x^46*z0^2 + x^44*z0^4 + x^45*z0^2 - x^43*z0^4 + x^42*z0^4 - x^45 - x^43*z0^2 - 2*x^41*z0^4 - x^42*z0^2 + 2*x^40*y*z0^3 + x^40*z0^4 - x^41*z0^2 - x^39*y*z0^3 + x^42 + 2*x^40*y*z0 - 2*x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + x^39*y*z0 + 2*x^39*z0^2 - x^37*z0^4 + 2*x^40 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + x^36*z0^4 - x^39 - 2*x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 + 2*x^35*z0^4 + x^38 - x^36*y*z0 - 2*x^36*z0^2 - x^34*y*z0^3 - 2*x^34*z0^4 - 2*x^37 - 2*x^35*y*z0 - x^35*z0^2 - x^33*y*z0^3 + 2*x^33*z0^4 - x^36 - 2*x^34*z0^2 - 2*x^32*y*z0^3 - 2*x^32*z0^4 + x^35 + x^33*y*z0 + x^33*z0^2 + x^31*y*z0^3 - x^31*z0^4 - 2*x^34 - 2*x^32*y*z0 + x^32*z0^2 - 2*x^30*y*z0^3 - 2*x^33 - x^29*y*z0^3 + 2*x^29*z0^4 + x^30*y*z0 - x^28*y*z0^3 - x^28*z0^4 + x^31 + x^29*y*z0 + x^29*z0^2 + x^27*y*z0^3 - x^27*z0^4 - 2*x^28*z0^2 - x^26*z0^4 - x^29 + x^27*y*z0 - 2*x^27*z0^2 - 2*x^25*y*z0^3 - x^25*z0^4 - 2*x^28 + 2*x^26*y*z0 + x^26*z0^2 - 2*x^24*y*z0^3 - 2*x^24*z0^4 + x^27 - 2*x^25*y*z0 + x^25*z0^2 + x^23*y*z0^3 + 2*x^23*z0^4 - 2*x^26 - 2*x^24*y*z0 + 2*x^22*y*z0^3 - 2*x^22*z0^4 + 2*x^23*y*z0 + 2*x^23*z0^2 + x^21*y*z0^3 + 2*x^24 + x^22*y^2 - 2*x^22*y*z0 + x^22*z0^2 - x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^23 + x^21*y*z0 - 2*x^21*z0^2 + 2*x^19*y*z0^3 - x^19*z0^4 - x^20*y*z0 + 2*x^20*z0^2 + 2*x^18*y*z0^3 + 2*x^18*z0^4 + 2*x^19*y*z0 + x^17*y*z0^3 + 2*x^20 - 2*x^18*y*z0 + 2*x^18*z0^2 + x^16*y*z0^3 - 2*x^16*z0^4 - 2*x^17*y*z0 - 2*x^17*z0^2 + 2*x^15*z0^4 + 2*x^18 + 2*x^16*y*z0 - 2*x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 - x^17 - x^15*z0^2 + 2*x^13*y*z0^3 - x^13*z0^4 - 2*x^16 + 2*x^14*y*z0 + 2*x^14*z0^2 - x^12*y*z0^3 - x^12*z0^4 - x^15 - x^13*y*z0 + 2*x^13*z0^2 - 2*x^11*z0^4 - 2*x^14 - 2*x^12*y*z0 + x^12*z0^2 + 2*x^10*z0^4 - 2*x^13 + x^11*y*z0 - 2*x^11*z0^2 - 2*x^9*y*z0^3 - 2*x^9*z0^4 - x^12 + 2*x^10*y*z0 + x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 + x^9*y*z0 + x^9*z0^2 + 2*x^7*y*z0^3 + x^7*z0^4 + 2*x^8*y*z0 + 2*x^6*y*z0^3 - x^6*z0^4 + x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + x^8 - x^6*y*z0 + 2*x^6*z0^2 + x^4*y*z0^3 + x^7 - 2*x^5*y*z0 + x^3*y*z0^3 - x^3*z0^4 - x^6 - 2*x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 - x^3*z0^2 - x^2*y*z0 - x^2*z0^2 + 2*x^3)/y) * dx, - ((-2*x^60*z0^3 + 2*x^61*z0 + 2*x^57*y^2*z0^3 + x^60*z0 - 2*x^58*y^2*z0 + x^59*z0 - x^57*y^2*z0 - 2*x^58*z0 - x^56*y^2*z0 + 2*x^54*y^2*z0^3 - x^57*z0 - x^56*z0 + 2*x^55*z0 + x^54*z0 + x^53*z0 - 2*x^52*z0 - x^51*z0 - x^50*z0 + 2*x^49*z0 + x^48*z0 + x^47*z0 - 2*x^46*z0 - x^45*z0 - x^44*z0 + 2*x^43*z0 + x^42*z0 + x^40*z0^3 + 2*x^38*y*z0^4 - 2*x^41*z0 + 2*x^39*y*z0^2 + x^39*z0^3 + x^40*y - x^40*z0 + 2*x^38*y*z0^2 - x^39*y - x^39*z0 + x^37*z0^3 + 2*x^35*y*z0^4 - x^38*z0 - 2*x^36*y*z0^2 - x^36*z0^3 + 2*x^37*y - x^37*z0 + x^35*y*z0^2 + 2*x^35*z0^3 - 2*x^33*y*z0^4 + 2*x^36*y - x^36*z0 - x^34*z0^3 - 2*x^32*y*z0^4 - 2*x^35*y + x^35*z0 + 2*x^33*y*z0^2 + x^33*z0^3 - x^32*y*z0^2 - x^32*z0^3 - 2*x^30*y*z0^4 - 2*x^33*y - 2*x^33*z0 + x^31*y*z0^2 - 2*x^31*z0^3 + x^29*y*z0^4 + x^32*y - 2*x^32*z0 + 2*x^30*y*z0^2 - 2*x^30*z0^3 - 2*x^31*y - x^31*z0 + x^29*z0^3 - 2*x^27*y*z0^4 + x^30*y - 2*x^30*z0 + 2*x^28*y*z0^2 + 2*x^28*z0^3 + 2*x^26*y*z0^4 - x^29*y + x^29*z0 + 2*x^27*y*z0^2 + 2*x^27*z0^3 + 2*x^25*y*z0^4 - x^28*z0 - x^26*y*z0^2 + x^26*z0^3 - x^27*y + x^27*z0 - x^25*y*z0^2 - x^25*z0^3 - x^23*y*z0^4 - 2*x^26*z0 - x^24*y*z0^2 + x^24*z0^3 - x^22*y*z0^4 - x^25*y - x^25*z0 + 2*x^23*z0^3 + 2*x^21*y*z0^4 - x^24*z0 + x^22*y^2*z0 + x^22*y*z0^2 - 2*x^22*z0^3 - x^20*y*z0^4 - x^23*y + 2*x^23*z0 - x^21*z0^3 + x^19*y*z0^4 - x^22*z0 + x^20*y*z0^2 - 2*x^20*z0^3 - 2*x^18*y*z0^4 + x^21*y - 2*x^19*y*z0^2 - x^17*y*z0^4 - x^20*y + x^18*y*z0^2 + 2*x^19*y - x^19*z0 + 2*x^17*y*z0^2 - 2*x^17*z0^3 - 2*x^15*y*z0^4 - 2*x^18*z0 - x^16*y*z0^2 + x^14*y*z0^4 - x^17*y - 2*x^13*y*z0^4 - x^16*y - x^16*z0 + x^14*y*z0^2 - 2*x^12*y*z0^4 - 2*x^13*y*z0^2 - 2*x^11*y*z0^4 + x^14*y - 2*x^14*z0 + 2*x^12*z0^3 - x^10*y*z0^4 - x^13*y + 2*x^13*z0 - x^11*y*z0^2 - 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 + 2*x^8*y*z0^4 - 2*x^7*y*z0^4 - 2*x^10*y + x^10*z0 - x^8*y*z0^2 - x^8*z0^3 - 2*x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 + x^8*y + 2*x^8*z0 - x^6*y*z0^2 + 2*x^4*y*z0^4 - x^7*y - x^7*z0 + 2*x^5*y*z0^2 - 2*x^5*z0^3 + 2*x^6*y - x^6*z0 - 2*x^4*y*z0^2 - x^4*z0^3 - 2*x^2*y*z0^4 + x^5*y - x^3*y*z0^2 - 2*x^4*y - 2*x^2*y*z0^2 - x^2*z0^3 + x^3*z0 - 2*x^2*y - 2*x^2*z0)/y) * dx, - ((x^61*z0^4 + 2*x^60*z0^4 - x^58*y^2*z0^4 + x^61*z0^2 - 2*x^57*y^2*z0^4 + x^60*z0^2 - x^58*y^2*z0^2 - x^58*z0^4 - x^61 - x^57*y^2*z0^2 - 2*x^57*z0^4 - 2*x^60 + x^58*y^2 - x^58*z0^2 + 2*x^57*y^2 - x^57*z0^2 + x^55*z0^4 + x^58 + 2*x^54*z0^4 + 2*x^57 + x^55*z0^2 + x^54*z0^2 - x^52*z0^4 - x^55 - 2*x^51*z0^4 - 2*x^54 - x^52*z0^2 - x^51*z0^2 + x^49*z0^4 + x^52 + 2*x^48*z0^4 + 2*x^51 + x^49*z0^2 + x^48*z0^2 - x^46*z0^4 - x^49 - 2*x^45*z0^4 - 2*x^48 - x^46*z0^2 - x^45*z0^2 + x^43*z0^4 + x^46 + 2*x^42*z0^4 + 2*x^45 + x^43*z0^2 - 2*x^41*z0^4 + x^42*z0^2 - 2*x^40*y*z0^3 - x^43 + x^41*z0^2 + x^39*y*z0^3 - x^39*z0^4 - 2*x^42 - 2*x^40*y*z0 - x^40*z0^2 + x^38*z0^4 - 2*x^41 + 2*x^39*y*z0 - 2*x^39*z0^2 + x^37*y*z0^3 - x^37*z0^4 - 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 + x^37*z0^2 + 2*x^35*y*z0^3 + 2*x^35*z0^4 + x^38 + 2*x^36*y*z0 + 2*x^36*z0^2 + x^34*y*z0^3 + x^34*z0^4 + 2*x^37 - x^35*z0^2 - 2*x^33*y*z0^3 + 2*x^33*z0^4 + 2*x^36 - x^34*y*z0 + x^34*z0^2 - x^32*y*z0^3 - 2*x^32*z0^4 + x^35 - x^33*y*z0 + 2*x^33*z0^2 + 2*x^31*y*z0^3 - 2*x^31*z0^4 + 2*x^34 + 2*x^32*y*z0 + x^32*z0^2 - 2*x^30*y*z0^3 - x^30*z0^4 - 2*x^31*y*z0 + 2*x^31*z0^2 - 2*x^29*z0^4 - 2*x^32 + 2*x^30*y*z0 + 2*x^28*y*z0^3 - x^31 - 2*x^27*y*z0^3 + 2*x^27*z0^4 + 2*x^30 + 2*x^28*y*z0 - x^28*z0^2 + x^26*y*z0^3 + x^26*z0^4 - x^29 + x^27*y*z0 + x^25*y*z0^3 - x^25*z0^4 + 2*x^28 - 2*x^26*z0^2 + 2*x^24*y*z0^3 - x^24*z0^4 - x^25*y*z0 - x^25*z0^2 - x^23*y*z0^3 - x^23*z0^4 + x^26 - x^24*z0^2 + x^22*y^2*z0^2 + x^22*y*z0^3 - 2*x^22*z0^4 - x^25 + x^23*y*z0 - x^21*y*z0^3 + 2*x^24 - 2*x^22*y*z0 + x^20*y*z0^3 + 2*x^20*z0^4 + 2*x^23 + 2*x^21*y*z0 - 2*x^21*z0^2 + x^19*y*z0^3 - x^19*z0^4 + 2*x^22 - 2*x^20*y*z0 - x^18*y*z0^3 - 2*x^18*z0^4 + x^21 + 2*x^19*z0^2 - x^17*y*z0^3 - x^17*z0^4 - 2*x^20 + 2*x^18*y*z0 - 2*x^16*y*z0^3 - 2*x^16*z0^4 + x^19 - x^17*y*z0 + 2*x^17*z0^2 + 2*x^15*y*z0^3 + x^15*z0^4 - x^16*z0^2 - x^17 + x^15*y*z0 - x^15*z0^2 + x^13*y*z0^3 - 2*x^13*z0^4 - x^16 - 2*x^14*z0^2 - x^12*y*z0^3 - x^12*z0^4 - 2*x^13*y*z0 + 2*x^13*z0^2 - 2*x^11*y*z0^3 + x^11*z0^4 - 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - 2*x^11*z0^2 - 2*x^9*y*z0^3 - x^9*z0^4 + x^12 + x^10*y*z0 - x^8*y*z0^3 + 2*x^8*z0^4 + 2*x^11 - x^7*y*z0^3 + x^7*z0^4 + x^10 - 2*x^8*z0^2 - 2*x^6*y*z0^3 + 2*x^6*z0^4 + 2*x^5*z0^4 + x^6*z0^2 + 2*x^7 + 2*x^5*z0^2 + 2*x^3*y*z0^3 + 2*x^3*z0^4 + x^6 + x^4*z0^2 - 2*x^2*y*z0^3 + 2*x^2*z0^4 + x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 + 2*x^3)/y) * dx, - ((-2*x^60*z0^3 - x^59*z0^3 + 2*x^57*y^2*z0^3 - x^60*z0 - 2*x^58*z0^3 + x^56*y^2*z0^3 + 2*x^59*z0 + x^57*y^2*z0 + x^57*z0^3 + 2*x^55*y^2*z0^3 - 2*x^56*y^2*z0 + x^56*z0^3 + x^54*y^2*z0^3 + x^57*z0 + 2*x^55*z0^3 - 2*x^56*z0 - x^54*z0^3 - x^53*z0^3 - x^54*z0 - 2*x^52*z0^3 + 2*x^53*z0 + x^51*z0^3 + x^50*z0^3 + x^51*z0 + 2*x^49*z0^3 - 2*x^50*z0 - x^48*z0^3 - x^47*z0^3 - x^48*z0 - 2*x^46*z0^3 + 2*x^47*z0 + x^45*z0^3 + x^44*z0^3 + x^45*z0 + 2*x^43*z0^3 - 2*x^44*z0 - x^42*z0^3 - x^41*z0^3 - x^42*z0 + x^40*z0^3 - 2*x^38*y*z0^4 + 2*x^41*z0 + x^39*z0^3 + 2*x^37*y*z0^4 + x^40*z0 - 2*x^38*y*z0^2 - 2*x^36*y*z0^4 - x^39*y - 2*x^37*y*z0^2 + 2*x^37*z0^3 + x^35*y*z0^4 + 2*x^38*y - x^36*y*z0^2 + x^36*z0^3 + x^37*z0 + x^35*z0^3 + x^33*y*z0^4 - x^36*y + x^36*z0 + 2*x^34*y*z0^2 + x^34*z0^3 + 2*x^35*y + 2*x^35*z0 + x^33*y*z0^2 + x^33*z0^3 + x^31*y*z0^4 - 2*x^34*y + 2*x^34*z0 + 2*x^32*y*z0^2 - x^32*z0^3 - 2*x^30*y*z0^4 + 2*x^33*y + x^29*y*z0^4 + 2*x^32*y + 2*x^30*z0^3 + x^28*y*z0^4 + 2*x^31*y + 2*x^31*z0 + x^29*y*z0^2 + 2*x^29*z0^3 - 2*x^27*y*z0^4 - x^30*y - 2*x^30*z0 + 2*x^28*z0^3 + 2*x^26*y*z0^4 + x^29*y + x^29*z0 - 2*x^27*y*z0^2 - x^27*z0^3 - x^25*y*z0^4 - 2*x^28*y - x^26*y*z0^2 + 2*x^26*z0^3 + x^24*y*z0^4 + 2*x^27*y + 2*x^27*z0 + 2*x^25*y*z0^2 + x^25*z0^3 - x^23*y*z0^4 + x^26*y + 2*x^26*z0 + 2*x^24*y*z0^2 + 2*x^24*z0^3 + x^22*y^2*z0^3 + x^22*y*z0^4 + x^25*y - 2*x^23*y*z0^2 + 2*x^23*z0^3 - x^21*y*z0^4 + x^24*y + 2*x^24*z0 + x^22*y*z0^2 - x^22*z0^3 + 2*x^20*y*z0^4 - x^23*y + x^21*z0^3 - x^22*y - x^20*z0^3 + 2*x^18*y*z0^4 - x^21*z0 - x^19*y*z0^2 - 2*x^19*z0^3 + 2*x^17*y*z0^4 - x^20*y + 2*x^20*z0 - 2*x^18*z0^3 + 2*x^16*y*z0^4 - 2*x^19*y + x^17*y*z0^2 + x^17*z0^3 + x^15*y*z0^4 + x^18*y - 2*x^18*z0 + 2*x^14*y*z0^4 - 2*x^17*y - x^17*z0 + 2*x^15*y*z0^2 + 2*x^15*z0^3 - 2*x^13*y*z0^4 + x^16*y + 2*x^16*z0 - x^14*y*z0^2 - x^14*z0^3 - x^12*y*z0^4 - 2*x^15*y - 2*x^13*y*z0^2 + 2*x^12*y*z0^2 + x^12*z0^3 - x^10*y*z0^4 + 2*x^13*y - 2*x^13*z0 + x^11*y*z0^2 + x^11*z0^3 + 2*x^10*y*z0^2 - x^8*y*z0^4 - 2*x^11*y + x^9*y*z0^2 - x^9*z0^3 + x^7*y*z0^4 + 2*x^10*y + 2*x^10*z0 - 2*x^8*y*z0^2 - x^8*z0^3 - 2*x^9*y + x^9*z0 - 2*x^7*z0^3 + x^8*y - x^8*z0 + x^6*z0^3 + x^4*y*z0^4 + 2*x^7*z0 + x^5*y*z0^2 - x^5*z0^3 - 2*x^6*y + 2*x^6*z0 - x^4*y*z0^2 - 2*x^4*z0^3 + x^5*y - 2*x^5*z0 + 2*x^3*z0^3 + x^4*y - x^4*z0 + x^2*y*z0^2 + 2*x^2*z0^3 - x^3*y + 2*x^3*z0 + 2*x^2*y - x^2*z0)/y) * dx, - ((-x^60*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 - x^57*y^2*z0^2 + x^57*z0^4 - x^60 + x^57*y^2 - x^57*z0^2 - x^54*z0^4 + x^57 + x^54*z0^2 + x^51*z0^4 - x^54 - x^51*z0^2 - x^48*z0^4 + x^51 + x^48*z0^2 + x^45*z0^4 - x^48 - x^45*z0^2 - x^42*z0^4 + x^45 + x^42*z0^2 + x^40*z0^4 - x^39*z0^4 - x^42 - 2*x^40*z0^2 - x^38*y*z0^3 + 2*x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 + x^37*z0^4 - x^40 + x^38*y*z0 + 2*x^36*z0^4 + x^39 + x^37*y*z0 - x^37*z0^2 - x^35*y*z0^3 - 2*x^36*y*z0 + x^36*z0^2 + x^34*y*z0^3 + 2*x^34*z0^4 + x^37 + 2*x^35*y*z0 + 2*x^33*z0^4 + 2*x^36 + x^34*y*z0 + x^32*y*z0^3 - 2*x^32*z0^4 + x^35 - 2*x^33*y*z0 + 2*x^33*z0^2 + 2*x^31*y*z0^3 - 2*x^31*z0^4 + 2*x^34 - 2*x^32*y*z0 + x^32*z0^2 + 2*x^30*y*z0^3 + x^30*z0^4 + x^33 - x^31*y*z0 + 2*x^31*z0^2 - 2*x^29*y*z0^3 + x^29*z0^4 - x^32 + x^30*y*z0 + x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 + x^29*y*z0 + 2*x^29*z0^2 + 2*x^27*y*z0^3 + x^27*z0^4 + 2*x^30 - x^28*y*z0 - 2*x^26*y*z0^3 + x^26*z0^4 + 2*x^29 - x^27*y*z0 - 2*x^25*y*z0^3 - 2*x^28 - x^26*y*z0 - x^26*z0^2 + 2*x^24*y*z0^3 + 2*x^24*z0^4 + x^22*y^2*z0^4 - 2*x^27 - 2*x^25*y*z0 - x^25*z0^2 + 2*x^23*y*z0^3 + x^23*z0^4 - x^26 + x^24*y*z0 - 2*x^24*z0^2 + x^22*z0^4 + x^25 - x^23*y*z0 - x^23*z0^2 + x^21*y*z0^3 + 2*x^22*z0^2 + 2*x^20*y*z0^3 - 2*x^23 - 2*x^21*y*z0 - x^21*z0^2 - x^19*z0^4 + 2*x^22 + x^20*y*z0 + 2*x^20*z0^2 - 2*x^18*y*z0^3 - x^21 + 2*x^19*y*z0 - 2*x^17*z0^4 + x^20 - x^18*y*z0 - x^18*z0^2 - x^16*y*z0^3 + x^16*z0^4 - 2*x^19 + x^17*y*z0 + x^17*z0^2 - 2*x^15*y*z0^3 + 2*x^15*z0^4 + 2*x^18 + x^16*y*z0 - x^16*z0^2 - 2*x^14*z0^4 + 2*x^17 - 2*x^15*y*z0 - x^15*z0^2 + 2*x^13*y*z0^3 - 2*x^13*z0^4 + x^14*z0^2 - x^12*y*z0^3 - 2*x^12*z0^4 - x^15 + x^13*y*z0 + 2*x^13*z0^2 - 2*x^11*z0^4 - 2*x^14 - x^12*y*z0 + x^12*z0^2 + 2*x^10*y*z0^3 + x^10*z0^4 - 2*x^13 + x^11*y*z0 + 2*x^11*z0^2 + 2*x^9*z0^4 + x^12 - 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*z0^4 + x^9*y*z0 - x^7*y*z0^3 - 2*x^7*z0^4 - x^8*z0^2 + 2*x^6*z0^4 + 2*x^9 - 2*x^7*y*z0 + 2*x^5*y*z0^3 + 2*x^5*z0^4 + x^8 - x^6*y*z0 + x^6*z0^2 - x^4*y*z0^3 - x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*y*z0^3 + x^3*z0^4 + x^6 + x^4*y*z0 - x^4*z0^2 - 2*x^2*z0^4 + 2*x^3*y*z0 - x^3*z0^2 + 2*x^2*y*z0 - x^3 + 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((2*x^61*z0^4 - 2*x^60*z0^4 - 2*x^58*y^2*z0^4 - x^61*z0^2 + 2*x^59*z0^4 + 2*x^57*y^2*z0^4 + 2*x^60*z0^2 + x^58*y^2*z0^2 - 2*x^58*z0^4 - 2*x^56*y^2*z0^4 + 2*x^61 - 2*x^57*y^2*z0^2 + 2*x^57*z0^4 - 2*x^58*y^2 + x^58*z0^2 - 2*x^56*z0^4 - 2*x^57*z0^2 + 2*x^55*z0^4 - 2*x^58 - 2*x^54*z0^4 - x^55*z0^2 + 2*x^53*z0^4 + 2*x^54*z0^2 - 2*x^52*z0^4 + 2*x^55 + 2*x^51*z0^4 + x^52*z0^2 - 2*x^50*z0^4 - 2*x^51*z0^2 + 2*x^49*z0^4 - 2*x^52 - 2*x^48*z0^4 - x^49*z0^2 + 2*x^47*z0^4 + 2*x^48*z0^2 - 2*x^46*z0^4 + 2*x^49 + 2*x^45*z0^4 + x^46*z0^2 - 2*x^44*z0^4 - 2*x^45*z0^2 + 2*x^43*z0^4 - 2*x^46 - 2*x^42*z0^4 - x^43*z0^2 + 2*x^42*z0^2 + x^40*y*z0^3 + 2*x^43 - x^41*z0^2 - x^39*y*z0^3 + 2*x^39*z0^4 + 2*x^40*y*z0 + 2*x^40*z0^2 - 2*x^38*y*z0^3 + x^38*z0^4 - 2*x^41 - x^39*z0^2 + x^37*y*z0^3 - 2*x^37*z0^4 + 2*x^40 - 2*x^38*z0^2 + 2*x^36*y*z0^3 - x^36*z0^4 + x^39 + x^37*y*z0 + x^37*z0^2 + x^35*z0^4 - 2*x^36*y*z0 + x^36*z0^2 + 2*x^34*y*z0^3 - x^37 + 2*x^35*y*z0 - 2*x^35*z0^2 - 2*x^33*y*z0^3 + 2*x^33*z0^4 + 2*x^34*y*z0 + x^32*y*z0^3 + x^32*z0^4 - x^35 - 2*x^33*y*z0 + 2*x^33*z0^2 - x^31*y*z0^3 + 2*x^31*z0^4 - 2*x^34 - 2*x^32*z0^2 - 2*x^30*y*z0^3 + 2*x^30*z0^4 + 2*x^33 - 2*x^29*y*z0^3 - x^29*z0^4 + x^32 - 2*x^30*y*z0 - x^30*z0^2 - x^28*y*z0^3 - x^29*y*z0 + 2*x^29*z0^2 + x^27*y*z0^3 + 2*x^30 - x^28*y*z0 - 2*x^28*z0^2 + 2*x^26*y*z0^3 - x^26*z0^4 - 2*x^27*z0^2 - 2*x^25*y*z0^3 + 2*x^25*z0^4 + 2*x^28 - x^26*z0^2 - x^24*y*z0^3 - x^24*z0^4 + x^27 - 2*x^25*y*z0 - x^23*y*z0^3 - x^23*z0^4 - x^26 - 2*x^24*y*z0 - 2*x^22*y*z0^3 - 2*x^22*z0^4 - 2*x^25 + x^23*y^2 - 2*x^23*y*z0 + x^23*z0^2 + 2*x^21*y*z0^3 - x^21*z0^4 - x^22*y*z0 + x^22*z0^2 - x^20*y*z0^3 - x^20*z0^4 + 2*x^23 + x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 - 2*x^19*z0^4 + x^22 - 2*x^20*y*z0 - x^20*z0^2 + 2*x^18*z0^4 + x^21 + 2*x^19*z0^2 + x^17*y*z0^3 - x^17*z0^4 - x^20 + 2*x^18*y*z0 - x^18*z0^2 - 2*x^16*z0^4 - 2*x^19 + 2*x^17*y*z0 - x^17*z0^2 - 2*x^15*y*z0^3 - 2*x^15*z0^4 + 2*x^18 - x^16*y*z0 + x^16*z0^2 + 2*x^14*y*z0^3 - x^14*z0^4 + x^17 - 2*x^15*z0^2 - x^13*y*z0^3 + 2*x^13*z0^4 - x^16 - x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 - x^12*z0^4 - x^15 - 2*x^13*y*z0 - x^13*z0^2 + 2*x^11*z0^4 - 2*x^14 - 2*x^10*y*z0^3 - 2*x^10*z0^4 + x^13 + 2*x^11*y*z0 - 2*x^11*z0^2 + 2*x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 - 2*x^10*y*z0 + x^10*z0^2 - x^8*y*z0^3 + 2*x^8*z0^4 + 2*x^11 - 2*x^9*y*z0 - x^7*y*z0^3 + x^7*z0^4 - x^10 + 2*x^8*y*z0 - x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 + x^9 - x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 - 2*x^5*z0^4 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + 2*x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^7 + x^5*z0^2 + 2*x^3*y*z0^3 + 2*x^3*z0^4 + x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 - 2*x^5 + 2*x^3*z0^2 - 2*x^2*y*z0 + x^2*z0^2 - x^3 + 2*x^2)/y) * dx, - ((-2*x^61*z0^3 - 2*x^60*z0^3 + 2*x^58*y^2*z0^3 - 2*x^61*z0 + 2*x^57*y^2*z0^3 + x^60*z0 + 2*x^58*y^2*z0 + x^58*z0^3 + 2*x^59*z0 - x^57*y^2*z0 - x^57*z0^3 + x^55*y^2*z0^3 + 2*x^58*z0 - 2*x^56*y^2*z0 - 2*x^54*y^2*z0^3 - x^57*z0 - x^55*z0^3 - 2*x^56*z0 + x^54*z0^3 - 2*x^55*z0 + x^54*z0 + x^52*z0^3 + 2*x^53*z0 - x^51*z0^3 + 2*x^52*z0 - x^51*z0 - x^49*z0^3 - 2*x^50*z0 + x^48*z0^3 - 2*x^49*z0 + x^48*z0 + x^46*z0^3 + 2*x^47*z0 - x^45*z0^3 + 2*x^46*z0 - x^45*z0 - x^43*z0^3 - 2*x^44*z0 + x^42*z0^3 - 2*x^43*z0 - 2*x^41*z0^3 - 2*x^39*y*z0^4 + x^42*z0 - x^40*y*z0^2 + 2*x^40*z0^3 + x^38*y*z0^4 - 2*x^39*y*z0^2 - 2*x^39*z0^3 - 2*x^37*y*z0^4 - x^40*y + x^40*z0 + x^38*y*z0^2 + x^38*z0^3 - x^36*y*z0^4 + 2*x^39*y - 2*x^37*y*z0^2 - 2*x^37*z0^3 - x^35*y*z0^4 - x^38*y + x^38*z0 - 2*x^36*y*z0^2 + 2*x^36*z0^3 + x^34*y*z0^4 - 2*x^37*y - 2*x^37*z0 - x^35*y*z0^2 - 2*x^35*z0^3 + x^33*y*z0^4 - x^36*y + x^36*z0 - x^34*y*z0^2 + x^34*z0^3 - 2*x^35*y - x^35*z0 + x^33*y*z0^2 - 2*x^33*z0^3 + x^31*y*z0^4 + 2*x^34*y + x^34*z0 + x^32*y*z0^2 + 2*x^32*z0^3 + x^33*y + 2*x^33*z0 - x^31*y*z0^2 + 2*x^29*y*z0^4 + 2*x^32*y + 2*x^32*z0 - 2*x^30*z0^3 + x^31*y + 2*x^31*z0 - x^29*y*z0^2 + x^29*z0^3 - x^30*y + 2*x^28*y*z0^2 - 2*x^26*y*z0^4 + 2*x^29*y - 2*x^27*y*z0^2 - 2*x^27*z0^3 - 2*x^25*y*z0^4 + 2*x^28*y + x^28*z0 + x^26*z0^3 + 2*x^24*y*z0^4 + 2*x^27*y + x^27*z0 - 2*x^25*y*z0^2 + x^25*z0^3 - x^26*y - 2*x^26*z0 + x^24*y*z0^2 - x^25*y + x^23*y^2*z0 + 2*x^23*y*z0^2 - 2*x^23*z0^3 - 2*x^21*y*z0^4 - x^22*y*z0^2 + x^22*z0^3 - x^23*y - 2*x^23*z0 + 2*x^21*y*z0^2 + x^21*z0^3 + 2*x^19*y*z0^4 - 2*x^22*y + 2*x^20*y*z0^2 - 2*x^20*z0^3 - 2*x^21*y + x^19*y*z0^2 - x^19*z0^3 - 2*x^20*y + x^18*y*z0^2 - 2*x^18*z0^3 + x^19*y - x^19*z0 + x^17*z0^3 - 2*x^15*y*z0^4 + x^18*y + x^16*y*z0^2 + x^16*z0^3 + x^14*y*z0^4 + 2*x^17*y + 2*x^17*z0 - 2*x^15*y*z0^2 - x^15*z0^3 + x^16*y - 2*x^14*y*z0^2 - 2*x^12*y*z0^4 - 2*x^15*z0 - 2*x^13*y*z0^2 + 2*x^13*z0^3 + x^11*y*z0^4 - 2*x^14*y + 2*x^14*z0 + x^12*y*z0^2 - 2*x^12*z0^3 + 2*x^10*y*z0^4 + x^13*y + 2*x^13*z0 + x^11*y*z0^2 + 2*x^11*z0^3 - 2*x^9*y*z0^4 + 2*x^10*y*z0^2 + 2*x^9*y*z0^2 + x^9*z0^3 - x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^9*z0 - 2*x^7*y*z0^2 - x^7*z0^3 - 2*x^5*y*z0^4 - x^8*y - 2*x^8*z0 + x^6*y*z0^2 - x^6*z0^3 + 2*x^4*y*z0^4 + 2*x^7*z0 + x^3*y*z0^4 - 2*x^6*y + 2*x^6*z0 + 2*x^4*z0^3 - 2*x^5*y + 2*x^5*z0 - x^3*z0^3 - 2*x^4*z0 - 2*x^2*y*z0^2 + 2*x^2*z0^3 - 2*x^3*y + x^3*z0 - 2*x^2*y + x^2*z0)/y) * dx, - ((2*x^61*z0^4 - x^60*z0^4 - 2*x^58*y^2*z0^4 + 2*x^61*z0^2 - x^59*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 - 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 + x^61 - x^57*y^2*z0^2 + x^57*z0^4 - 2*x^60 - x^58*y^2 - 2*x^58*z0^2 + x^56*z0^4 + 2*x^57*y^2 - x^57*z0^2 + 2*x^55*z0^4 - x^58 - x^54*z0^4 + 2*x^57 + 2*x^55*z0^2 - x^53*z0^4 + x^54*z0^2 - 2*x^52*z0^4 + x^55 + x^51*z0^4 - 2*x^54 - 2*x^52*z0^2 + x^50*z0^4 - x^51*z0^2 + 2*x^49*z0^4 - x^52 - x^48*z0^4 + 2*x^51 + 2*x^49*z0^2 - x^47*z0^4 + x^48*z0^2 - 2*x^46*z0^4 + x^49 + x^45*z0^4 - 2*x^48 - 2*x^46*z0^2 + x^44*z0^4 - x^45*z0^2 + 2*x^43*z0^4 - x^46 - x^42*z0^4 + 2*x^45 + 2*x^43*z0^2 - x^41*z0^4 + x^42*z0^2 + x^40*y*z0^3 + 2*x^40*z0^4 + x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^39*z0^4 - 2*x^42 + x^40*y*z0 + x^38*y*z0^3 + 2*x^39*y*z0 + 2*x^39*z0^2 + x^37*y*z0^3 + x^37*z0^4 + 2*x^40 - x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 - 2*x^37*y*z0 - x^37*z0^2 + 2*x^35*y*z0^3 - 2*x^38 + x^36*y*z0 - 2*x^36*z0^2 + x^34*y*z0^3 - x^37 + x^35*y*z0 + x^33*y*z0^3 + x^34*y*z0 - x^34*z0^2 + x^32*y*z0^3 - x^32*z0^4 + x^35 - x^33*y*z0 - x^33*z0^2 + x^31*y*z0^3 - x^34 + x^32*y*z0 - x^32*z0^2 + x^30*y*z0^3 + 2*x^33 + 2*x^31*y*z0 + 2*x^31*z0^2 + x^29*z0^4 + 2*x^32 + 2*x^30*y*z0 + x^30*z0^2 + x^28*z0^4 - x^29*z0^2 - 2*x^27*y*z0^3 + x^27*z0^4 - x^30 - 2*x^28*y*z0 + 2*x^28*z0^2 + x^26*y*z0^3 + 2*x^29 - x^27*y*z0 - x^27*z0^2 - 2*x^25*y*z0^3 - x^25*z0^4 - x^28 + 2*x^26*y*z0 - x^26*z0^2 + 2*x^24*y*z0^3 + x^24*z0^4 + x^27 - x^25*y*z0 + 2*x^25*z0^2 + x^23*y^2*z0^2 + 2*x^23*y*z0^3 - 2*x^24*y*z0 + x^24*z0^2 + x^22*y*z0^3 + x^22*z0^4 - x^25 - 2*x^23*y*z0 + 2*x^23*z0^2 - 2*x^21*y*z0^3 + 2*x^21*z0^4 + 2*x^24 + 2*x^22*y*z0 - x^20*y*z0^3 - x^20*z0^4 + 2*x^21*y*z0 + x^21*z0^2 + 2*x^19*z0^4 - x^22 - 2*x^18*y*z0^3 + x^21 - 2*x^19*y*z0 - x^19*z0^2 - x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^16*z0^4 + 2*x^19 + x^17*z0^2 - x^15*y*z0^3 + 2*x^18 - 2*x^16*y*z0 - x^16*z0^2 + 2*x^14*y*z0^3 - 2*x^17 - x^15*z0^2 - 2*x^14*y*z0 + x^14*z0^2 - 2*x^12*y*z0^3 - 2*x^15 + 2*x^13*z0^2 - 2*x^11*y*z0^3 + 2*x^11*z0^4 + 2*x^14 + 2*x^12*y*z0 - 2*x^10*y*z0^3 - 2*x^13 + 2*x^11*y*z0 + 2*x^11*z0^2 + 2*x^9*y*z0^3 + x^9*z0^4 - 2*x^12 + x^9*y*z0 + x^9*z0^2 + x^7*z0^4 + x^10 - 2*x^8*y*z0 - x^6*y*z0^3 + x^6*z0^4 + 2*x^9 + x^7*y*z0 - 2*x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 - 2*x^7 + x^5*y*z0 - x^3*y*z0^3 + x^6 + x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - x^3*y*z0 - x^3*z0^2 + x^2*z0^2 - x^3 + 2*x^2)/y) * dx, - ((x^61*z0^3 - x^58*y^2*z0^3 - x^61*z0 + x^59*z0^3 + x^58*y^2*z0 - x^56*y^2*z0^3 - 2*x^59*z0 + x^57*z0^3 - x^55*y^2*z0^3 + x^58*z0 + 2*x^56*y^2*z0 - x^56*z0^3 - x^54*y^2*z0^3 + 2*x^56*z0 - x^54*z0^3 - x^55*z0 + x^53*z0^3 - 2*x^53*z0 + x^51*z0^3 + x^52*z0 - x^50*z0^3 + 2*x^50*z0 - x^48*z0^3 - x^49*z0 + x^47*z0^3 - 2*x^47*z0 + x^45*z0^3 + x^46*z0 - x^44*z0^3 + 2*x^44*z0 - x^42*z0^3 - x^43*z0 + 2*x^41*z0^3 + x^39*y*z0^4 - 2*x^40*y*z0^2 + 2*x^40*z0^3 + x^38*y*z0^4 + 2*x^41*z0 - x^39*y*z0^2 + 2*x^37*y*z0^4 + 2*x^40*y - 2*x^40*z0 - 2*x^38*y*z0^2 + 2*x^38*z0^3 + x^39*y + 2*x^39*z0 - 2*x^37*y*z0^2 + x^37*z0^3 - x^35*y*z0^4 + 2*x^38*y - 2*x^38*z0 - 2*x^36*y*z0^2 - 2*x^36*z0^3 - 2*x^34*y*z0^4 - x^37*y + x^37*z0 - x^35*y*z0^2 - x^33*y*z0^4 + 2*x^36*z0 + 2*x^34*y*z0^2 - x^34*z0^3 - 2*x^32*y*z0^4 - 2*x^33*z0^3 + 2*x^31*y*z0^4 - 2*x^34*y + x^34*z0 - 2*x^32*y*z0^2 - 2*x^32*z0^3 + 2*x^33*y + 2*x^33*z0 + x^31*y*z0^2 + 2*x^31*z0^3 + 2*x^29*y*z0^4 - x^32*y - 2*x^32*z0 - 2*x^30*y*z0^2 + 2*x^30*z0^3 - 2*x^28*y*z0^4 - 2*x^31*y + 2*x^31*z0 + 2*x^29*y*z0^2 - x^29*z0^3 - x^30*y - x^28*y*z0^2 + x^28*z0^3 + x^26*y*z0^4 + 2*x^29*y + 2*x^29*z0 + x^27*y*z0^2 + x^27*z0^3 + x^25*y*z0^4 - 2*x^28*z0 - x^26*y*z0^2 - 2*x^27*y + 2*x^25*z0^3 + x^23*y^2*z0^3 - x^23*y*z0^4 - x^26*z0 + x^24*y*z0^2 - 2*x^24*z0^3 - x^22*y*z0^4 + 2*x^25*y - 2*x^23*y*z0^2 + 2*x^21*y*z0^4 - x^24*y + x^24*z0 - 2*x^22*y*z0^2 - x^22*z0^3 - 2*x^20*y*z0^4 + 2*x^23*y + x^23*z0 - x^21*y*z0^2 - 2*x^21*z0^3 - x^22*y + 2*x^22*z0 + x^20*y*z0^2 + 2*x^18*y*z0^4 + 2*x^21*y + x^21*z0 + 2*x^19*y*z0^2 - 2*x^19*z0^3 - 2*x^17*y*z0^4 - 2*x^20*z0 - x^18*y*z0^2 - 2*x^18*z0^3 + 2*x^19*y + 2*x^19*z0 - 2*x^17*z0^3 - x^15*y*z0^4 - 2*x^18*y + x^16*y*z0^2 - 2*x^16*z0^3 + 2*x^14*y*z0^4 + x^17*y + 2*x^17*z0 + 2*x^15*y*z0^2 - x^15*z0^3 - x^13*y*z0^4 + x^16*y - 2*x^16*z0 - 2*x^14*y*z0^2 - x^12*y*z0^4 + x^15*y - x^15*z0 - x^13*y*z0^2 - x^13*z0^3 + 2*x^11*y*z0^4 + 2*x^14*y + 2*x^14*z0 + x^10*y*z0^4 + x^13*y + x^13*z0 + x^11*y*z0^2 + 2*x^11*z0^3 + x^9*y*z0^4 - 2*x^12*y + 2*x^10*y*z0^2 + x^10*z0^3 - x^8*y*z0^4 + x^11*y + x^9*y*z0^2 + x^9*z0^3 - 2*x^7*y*z0^4 + x^10*y - x^10*z0 - 2*x^8*y*z0^2 + 2*x^9*y - 2*x^7*y*z0^2 + x^5*y*z0^4 - x^8*y + 2*x^8*z0 - x^6*y*z0^2 - 2*x^6*z0^3 - x^4*y*z0^4 + x^7*y - x^5*y*z0^2 - x^5*z0^3 + x^6*y - x^6*z0 + 2*x^4*y*z0^2 + 2*x^4*z0^3 - x^2*y*z0^4 + x^3*z0^3 + x^4*z0 + 2*x^2*y*z0^2 + x^3*y + x^2*y + 2*x^2*z0)/y) * dx, - ((x^60*z0^4 + x^61*z0^2 - x^59*z0^4 - x^57*y^2*z0^4 + x^60*z0^2 - x^58*y^2*z0^2 + x^56*y^2*z0^4 + x^61 - x^57*y^2*z0^2 - x^57*z0^4 - x^60 - x^58*y^2 - x^58*z0^2 + x^56*z0^4 + x^57*y^2 - x^57*z0^2 - x^58 + x^54*z0^4 + x^57 + x^55*z0^2 - x^53*z0^4 + x^54*z0^2 + x^55 - x^51*z0^4 - x^54 - x^52*z0^2 + x^50*z0^4 - x^51*z0^2 - x^52 + x^48*z0^4 + x^51 + x^49*z0^2 - x^47*z0^4 + x^48*z0^2 + x^49 - x^45*z0^4 - x^48 - x^46*z0^2 + x^44*z0^4 - x^45*z0^2 - x^46 + x^42*z0^4 + x^45 + x^43*z0^2 + 2*x^41*z0^4 + x^42*z0^2 + x^40*z0^4 + x^43 + x^41*z0^2 + x^39*y*z0^3 - x^39*z0^4 - x^42 - 2*x^40*y*z0 - 2*x^40*z0^2 - 2*x^38*y*z0^3 + x^38*z0^4 - 2*x^41 - x^39*y*z0 - 2*x^39*z0^2 + x^37*y*z0^3 + x^37*z0^4 - x^40 + 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - x^36*z0^4 - 2*x^39 + 2*x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 + 2*x^35*z0^4 - x^38 - 2*x^36*y*z0 + 2*x^36*z0^2 + x^34*y*z0^3 + x^34*z0^4 + 2*x^37 + x^35*z0^2 - 2*x^33*y*z0^3 + x^33*z0^4 - 2*x^36 - 2*x^34*y*z0 + 2*x^34*z0^2 - 2*x^32*y*z0^3 + 2*x^32*z0^4 + 2*x^35 - x^33*y*z0 - x^33*z0^2 + 2*x^31*y*z0^3 + x^31*z0^4 + x^32*y*z0 - x^32*z0^2 - 2*x^30*y*z0^3 - x^30*z0^4 - 2*x^33 + x^31*y*z0 - 2*x^31*z0^2 - 2*x^29*y*z0^3 + x^29*z0^4 + x^30*y*z0 - x^30*z0^2 - x^28*z0^4 - 2*x^31 + 2*x^29*y*z0 + 2*x^29*z0^2 - 2*x^27*y*z0^3 - 2*x^27*z0^4 + 2*x^30 + 2*x^28*y*z0 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^29 + x^27*y*z0 + 2*x^27*z0^2 - 2*x^25*y*z0^3 + x^23*y^2*z0^4 - x^28 + x^26*y*z0 + 2*x^26*z0^2 + 2*x^24*y*z0^3 + 2*x^24*z0^4 - 2*x^27 - x^25*y*z0 + x^25*z0^2 - 2*x^23*y*z0^3 + 2*x^23*z0^4 + x^26 - x^24*y*z0 + x^24*z0^2 + 2*x^22*y*z0^3 - 2*x^22*z0^4 + 2*x^25 - x^23*y*z0 - x^23*z0^2 - x^21*y*z0^3 - 2*x^21*z0^4 + 2*x^24 + x^22*y*z0 + 2*x^22*z0^2 + x^20*y*z0^3 - 2*x^20*z0^4 + 2*x^21*y*z0 - 2*x^21*z0^2 - 2*x^19*y*z0^3 + x^22 - x^20*y*z0 + 2*x^20*z0^2 + 2*x^18*z0^4 + x^21 + x^19*y*z0 - 2*x^18*y*z0 + x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 - x^19 - x^17*y*z0 - x^17*z0^2 + 2*x^15*z0^4 - x^18 + 2*x^16*y*z0 - x^16*z0^2 + x^14*y*z0^3 - 2*x^17 + 2*x^15*y*z0 + x^15*z0^2 + x^13*y*z0^3 - x^13*z0^4 + 2*x^16 + x^12*y*z0^3 - x^12*z0^4 + 2*x^15 + x^13*y*z0 - x^11*y*z0^3 - 2*x^11*z0^4 - 2*x^14 + x^12*y*z0 - x^10*z0^4 + x^13 + 2*x^11*y*z0 + x^11*z0^2 - x^9*y*z0^3 - 2*x^9*z0^4 - x^12 + 2*x^10*y*z0 - 2*x^8*z0^4 - 2*x^11 + x^9*y*z0 - x^9*z0^2 + x^7*y*z0^3 - 2*x^7*z0^4 - x^10 + x^8*z0^2 + x^6*y*z0^3 + x^6*z0^4 + x^9 - 2*x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 - 2*x^5*z0^4 + 2*x^8 - x^6*z0^2 + 2*x^4*y*z0^3 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*y*z0 + 2*x^3*y*z0^3 - x^3*z0^4 - 2*x^6 - 2*x^4*z0^2 - 2*x^2*y*z0^3 + x^2*z0^4 - x^5 - x^3*y*z0 - 2*x^3*z0^2 - 2*x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-2*x^61*z0^4 - x^60*z0^4 + 2*x^58*y^2*z0^4 - 2*x^61*z0^2 + x^57*y^2*z0^4 + 2*x^58*y^2*z0^2 + 2*x^58*z0^4 + x^61 + x^57*z0^4 + 2*x^60 - x^58*y^2 + 2*x^58*z0^2 - 2*x^57*y^2 - 2*x^55*z0^4 - x^58 - x^54*z0^4 - 2*x^57 - 2*x^55*z0^2 + 2*x^52*z0^4 + x^55 + x^51*z0^4 + 2*x^54 + 2*x^52*z0^2 - 2*x^49*z0^4 - x^52 - x^48*z0^4 - 2*x^51 - 2*x^49*z0^2 + 2*x^46*z0^4 + x^49 + x^45*z0^4 + 2*x^48 + 2*x^46*z0^2 - 2*x^43*z0^4 - x^46 - x^42*z0^4 - 2*x^45 - 2*x^43*z0^2 + x^41*z0^4 - x^40*y*z0^3 + 2*x^40*z0^4 + x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 + 2*x^42 - x^40*y*z0 + 2*x^40*z0^2 - x^38*y*z0^3 + 2*x^38*z0^4 + x^41 - x^39*y*z0 + 2*x^39*z0^2 + 2*x^37*y*z0^3 - x^37*z0^4 + x^40 + x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 + x^39 + 2*x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 + x^35*z0^4 + 2*x^38 - x^36*y*z0 - 2*x^36*z0^2 + 2*x^34*z0^4 + x^37 + 2*x^35*z0^2 - x^33*y*z0^3 - x^34*y*z0 - x^34*z0^2 - x^32*y*z0^3 + x^32*z0^4 - x^35 - 2*x^33*y*z0 - x^31*z0^4 - x^32*y*z0 - x^32*z0^2 - x^30*z0^4 - 2*x^33 - x^31*y*z0 - x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - 2*x^32 + x^30*y*z0 + x^28*y*z0^3 - x^28*z0^4 - x^31 + x^29*z0^2 + 2*x^27*y*z0^3 + 2*x^30 - x^28*y*z0 - x^28*z0^2 - x^26*y*z0^3 - 2*x^29 + 2*x^27*y*z0 + x^27*z0^2 - 2*x^25*y*z0^3 - x^25*z0^4 + x^28 + x^26*z0^2 - x^27 - x^25*y*z0 - 2*x^25*z0^2 - 2*x^23*y*z0^3 - 2*x^23*z0^4 - x^26 + x^24*y^2 + 2*x^24*y*z0 + 2*x^24*z0^2 + 2*x^22*y*z0^3 + x^22*z0^4 - 2*x^25 - 2*x^23*y*z0 + x^23*z0^2 + 2*x^24 + x^22*y*z0 - x^22*z0^2 - x^20*y*z0^3 - x^20*z0^4 - 2*x^23 + 2*x^21*z0^2 + x^19*y*z0^3 + 2*x^19*z0^4 + x^22 + 2*x^20*y*z0 - 2*x^20*z0^2 + 2*x^18*y*z0^3 - x^18*z0^4 + 2*x^21 + 2*x^19*z0^2 + 2*x^17*y*z0^3 + 2*x^17*z0^4 - 2*x^20 + x^18*y*z0 + 2*x^16*y*z0^3 + x^16*z0^4 - 2*x^19 + x^17*y*z0 + x^17*z0^2 + 2*x^15*y*z0^3 - 2*x^15*z0^4 + 2*x^18 - 2*x^16*y*z0 - x^14*y*z0^3 + x^17 + x^15*y*z0 - x^15*z0^2 - 2*x^13*y*z0^3 - x^13*z0^4 + 2*x^16 - x^14*y*z0 - x^14*z0^2 - 2*x^12*y*z0^3 + 2*x^12*z0^4 + x^13*y*z0 - x^13*z0^2 - 2*x^11*y*z0^3 + 2*x^11*z0^4 - 2*x^14 + x^12*y*z0 + x^12*z0^2 - x^10*z0^4 + 2*x^13 + x^11*y*z0 - 2*x^9*y*z0^3 + 2*x^9*z0^4 - 2*x^12 + 2*x^8*z0^4 + x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 + 2*x^7*y*z0^3 + 2*x^7*z0^4 + 2*x^10 - 2*x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 - x^5*z0^4 + x^6*y*z0 + x^4*y*z0^3 + x^4*z0^4 - 2*x^7 - 2*x^5*y*z0 + 2*x^3*y*z0^3 + 2*x^3*z0^4 + x^6 + x^4*y*z0 + 2*x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 - x^5 + 2*x^3*y*z0 + 2*x^3*z0^2 + x^2*y*z0 - 2*x^2*z0^2 + 2*x^2)/y) * dx, - ((-x^61*z0^3 + 2*x^60*z0^3 + x^58*y^2*z0^3 + x^61*z0 - 2*x^59*z0^3 - 2*x^57*y^2*z0^3 + x^60*z0 - x^58*y^2*z0 - 2*x^58*z0^3 + 2*x^56*y^2*z0^3 - x^57*y^2*z0 - 2*x^55*y^2*z0^3 - x^58*z0 + 2*x^56*z0^3 - 2*x^54*y^2*z0^3 - x^57*z0 + 2*x^55*z0^3 + x^55*z0 - 2*x^53*z0^3 + x^54*z0 - 2*x^52*z0^3 - x^52*z0 + 2*x^50*z0^3 - x^51*z0 + 2*x^49*z0^3 + x^49*z0 - 2*x^47*z0^3 + x^48*z0 - 2*x^46*z0^3 - x^46*z0 + 2*x^44*z0^3 - x^45*z0 + 2*x^43*z0^3 + x^43*z0 + 2*x^41*z0^3 - x^39*y*z0^4 + x^42*z0 + 2*x^40*y*z0^2 - 2*x^40*z0^3 + x^38*y*z0^4 + x^41*z0 + x^39*y*z0^2 + 2*x^39*z0^3 + 2*x^37*y*z0^4 - 2*x^40*y + x^40*z0 - x^38*y*z0^2 - 2*x^38*z0^3 - 2*x^36*y*z0^4 - 2*x^39*z0 + x^37*y*z0^2 - x^37*z0^3 + x^35*y*z0^4 - x^38*y + 2*x^38*z0 - 2*x^36*y*z0^2 + 2*x^36*z0^3 + 2*x^34*y*z0^4 + x^37*y - x^37*z0 + 2*x^35*y*z0^2 - 2*x^33*y*z0^4 + 2*x^36*z0 + x^34*y*z0^2 + x^34*z0^3 - 2*x^32*y*z0^4 - 2*x^35*z0 - 2*x^33*y*z0^2 + 2*x^33*z0^3 + 2*x^31*y*z0^4 + x^34*z0 + 2*x^32*y*z0^2 - x^32*z0^3 + 2*x^30*y*z0^4 - 2*x^33*y + x^33*z0 + 2*x^31*y*z0^2 + x^31*z0^3 + x^29*y*z0^4 + 2*x^32*y + x^32*z0 - x^30*y*z0^2 - 2*x^30*z0^3 - x^28*y*z0^4 + x^31*z0 + x^29*y*z0^2 - x^29*z0^3 - x^27*y*z0^4 + x^30*y - 2*x^28*y*z0^2 - 2*x^28*z0^3 - 2*x^26*y*z0^4 - 2*x^29*y - 2*x^29*z0 - x^27*z0^3 - x^28*y - 2*x^28*z0 + 2*x^26*y*z0^2 + x^24*y*z0^4 - 2*x^27*y - x^25*z0^3 + x^23*y*z0^4 + 2*x^26*z0 + x^24*y^2*z0 + 2*x^24*y*z0^2 - 2*x^24*z0^3 + 2*x^22*y*z0^4 - x^25*y + 2*x^25*z0 + x^23*y*z0^2 - x^23*z0^3 + x^21*y*z0^4 + 2*x^24*y - x^24*z0 - 2*x^22*y*z0^2 - 2*x^22*z0^3 - x^20*y*z0^4 + x^23*y - x^23*z0 + 2*x^21*y*z0^2 + 2*x^21*z0^3 + x^22*y + x^22*z0 + x^20*y*z0^2 - x^19*z0^3 - 2*x^17*y*z0^4 + x^20*z0 + x^18*y*z0^2 - x^18*z0^3 - 2*x^16*y*z0^4 + x^19*y - x^17*y*z0^2 - 2*x^17*z0^3 + 2*x^15*y*z0^4 - x^18*y - 2*x^18*z0 + 2*x^16*y*z0^2 + 2*x^16*z0^3 + 2*x^14*y*z0^4 + x^17*y - x^17*z0 + x^15*y*z0^2 - 2*x^15*z0^3 - x^16*y + 2*x^16*z0 + 2*x^14*y*z0^2 - 2*x^14*z0^3 + 2*x^15*y + x^15*z0 - 2*x^13*z0^3 - 2*x^11*y*z0^4 + 2*x^14*y - 2*x^12*y*z0^2 + x^13*z0 + 2*x^11*y*z0^2 - 2*x^11*z0^3 + x^9*y*z0^4 - 2*x^12*y + 2*x^10*y*z0^2 - x^10*z0^3 + 2*x^8*y*z0^4 - x^11*y - x^9*y*z0^2 - 2*x^9*z0^3 + x^7*y*z0^4 + 2*x^10*y + x^10*z0 - 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^9*y + x^7*y*z0^2 + 2*x^5*y*z0^4 - x^8*z0 - x^6*y*z0^2 - 2*x^6*z0^3 - x^7*y + 2*x^7*z0 + 2*x^5*z0^3 - 2*x^3*y*z0^4 - x^6*y - x^6*z0 + 2*x^2*y*z0^4 + x^5*y + x^5*z0 - x^3*y*z0^2 + 2*x^3*z0^3 - x^4*y - 2*x^2*z0^3 + x^3*z0 + 2*x^2*y)/y) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 - x^59*z0^4 - 2*x^60*z0^2 - x^58*z0^4 + x^56*y^2*z0^4 - 2*x^61 + 2*x^57*y^2*z0^2 + x^60 + 2*x^58*y^2 + x^56*z0^4 - x^57*y^2 + 2*x^57*z0^2 + x^55*z0^4 + 2*x^58 - x^57 - x^53*z0^4 - 2*x^54*z0^2 - x^52*z0^4 - 2*x^55 + x^54 + x^50*z0^4 + 2*x^51*z0^2 + x^49*z0^4 + 2*x^52 - x^51 - x^47*z0^4 - 2*x^48*z0^2 - x^46*z0^4 - 2*x^49 + x^48 + x^44*z0^4 + 2*x^45*z0^2 + x^43*z0^4 + 2*x^46 - x^45 - x^41*z0^4 - 2*x^42*z0^2 - 2*x^40*y*z0^3 + x^40*z0^4 - 2*x^43 + x^39*z0^4 + x^42 + 2*x^40*z0^2 - x^38*y*z0^3 + 2*x^39*z0^2 - 2*x^37*y*z0^3 - 2*x^37*z0^4 + 2*x^40 + x^38*y*z0 - 2*x^39 + 2*x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 - 2*x^38 - 2*x^36*y*z0 - 2*x^36*z0^2 - 2*x^34*y*z0^3 - x^35*y*z0 - 2*x^35*z0^2 + 2*x^33*y*z0^3 - x^33*z0^4 - x^36 + 2*x^34*y*z0 + 2*x^34*z0^2 - x^32*z0^4 + 2*x^35 - 2*x^33*y*z0 - x^33*z0^2 - 2*x^31*y*z0^3 - 2*x^31*z0^4 - x^32*y*z0 - 2*x^32*z0^2 - 2*x^30*y*z0^3 - 2*x^33 + x^31*y*z0 - 2*x^29*y*z0^3 + x^29*z0^4 + 2*x^30*y*z0 + 2*x^30*z0^2 - x^28*y*z0^3 - x^28*z0^4 + 2*x^31 - x^29*y*z0 + 2*x^27*y*z0^3 - x^30 + 2*x^28*y*z0 - 2*x^26*y*z0^3 + x^29 + 2*x^27*y*z0 + x^27*z0^2 - 2*x^25*y*z0^3 + 2*x^25*z0^4 - 2*x^28 - 2*x^26*y*z0 - 2*x^26*z0^2 + x^24*y^2*z0^2 + x^24*y*z0^3 - 2*x^24*z0^4 - x^27 + 2*x^25*y*z0 - 2*x^25*z0^2 + 2*x^23*y*z0^3 - 2*x^23*z0^4 - x^26 + x^24*y*z0 + x^24*z0^2 - x^22*y*z0^3 + x^23*y*z0 + x^23*z0^2 + x^21*y*z0^3 - x^21*z0^4 + 2*x^24 - 2*x^22*y*z0 - 2*x^22*z0^2 - x^20*y*z0^3 - x^20*z0^4 + 2*x^23 - x^21*y*z0 + x^21*z0^2 + x^19*z0^4 + 2*x^22 + x^20*y*z0 + 2*x^20*z0^2 - x^19*y*z0 - x^17*z0^4 - x^18*z0^2 + 2*x^16*y*z0^3 - 2*x^16*z0^4 - x^19 + 2*x^17*y*z0 - x^17*z0^2 + x^15*y*z0^3 + 2*x^18 - x^16*y*z0 + 2*x^14*z0^4 + 2*x^17 - x^15*y*z0 + x^13*y*z0^3 - 2*x^14*y*z0 - x^14*z0^2 - 2*x^12*y*z0^3 + 2*x^15 + 2*x^13*y*z0 - x^13*z0^2 + 2*x^11*y*z0^3 + x^11*z0^4 - 2*x^14 + x^12*y*z0 - x^12*z0^2 + 2*x^10*z0^4 + 2*x^13 - 2*x^11*y*z0 - x^9*y*z0^3 + x^9*z0^4 + x^12 - x^10*y*z0 + 2*x^10*z0^2 - x^8*y*z0^3 - 2*x^11 + x^9*z0^2 + x^7*y*z0^3 - 2*x^7*z0^4 - x^10 + x^8*y*z0 - x^8*z0^2 + 2*x^6*y*z0^3 - 2*x^9 + 2*x^7*y*z0 + x^7*z0^2 + 2*x^5*y*z0^3 - x^5*z0^4 - x^8 + 2*x^6*y*z0 - 2*x^6*z0^2 + 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + 2*x^5*y*z0 + x^5*z0^2 + x^3*y*z0^3 + x^3*z0^4 + 2*x^6 - 2*x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 + x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 + x^2*z0^2 - x^3 - x^2)/y) * dx, - ((-2*x^61*z0^3 + x^60*z0^3 + 2*x^58*y^2*z0^3 + x^61*z0 - 2*x^59*z0^3 - x^57*y^2*z0^3 + x^60*z0 - x^58*y^2*z0 + x^58*z0^3 + 2*x^56*y^2*z0^3 - x^59*z0 - x^57*y^2*z0 - 2*x^57*z0^3 + x^55*y^2*z0^3 - x^58*z0 + x^56*y^2*z0 + 2*x^56*z0^3 + x^54*y^2*z0^3 - x^57*z0 - x^55*z0^3 + x^56*z0 + 2*x^54*z0^3 + x^55*z0 - 2*x^53*z0^3 + x^54*z0 + x^52*z0^3 - x^53*z0 - 2*x^51*z0^3 - x^52*z0 + 2*x^50*z0^3 - x^51*z0 - x^49*z0^3 + x^50*z0 + 2*x^48*z0^3 + x^49*z0 - 2*x^47*z0^3 + x^48*z0 + x^46*z0^3 - x^47*z0 - 2*x^45*z0^3 - x^46*z0 + 2*x^44*z0^3 - x^45*z0 - x^43*z0^3 + x^44*z0 + 2*x^42*z0^3 + x^43*z0 + x^41*z0^3 - 2*x^39*y*z0^4 + x^42*z0 - x^40*y*z0^2 + x^40*z0^3 - x^38*y*z0^4 + x^39*y*z0^2 - 2*x^37*y*z0^4 - 2*x^40*y + x^38*y*z0^2 + x^38*z0^3 + x^39*y + x^39*z0 - 2*x^37*y*z0^2 + x^35*y*z0^4 - x^38*y + 2*x^38*z0 + x^36*y*z0^2 - x^36*z0^3 - x^34*y*z0^4 + x^37*y + x^35*y*z0^2 + x^35*z0^3 + 2*x^33*y*z0^4 - x^36*y + x^36*z0 + 2*x^34*y*z0^2 + 2*x^34*z0^3 - x^32*y*z0^4 + x^35*y + x^35*z0 - 2*x^33*z0^3 - 2*x^31*y*z0^4 - x^34*y + x^34*z0 + x^32*y*z0^2 - x^32*z0^3 - x^33*y - 2*x^31*y*z0^2 + x^31*z0^3 - 2*x^29*y*z0^4 - x^32*z0 + x^30*y*z0^2 + 2*x^30*z0^3 + 2*x^28*y*z0^4 - 2*x^31*z0 + 2*x^27*y*z0^4 - x^28*z0^3 - 2*x^26*y*z0^4 - x^29*y + x^29*z0 - 2*x^27*y*z0^2 - x^27*z0^3 + x^25*y*z0^4 - 2*x^28*y - x^28*z0 - x^26*y*z0^2 + 2*x^26*z0^3 + x^24*y^2*z0^3 + x^27*y - x^27*z0 + 2*x^25*y*z0^2 - x^23*y*z0^4 + 2*x^26*y + x^26*z0 - x^22*y*z0^4 - 2*x^25*z0 - x^23*y*z0^2 - 2*x^21*y*z0^4 + 2*x^24*y - x^24*z0 + 2*x^22*z0^3 + 2*x^23*y + 2*x^19*y*z0^4 - 2*x^22*z0 + x^20*y*z0^2 + 2*x^20*z0^3 + 2*x^18*y*z0^4 + x^21*z0 - x^19*z0^3 - 2*x^17*y*z0^4 + x^20*y + x^20*z0 + x^18*y*z0^2 + 2*x^18*z0^3 + x^16*y*z0^4 - 2*x^19*y - 2*x^19*z0 + 2*x^17*z0^3 - x^15*y*z0^4 - x^18*z0 + 2*x^16*y*z0^2 + 2*x^16*z0^3 - x^14*y*z0^4 - x^17*y + 2*x^17*z0 - 2*x^15*y*z0^2 - 2*x^15*z0^3 - 2*x^13*y*z0^4 - 2*x^16*z0 + x^14*y*z0^2 - 2*x^14*z0^3 + x^12*y*z0^4 + x^15*z0 - x^13*y*z0^2 + x^13*z0^3 - x^14*y + 2*x^14*z0 + 2*x^12*z0^3 + 2*x^10*y*z0^4 + x^13*y - 2*x^13*z0 + x^11*y*z0^2 + x^11*z0^3 - x^9*y*z0^4 - x^12*y + x^12*z0 + x^10*z0^3 - 2*x^8*y*z0^4 + 2*x^11*y + 2*x^11*z0 - 2*x^9*y*z0^2 + 2*x^9*z0^3 + 2*x^7*y*z0^4 - x^10*y - x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 - 2*x^6*y*z0^4 + x^9*y + 2*x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 + x^8*y + x^8*z0 + 2*x^6*y*z0^2 + x^4*y*z0^4 + x^7*z0 - x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - x^6*y - 2*x^6*z0 - 2*x^4*z0^3 - x^2*y*z0^4 - x^5*y - x^5*z0 + 2*x^3*y*z0^2 - 2*x^3*z0^3 + 2*x^4*z0 + 2*x^2*y*z0^2 + 2*x^3*y + 2*x^3*z0 - 2*x^2*y)/y) * dx, - ((-2*x^61*z0^4 + x^60*z0^4 + 2*x^58*y^2*z0^4 + 2*x^61*z0^2 + x^59*z0^4 - x^57*y^2*z0^4 + x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^58*z0^4 - x^56*y^2*z0^4 - x^61 - x^57*y^2*z0^2 - x^57*z0^4 - 2*x^60 + x^58*y^2 - 2*x^58*z0^2 - x^56*z0^4 + 2*x^57*y^2 - x^57*z0^2 - 2*x^55*z0^4 + x^58 + x^54*z0^4 + 2*x^57 + 2*x^55*z0^2 + x^53*z0^4 + x^54*z0^2 + 2*x^52*z0^4 - x^55 - x^51*z0^4 - 2*x^54 - 2*x^52*z0^2 - x^50*z0^4 - x^51*z0^2 - 2*x^49*z0^4 + x^52 + x^48*z0^4 + 2*x^51 + 2*x^49*z0^2 + x^47*z0^4 + x^48*z0^2 + 2*x^46*z0^4 - x^49 - x^45*z0^4 - 2*x^48 - 2*x^46*z0^2 - x^44*z0^4 - x^45*z0^2 - 2*x^43*z0^4 + x^46 + x^42*z0^4 + 2*x^45 + 2*x^43*z0^2 + x^41*z0^4 + x^42*z0^2 - x^40*y*z0^3 - 2*x^40*z0^4 - x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - 2*x^42 + x^40*y*z0 + x^38*y*z0^3 - 2*x^39*y*z0 + 2*x^39*z0^2 + 2*x^40 - x^38*z0^2 + x^36*y*z0^3 - x^39 - 2*x^37*y*z0 - 2*x^37*z0^2 + x^35*y*z0^3 - x^35*z0^4 + 2*x^38 - x^36*y*z0 - 2*x^36*z0^2 + x^34*y*z0^3 - 2*x^34*z0^4 + x^37 + x^35*y*z0 + 2*x^33*y*z0^3 - x^33*z0^4 - x^36 + x^34*z0^2 - x^32*y*z0^3 - 2*x^32*z0^4 + 2*x^35 + x^33*z0^2 + 2*x^31*y*z0^3 - x^31*z0^4 + 2*x^34 + x^32*y*z0 - 2*x^32*z0^2 + 2*x^30*y*z0^3 - x^30*z0^4 - 2*x^33 - x^31*y*z0 + x^31*z0^2 + x^29*y*z0^3 - x^29*z0^4 - x^32 - 2*x^30*y*z0 - x^30*z0^2 - x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^31 + 2*x^29*z0^2 - x^27*z0^4 - 2*x^30 - x^28*z0^2 + x^26*y*z0^3 - x^26*z0^4 + x^24*y^2*z0^4 - 2*x^29 - 2*x^27*y*z0 - 2*x^27*z0^2 - x^25*y*z0^3 + x^25*z0^4 + 2*x^28 + x^26*y*z0 + x^26*z0^2 + 2*x^24*y*z0^3 - 2*x^24*z0^4 + x^25*y*z0 + 2*x^26 - x^24*y*z0 + 2*x^24*z0^2 - 2*x^22*y*z0^3 - x^22*z0^4 + 2*x^23*y*z0 - x^23*z0^2 + x^21*y*z0^3 - x^21*z0^4 - x^24 + 2*x^22*y*z0 - x^22*z0^2 + x^20*y*z0^3 + 2*x^20*z0^4 + 2*x^21*y*z0 - 2*x^21*z0^2 + 2*x^19*y*z0^3 + 2*x^19*z0^4 + 2*x^22 + 2*x^20*y*z0 - x^20*z0^2 - 2*x^18*y*z0^3 + x^18*z0^4 + 2*x^21 + 2*x^19*y*z0 + x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 - x^20 - 2*x^18*y*z0 - x^18*z0^2 - 2*x^16*y*z0^3 + x^16*z0^4 - x^19 - x^17*y*z0 + 2*x^17*z0^2 - 2*x^15*z0^4 + 2*x^18 + x^16*y*z0 + x^16*z0^2 + x^14*y*z0^3 - x^14*z0^4 - 2*x^15*z0^2 + x^13*y*z0^3 - x^13*z0^4 - 2*x^16 - 2*x^14*y*z0 - 2*x^12*y*z0^3 - 2*x^12*z0^4 + x^15 + x^13*z0^2 - 2*x^11*y*z0^3 - x^11*z0^4 + 2*x^14 - x^12*z0^2 - 2*x^10*y*z0^3 + x^13 + 2*x^11*z0^2 + 2*x^9*y*z0^3 + x^9*z0^4 + 2*x^12 - 2*x^10*y*z0 + x^10*z0^2 + x^8*y*z0^3 - 2*x^8*z0^4 + 2*x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 - x^10 + 2*x^8*y*z0 - x^6*y*z0^3 + 2*x^6*z0^4 + x^9 - 2*x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 - x^4*z0^4 + x^5*y*z0 + 2*x^5*z0^2 - x^3*z0^4 - x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 - x^2*z0^4 - x^5 + x^3*y*z0 - x^3*z0^2 + x^2*y*z0 - x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 - x^60*z0^4 + x^58*y^2*z0^4 + 2*x^61*z0^2 + x^59*z0^4 + x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 + x^58*z0^4 - x^56*y^2*z0^4 + 2*x^61 + x^57*y^2*z0^2 + x^57*z0^4 + 2*x^60 - 2*x^58*y^2 - 2*x^58*z0^2 - x^56*z0^4 - 2*x^57*y^2 + x^57*z0^2 - x^55*z0^4 - 2*x^58 - x^54*z0^4 - 2*x^57 + 2*x^55*z0^2 + x^53*z0^4 - x^54*z0^2 + x^52*z0^4 + 2*x^55 + x^51*z0^4 + 2*x^54 - 2*x^52*z0^2 - x^50*z0^4 + x^51*z0^2 - x^49*z0^4 - 2*x^52 - x^48*z0^4 - 2*x^51 + 2*x^49*z0^2 + x^47*z0^4 - x^48*z0^2 + x^46*z0^4 + 2*x^49 + x^45*z0^4 + 2*x^48 - 2*x^46*z0^2 - x^44*z0^4 + x^45*z0^2 - x^43*z0^4 - 2*x^46 - x^42*z0^4 - 2*x^45 + 2*x^43*z0^2 + x^41*z0^4 - x^42*z0^2 + 2*x^40*y*z0^3 + 2*x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + x^39*z0^4 + 2*x^42 + x^40*y*z0 - x^40*z0^2 - x^38*y*z0^3 + 2*x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 + x^37*z0^4 + x^40 - x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + x^39 - x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 + 2*x^35*z0^4 + 2*x^38 + x^36*z0^2 - x^34*y*z0^3 + 2*x^37 + 2*x^35*y*z0 - x^35*z0^2 - 2*x^33*z0^4 - x^36 - 2*x^34*y*z0 + 2*x^34*z0^2 - x^32*y*z0^3 + x^32*z0^4 + 2*x^33*y*z0 + x^33*z0^2 - 2*x^31*y*z0^3 - x^34 - x^30*z0^4 - 2*x^33 - x^31*y*z0 + 2*x^31*z0^2 - x^29*y*z0^3 + x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 + 2*x^30*z0^2 - 2*x^28*y*z0^3 + 2*x^28*z0^4 - 2*x^31 - 2*x^29*y*z0 + x^29*z0^2 - 2*x^27*y*z0^3 + x^27*z0^4 + x^28*y*z0 - x^28*z0^2 - x^26*y*z0^3 - 2*x^26*z0^4 - x^29 + 2*x^27*y*z0 - 2*x^27*z0^2 - 2*x^25*y*z0^3 - x^25*z0^4 + 2*x^28 + x^26*y*z0 - x^26*z0^2 - 2*x^24*y*z0^3 + x^24*z0^4 + x^27 + x^25*y^2 - 2*x^25*y*z0 + 2*x^25*z0^2 - 2*x^23*y*z0^3 - x^23*z0^4 - 2*x^24*y*z0 + 2*x^22*z0^4 - 2*x^25 + 2*x^23*y*z0 + x^23*z0^2 - 2*x^21*y*z0^3 + x^21*z0^4 + x^24 - x^22*y*z0 + x^22*z0^2 - x^20*y*z0^3 + x^20*z0^4 + x^23 + x^21*y*z0 + 2*x^21*z0^2 - x^19*y*z0^3 + x^19*z0^4 - 2*x^22 - x^20*y*z0 - x^18*y*z0^3 - x^18*z0^4 - 2*x^21 + 2*x^19*y*z0 - 2*x^19*z0^2 + x^17*z0^4 - x^20 - 2*x^18*y*z0 - x^18*z0^2 - 2*x^16*y*z0^3 - x^16*z0^4 - 2*x^19 - 2*x^17*z0^2 - 2*x^15*z0^4 - x^18 + x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 - 2*x^17 - 2*x^15*y*z0 - 2*x^15*z0^2 + x^13*y*z0^3 - 2*x^13*z0^4 + 2*x^16 + x^14*z0^2 - x^12*y*z0^3 + x^12*z0^4 + 2*x^15 - 2*x^13*y*z0 - 2*x^13*z0^2 + x^11*y*z0^3 - x^14 + x^12*y*z0 + x^12*z0^2 + x^10*y*z0^3 + 2*x^10*z0^4 - x^11*y*z0 + 2*x^11*z0^2 - x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 - x^8*z0^4 - 2*x^9*y*z0 - 2*x^9*z0^2 - 2*x^7*y*z0^3 - 2*x^7*z0^4 + x^10 + 2*x^8*y*z0 + x^6*z0^4 - 2*x^9 - x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + 2*x^5*z0^4 + x^8 + x^6*y*z0 - x^6*z0^2 + x^4*y*z0^3 + x^4*z0^4 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^6 - x^4*y*z0 + 2*x^4*z0^2 - 2*x^2*z0^4 - 2*x^3*y*z0 + 2*x^2*y*z0 + 2*x^2*z0^2)/y) * dx, - ((-x^61*z0^3 - x^60*z0^3 + x^58*y^2*z0^3 + x^59*z0^3 + x^57*y^2*z0^3 - x^60*z0 + x^58*z0^3 - x^56*y^2*z0^3 + x^59*z0 + x^57*y^2*z0 + x^57*z0^3 - x^56*y^2*z0 - x^56*z0^3 + x^57*z0 - x^55*z0^3 - x^56*z0 - x^54*z0^3 + x^53*z0^3 - x^54*z0 + x^52*z0^3 + x^53*z0 + x^51*z0^3 - x^50*z0^3 + x^51*z0 - x^49*z0^3 - x^50*z0 - x^48*z0^3 + x^47*z0^3 - x^48*z0 + x^46*z0^3 + x^47*z0 + x^45*z0^3 - x^44*z0^3 + x^45*z0 - x^43*z0^3 - x^44*z0 - x^42*z0^3 - x^39*y*z0^4 - x^42*z0 + 2*x^40*y*z0^2 - 2*x^40*z0^3 + x^41*z0 + x^37*y*z0^4 + 2*x^40*z0 - 2*x^38*z0^3 - x^36*y*z0^4 + x^39*y - 2*x^39*z0 - 2*x^37*y*z0^2 + 2*x^35*y*z0^4 - x^38*y + 2*x^36*y*z0^2 - 2*x^36*z0^3 - 2*x^34*y*z0^4 - x^37*z0 + x^35*y*z0^2 + 2*x^35*z0^3 - x^33*y*z0^4 - 2*x^34*y*z0^2 - x^34*z0^3 + 2*x^32*y*z0^4 + x^35*y + x^33*y*z0^2 + 2*x^31*y*z0^4 - 2*x^34*y + 2*x^34*z0 + x^30*y*z0^4 - x^33*y - x^33*z0 - x^31*y*z0^2 + 2*x^31*z0^3 + x^29*y*z0^4 - 2*x^30*z0^3 + 2*x^28*y*z0^4 + 2*x^31*y + x^31*z0 - 2*x^29*y*z0^2 + 2*x^29*z0^3 + 2*x^27*y*z0^4 + x^30*y - x^30*z0 - 2*x^28*y*z0^2 - x^28*z0^3 - x^26*y*z0^4 + 2*x^29*y - 2*x^29*z0 - x^27*z0^3 - x^25*y*z0^4 - 2*x^28*y + x^28*z0 - 2*x^27*y + x^27*z0 + x^25*y^2*z0 - 2*x^25*y*z0^2 - 2*x^25*z0^3 - x^26*y + x^24*z0^3 + 2*x^22*y*z0^4 - x^25*y - 2*x^23*y*z0^2 + x^23*z0^3 - x^21*y*z0^4 - x^24*y - 2*x^24*z0 - 2*x^22*y*z0^2 + 2*x^22*z0^3 - x^20*y*z0^4 + x^23*z0 + 2*x^19*y*z0^4 - x^20*z0^3 + x^18*y*z0^4 - 2*x^21*y + x^21*z0 - 2*x^19*y*z0^2 - x^17*y*z0^4 - 2*x^20*z0 + x^18*y*z0^2 + 2*x^18*z0^3 + x^19*y - x^17*y*z0^2 - 2*x^17*z0^3 - 2*x^15*y*z0^4 + x^18*y - x^18*z0 + x^16*y*z0^2 + x^16*z0^3 + x^17*y - x^15*y*z0^2 - 2*x^15*z0^3 + x^13*y*z0^4 + x^16*z0 + 2*x^14*y*z0^2 + x^14*z0^3 + x^15*z0 - x^13*y*z0^2 - 2*x^12*y*z0^2 + x^10*y*z0^4 - x^13*y - 2*x^11*z0^3 - x^12*y - 2*x^12*z0 + x^10*y*z0^2 + x^8*y*z0^4 + 2*x^11*y + x^11*z0 - 2*x^9*y*z0^2 - 2*x^9*z0^3 - x^10*y + 2*x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^9*y - x^9*z0 - x^7*y*z0^2 - x^7*z0^3 + 2*x^8*y + x^8*z0 + x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^7*y - x^7*z0 - x^5*z0^3 + x^3*y*z0^4 - 2*x^6*z0 - 2*x^4*y*z0^2 + 2*x^4*z0^3 - x^5*y - x^3*y*z0^2 + x^4*y - 2*x^4*z0 + x^2*y*z0^2 + 2*x^2*z0^3 - 2*x^3*y + x^3*z0 + x^2*z0)/y) * dx, - ((2*x^61*z0^4 - 2*x^60*z0^4 - 2*x^58*y^2*z0^4 + 2*x^57*y^2*z0^4 - 2*x^60*z0^2 - 2*x^58*z0^4 - 2*x^61 + 2*x^57*y^2*z0^2 + 2*x^57*z0^4 + x^60 + 2*x^58*y^2 - x^57*y^2 + 2*x^57*z0^2 + 2*x^55*z0^4 + 2*x^58 - 2*x^54*z0^4 - x^57 - 2*x^54*z0^2 - 2*x^52*z0^4 - 2*x^55 + 2*x^51*z0^4 + x^54 + 2*x^51*z0^2 + 2*x^49*z0^4 + 2*x^52 - 2*x^48*z0^4 - x^51 - 2*x^48*z0^2 - 2*x^46*z0^4 - 2*x^49 + 2*x^45*z0^4 + x^48 + 2*x^45*z0^2 + 2*x^43*z0^4 + 2*x^46 - 2*x^42*z0^4 - x^45 + x^41*z0^4 - 2*x^42*z0^2 + x^40*y*z0^3 - x^40*z0^4 - 2*x^43 - x^39*z0^4 + x^42 + 2*x^38*y*z0^3 + 2*x^38*z0^4 + x^41 + x^39*y*z0 + 2*x^39*z0^2 - 2*x^37*y*z0^3 - 2*x^37*z0^4 - 2*x^40 - 2*x^38*y*z0 - x^39 - 2*x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 - x^35*z0^4 + 2*x^38 + 2*x^36*y*z0 - 2*x^36*z0^2 - 2*x^34*y*z0^3 + 2*x^37 + x^35*y*z0 - 2*x^35*z0^2 - x^33*y*z0^3 - x^33*z0^4 + x^34*z0^2 + x^32*y*z0^3 - 2*x^32*z0^4 + x^33*y*z0 + x^33*z0^2 - x^34 + 2*x^32*y*z0 - 2*x^32*z0^2 + x^30*y*z0^3 + x^33 + x^31*z0^2 + 2*x^29*z0^4 + x^30*y*z0 - 2*x^30*z0^2 - x^28*y*z0^3 + x^28*z0^4 - 2*x^31 + 2*x^29*y*z0 + 2*x^29*z0^2 - x^27*y*z0^3 - x^27*z0^4 - 2*x^30 - x^28*y*z0 + 2*x^28*z0^2 + 2*x^26*y*z0^3 + x^26*z0^4 + 2*x^29 - x^27*y*z0 + x^27*z0^2 + x^25*y^2*z0^2 - x^25*y*z0^3 - x^25*z0^4 + x^28 - x^26*y*z0 + x^26*z0^2 + x^24*y*z0^3 + x^24*z0^4 - x^27 + x^25*y*z0 - 2*x^25*z0^2 + x^23*y*z0^3 + x^23*z0^4 + x^26 - 2*x^24*y*z0 + 2*x^24*z0^2 - 2*x^22*y*z0^3 - x^22*z0^4 - 2*x^25 + 2*x^23*y*z0 + 2*x^23*z0^2 + x^21*y*z0^3 - 2*x^21*z0^4 + 2*x^22*y*z0 + x^20*y*z0^3 - x^20*z0^4 - 2*x^23 - 2*x^21*y*z0 - x^21*z0^2 + 2*x^19*y*z0^3 + 2*x^19*z0^4 - 2*x^22 - 2*x^20*y*z0 + x^20*z0^2 - 2*x^18*y*z0^3 + 2*x^18*z0^4 + x^21 - 2*x^19*y*z0 - 2*x^19*z0^2 - 2*x^17*y*z0^3 + 2*x^20 + x^18*y*z0 + 2*x^18*z0^2 + 2*x^16*y*z0^3 - 2*x^16*z0^4 + 2*x^19 - x^17*y*z0 - x^17*z0^2 + 2*x^15*y*z0^3 + 2*x^15*z0^4 - 2*x^18 - x^16*y*z0 + 2*x^16*z0^2 - x^14*y*z0^3 - x^17 - 2*x^15*y*z0 + 2*x^13*z0^4 + 2*x^16 - x^14*y*z0 + x^12*y*z0^3 + 2*x^12*z0^4 - 2*x^13*y*z0 + 2*x^13*z0^2 - 2*x^11*y*z0^3 + x^11*z0^4 - 2*x^12*y*z0 - x^12*z0^2 - x^10*y*z0^3 - x^10*z0^4 - x^13 - x^11*y*z0 - 2*x^11*z0^2 + x^9*y*z0^3 + 2*x^9*z0^4 - x^12 - 2*x^10*y*z0 - x^8*y*z0^3 + 2*x^11 + x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 + 2*x^8*y*z0 + x^8*z0^2 - x^6*y*z0^3 + 2*x^6*z0^4 + 2*x^9 - x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 - x^6*y*z0 - x^4*y*z0^3 + x^4*z0^4 - x^7 + 2*x^5*y*z0 - 2*x^5*z0^2 + x^3*y*z0^3 + x^6 + x^4*y*z0 - 2*x^2*y*z0^3 - x^2*z0^4 + x^3*y*z0 + x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - 2*x^3 + x^2)/y) * dx, - ((-2*x^61*z0^3 + x^60*z0^3 + 2*x^58*y^2*z0^3 + x^61*z0 + 2*x^59*z0^3 - x^57*y^2*z0^3 + 2*x^60*z0 - x^58*y^2*z0 - 2*x^56*y^2*z0^3 + x^59*z0 - 2*x^57*y^2*z0 + 2*x^57*z0^3 + 2*x^55*y^2*z0^3 - x^58*z0 - x^56*y^2*z0 - 2*x^56*z0^3 + 2*x^54*y^2*z0^3 - 2*x^57*z0 - x^56*z0 - 2*x^54*z0^3 + x^55*z0 + 2*x^53*z0^3 + 2*x^54*z0 + x^53*z0 + 2*x^51*z0^3 - x^52*z0 - 2*x^50*z0^3 - 2*x^51*z0 - x^50*z0 - 2*x^48*z0^3 + x^49*z0 + 2*x^47*z0^3 + 2*x^48*z0 + x^47*z0 + 2*x^45*z0^3 - x^46*z0 - 2*x^44*z0^3 - 2*x^45*z0 - x^44*z0 - 2*x^42*z0^3 + x^43*z0 - 2*x^39*y*z0^4 + 2*x^42*z0 - x^40*y*z0^2 - 2*x^40*z0^3 + 2*x^38*y*z0^4 + 2*x^41*z0 + x^39*y*z0^2 - x^39*z0^3 - x^37*y*z0^4 - 2*x^40*y + 2*x^40*z0 - 2*x^38*y*z0^2 + x^38*z0^3 - 2*x^36*y*z0^4 + x^39*y - x^39*z0 + x^35*y*z0^4 + 2*x^38*z0 + 2*x^36*z0^3 + x^34*y*z0^4 + x^37*y - 2*x^37*z0 - 2*x^35*y*z0^2 - x^35*z0^3 + x^33*y*z0^4 + 2*x^36*y - x^36*z0 + x^34*y*z0^2 - 2*x^34*z0^3 + 2*x^32*y*z0^4 + 2*x^35*y + 2*x^35*z0 + 2*x^33*z0^3 - x^31*y*z0^4 + x^34*y - x^32*z0^3 + x^30*y*z0^4 + 2*x^33*z0 + x^31*y*z0^2 + 2*x^31*z0^3 - x^29*y*z0^4 - x^32*y - x^32*z0 - x^30*y*z0^2 + 2*x^30*z0^3 + x^28*y*z0^4 + x^31*z0 + 2*x^29*y*z0^2 + 2*x^29*z0^3 - x^27*y*z0^4 - x^30*y + x^30*z0 - 2*x^28*y*z0^2 - 2*x^28*z0^3 - 2*x^26*y*z0^4 - 2*x^29*y + x^29*z0 - 2*x^27*z0^3 + x^25*y^2*z0^3 + 2*x^28*y - 2*x^28*z0 + x^26*y*z0^2 + 2*x^26*z0^3 - 2*x^27*y - x^27*z0 + x^25*y*z0^2 + 2*x^23*y*z0^4 + 2*x^26*z0 + x^24*y*z0^2 - x^24*z0^3 - x^22*y*z0^4 - x^25*y + x^25*z0 + x^23*y*z0^2 + 2*x^23*z0^3 - 2*x^24*y - 2*x^24*z0 + x^22*y*z0^2 + 2*x^22*z0^3 - 2*x^20*y*z0^4 - 2*x^23*y - x^23*z0 + x^21*y*z0^2 + 2*x^19*y*z0^4 - 2*x^22*y + x^22*z0 + 2*x^20*y*z0^2 + x^20*z0^3 - x^18*y*z0^4 - x^21*y - x^19*y*z0^2 + 2*x^17*y*z0^4 - x^20*y - 2*x^18*y*z0^2 - 2*x^16*y*z0^4 + 2*x^19*y - 2*x^19*z0 + x^17*z0^3 - 2*x^15*y*z0^4 + 2*x^18*y + x^18*z0 + x^16*z0^3 + 2*x^14*y*z0^4 - 2*x^17*y + 2*x^15*y*z0^2 + x^13*y*z0^4 + 2*x^16*y - 2*x^16*z0 + x^14*y*z0^2 + 2*x^14*z0^3 + 2*x^15*y + 2*x^15*z0 - 2*x^13*z0^3 - 2*x^11*y*z0^4 + 2*x^12*y*z0^2 + 2*x^12*z0^3 - 2*x^13*y - x^11*y*z0^2 - x^11*z0^3 - 2*x^12*y + 2*x^12*z0 + x^10*y*z0^2 - x^10*z0^3 - 2*x^8*y*z0^4 - 2*x^11*y - x^11*z0 + x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y - x^10*z0 + x^8*y*z0^2 + 2*x^8*z0^3 - x^6*y*z0^4 - x^9*y + 2*x^9*z0 + 2*x^7*y*z0^2 - x^7*z0^3 - 2*x^8*y - x^8*z0 - x^6*y*z0^2 - x^6*z0^3 + 2*x^4*y*z0^4 - x^7*y - x^7*z0 - x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - x^6*y + 2*x^4*y*z0^2 + 2*x^4*z0^3 + 2*x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - 2*x^3*y*z0^2 - x^3*z0^3 - x^4*y + 2*x^4*z0 + 2*x^3*y + 2*x^3*z0)/y) * dx, - ((x^61*z0^4 + x^60*z0^4 - x^58*y^2*z0^4 + 2*x^61*z0^2 - 2*x^59*z0^4 - x^57*y^2*z0^4 - 2*x^58*y^2*z0^2 - x^58*z0^4 + 2*x^56*y^2*z0^4 + x^61 - x^57*z0^4 - 2*x^60 - x^58*y^2 - 2*x^58*z0^2 + 2*x^56*z0^4 + 2*x^57*y^2 + x^55*z0^4 - x^58 + x^54*z0^4 + 2*x^57 + 2*x^55*z0^2 - 2*x^53*z0^4 - x^52*z0^4 + x^55 - x^51*z0^4 - 2*x^54 - 2*x^52*z0^2 + 2*x^50*z0^4 + x^49*z0^4 - x^52 + x^48*z0^4 + 2*x^51 + 2*x^49*z0^2 - 2*x^47*z0^4 - x^46*z0^4 + x^49 - x^45*z0^4 - 2*x^48 - 2*x^46*z0^2 + 2*x^44*z0^4 + x^43*z0^4 - x^46 + x^42*z0^4 + 2*x^45 + 2*x^43*z0^2 + 2*x^41*z0^4 - 2*x^40*y*z0^3 + x^40*z0^4 + x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 - 2*x^42 + x^40*y*z0 + x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + x^39*y*z0 - 2*x^39*z0^2 - x^37*y*z0^3 - x^37*z0^4 - 2*x^40 + 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 + 2*x^39 + 2*x^37*y*z0 - 2*x^37*z0^2 - x^35*y*z0^3 - x^35*z0^4 - x^38 + 2*x^36*y*z0 + 2*x^36*z0^2 + x^34*z0^4 - x^37 + x^35*y*z0 - 2*x^35*z0^2 - x^33*y*z0^3 + 2*x^33*z0^4 - x^36 - 2*x^34*y*z0 + 2*x^34*z0^2 - x^32*z0^4 - x^33*y*z0 - x^33*z0^2 + x^31*y*z0^3 + 2*x^31*z0^4 + 2*x^32*y*z0 + 2*x^32*z0^2 - x^30*y*z0^3 + x^30*z0^4 - x^33 + 2*x^31*y*z0 + x^31*z0^2 + 2*x^29*y*z0^3 - x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 - 2*x^30*z0^2 + 2*x^28*z0^4 - 2*x^31 - 2*x^29*z0^2 + 2*x^27*y*z0^3 - 2*x^27*z0^4 + x^25*y^2*z0^4 + x^30 + x^28*y*z0 + x^26*y*z0^3 - x^26*z0^4 + x^29 - x^27*y*z0 - x^27*z0^2 - 2*x^25*z0^4 - x^28 + x^26*y*z0 - 2*x^26*z0^2 - 2*x^27 - 2*x^25*y*z0 - x^25*z0^2 - x^23*y*z0^3 - x^23*z0^4 - 2*x^26 + x^24*y*z0 + x^24*z0^2 + 2*x^22*y*z0^3 + x^22*z0^4 + x^25 + 2*x^23*y*z0 - x^23*z0^2 - 2*x^21*y*z0^3 - x^22*z0^2 - x^20*y*z0^3 - x^20*z0^4 - 2*x^23 - x^19*y*z0^3 + x^19*z0^4 + 2*x^22 - 2*x^20*y*z0 - 2*x^20*z0^2 + 2*x^18*y*z0^3 - 2*x^18*z0^4 + x^21 - x^19*y*z0 - 2*x^19*z0^2 + x^17*y*z0^3 + x^17*z0^4 + 2*x^18*y*z0 + 2*x^18*z0^2 - 2*x^16*z0^4 - x^19 + 2*x^17*y*z0 - x^15*z0^4 + x^18 + 2*x^16*y*z0 + x^16*z0^2 - 2*x^14*y*z0^3 - 2*x^14*z0^4 - x^17 - x^15*y*z0 + 2*x^15*z0^2 - 2*x^13*z0^4 + x^16 - x^14*z0^2 - 2*x^12*y*z0^3 - x^12*z0^4 - x^15 - x^13*y*z0 + 2*x^13*z0^2 + 2*x^11*y*z0^3 - 2*x^11*z0^4 - x^14 - 2*x^12*y*z0 - 2*x^12*z0^2 - x^10*y*z0^3 + 2*x^10*z0^4 - 2*x^13 + 2*x^11*y*z0 - 2*x^11*z0^2 + x^9*y*z0^3 - x^12 + 2*x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^9*y*z0 - x^9*z0^2 + 2*x^7*y*z0^3 - 2*x^7*z0^4 + x^10 + 2*x^8*y*z0 + 2*x^8*z0^2 + 2*x^6*y*z0^3 + x^6*z0^4 - x^9 + x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 - 2*x^6*y*z0 + 2*x^4*y*z0^3 - 2*x^7 + 2*x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 + 2*x^5 - x^3*y*z0 - 2*x^3*z0^2 + x^3 - 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-2*x^60*z0^4 + 2*x^61*z0^2 - x^59*z0^4 + 2*x^57*y^2*z0^4 + 2*x^60*z0^2 - 2*x^58*y^2*z0^2 + x^56*y^2*z0^4 - x^61 - 2*x^57*y^2*z0^2 + 2*x^57*z0^4 - 2*x^60 + x^58*y^2 - 2*x^58*z0^2 + x^56*z0^4 + 2*x^57*y^2 - 2*x^57*z0^2 + x^58 - 2*x^54*z0^4 + 2*x^57 + 2*x^55*z0^2 - x^53*z0^4 + 2*x^54*z0^2 - x^55 + 2*x^51*z0^4 - 2*x^54 - 2*x^52*z0^2 + x^50*z0^4 - 2*x^51*z0^2 + x^52 - 2*x^48*z0^4 + 2*x^51 + 2*x^49*z0^2 - x^47*z0^4 + 2*x^48*z0^2 - x^49 + 2*x^45*z0^4 - 2*x^48 - 2*x^46*z0^2 + x^44*z0^4 - 2*x^45*z0^2 + x^46 - 2*x^42*z0^4 + 2*x^45 + 2*x^43*z0^2 + x^41*z0^4 + 2*x^42*z0^2 - x^40*z0^4 - x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^39*z0^4 - 2*x^42 + x^40*y*z0 - x^40*z0^2 - x^38*y*z0^3 - x^38*z0^4 + 2*x^41 - 2*x^39*y*z0 + x^39*z0^2 + x^37*y*z0^3 - 2*x^37*z0^4 - x^40 + 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 - x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 - 2*x^35*z0^4 + 2*x^38 + x^36*y*z0 - x^36*z0^2 + 2*x^34*y*z0^3 + x^34*z0^4 - x^37 + 2*x^35*z0^2 - x^33*y*z0^3 + 2*x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 + x^34*z0^2 - x^32*z0^4 + x^35 - x^33*y*z0 - x^33*z0^2 - 2*x^31*z0^4 + 2*x^34 + 2*x^32*y*z0 + x^32*z0^2 + x^30*y*z0^3 + x^30*z0^4 - 2*x^33 + 2*x^31*z0^2 - x^29*y*z0^3 + 2*x^29*z0^4 + x^32 + 2*x^30*y*z0 + x^30*z0^2 + 2*x^28*y*z0^3 - 2*x^28*z0^4 - x^31 - x^29*y*z0 - x^29*z0^2 + x^27*y*z0^3 - 2*x^30 + x^28*y*z0 + x^26*y*z0^3 + 2*x^26*z0^4 - x^27*z0^2 - x^25*y*z0^3 - 2*x^25*z0^4 + x^26*y^2 + 2*x^26*y*z0 + x^26*z0^2 - x^24*y*z0^3 + 2*x^24*z0^4 + x^27 + x^25*y*z0 + x^25*z0^2 + 2*x^23*y*z0^3 + x^24*y*z0 - x^24*z0^2 + 2*x^22*y*z0^3 - 2*x^22*z0^4 + x^25 + 2*x^23*y*z0 + x^23*z0^2 - 2*x^21*y*z0^3 - 2*x^21*z0^4 + x^24 + x^22*y*z0 - x^20*y*z0^3 - 2*x^21*y*z0 + x^19*y*z0^3 + x^19*z0^4 + x^22 + x^20*y*z0 + x^20*z0^2 - x^18*z0^4 - x^21 + x^19*y*z0 + 2*x^17*z0^4 + 2*x^20 + x^18*y*z0 + x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 - x^17*y*z0 + x^17*z0^2 - 2*x^15*y*z0^3 - 2*x^15*z0^4 + x^18 + x^16*y*z0 - 2*x^16*z0^2 + 2*x^14*y*z0^3 - x^14*z0^4 + 2*x^17 + 2*x^15*y*z0 + x^15*z0^2 - x^13*y*z0^3 + 2*x^13*z0^4 + x^16 + 2*x^14*y*z0 + x^14*z0^2 - 2*x^12*y*z0^3 + x^13*y*z0 - 2*x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 - x^14 - 2*x^12*y*z0 + 2*x^10*y*z0^3 - 2*x^13 + x^11*y*z0 + x^11*z0^2 - x^9*y*z0^3 - x^9*z0^4 + x^12 + 2*x^10*y*z0 - 2*x^10*z0^2 + 2*x^8*y*z0^3 + x^8*z0^4 + x^11 + x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^8*z0^2 + x^6*y*z0^3 + x^6*z0^4 + x^9 + 2*x^7*y*z0 - 2*x^7*z0^2 - 2*x^5*y*z0^3 + x^5*z0^4 + 2*x^8 + x^6*y*z0 + 2*x^6*z0^2 + x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + x^5*y*z0 - x^5*z0^2 + 2*x^3*z0^4 - x^6 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*z0^2 + x^3 - 2*x^2)/y) * dx, - ((2*x^61*z0^3 - 2*x^60*z0^3 - 2*x^58*y^2*z0^3 + x^61*z0 - x^59*z0^3 + 2*x^57*y^2*z0^3 - x^58*y^2*z0 + x^58*z0^3 + x^56*y^2*z0^3 - 2*x^59*z0 + 2*x^57*z0^3 + 2*x^55*y^2*z0^3 - x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 - x^55*z0^3 + 2*x^56*z0 - 2*x^54*z0^3 + x^55*z0 - x^53*z0^3 + x^52*z0^3 - 2*x^53*z0 + 2*x^51*z0^3 - x^52*z0 + x^50*z0^3 - x^49*z0^3 + 2*x^50*z0 - 2*x^48*z0^3 + x^49*z0 - x^47*z0^3 + x^46*z0^3 - 2*x^47*z0 + 2*x^45*z0^3 - x^46*z0 + x^44*z0^3 - x^43*z0^3 + 2*x^44*z0 - 2*x^42*z0^3 + x^43*z0 + x^41*z0^3 + 2*x^39*y*z0^4 + x^40*y*z0^2 - x^40*z0^3 - x^41*z0 + x^39*y*z0^2 + x^39*z0^3 + 2*x^37*y*z0^4 - 2*x^40*y + x^38*y*z0^2 - x^38*z0^3 - x^36*y*z0^4 + x^39*y + 2*x^37*y*z0^2 + x^37*z0^3 + x^35*y*z0^4 - 2*x^38*y + 2*x^38*z0 - x^36*y*z0^2 + x^36*z0^3 - x^34*y*z0^4 + x^37*y + 2*x^37*z0 - 2*x^35*y*z0^2 - 2*x^35*z0^3 - x^33*y*z0^4 + 2*x^36*y - x^36*z0 + 2*x^34*y*z0^2 - x^32*y*z0^4 - x^35*y + 2*x^35*z0 + x^33*y*z0^2 + 2*x^33*z0^3 - 2*x^31*y*z0^4 + x^34*y - 2*x^34*z0 + 2*x^32*y*z0^2 + x^32*z0^3 - 2*x^30*y*z0^4 + 2*x^33*y + x^33*z0 + x^31*z0^3 - 2*x^32*z0 - 2*x^30*y*z0^2 + 2*x^30*z0^3 + 2*x^28*y*z0^4 + 2*x^31*y + x^31*z0 + 2*x^29*y*z0^2 + 2*x^29*z0^3 + 2*x^27*y*z0^4 + 2*x^30*y - 2*x^30*z0 + x^28*y*z0^2 - 2*x^28*z0^3 - 2*x^29*y - x^29*z0 - x^27*y*z0^2 - 2*x^27*z0^3 + x^25*y*z0^4 - 2*x^28*y + 2*x^28*z0 + x^26*y^2*z0 + 2*x^26*z0^3 - x^24*y*z0^4 - x^27*y - 2*x^27*z0 + 2*x^25*y*z0^2 - x^25*z0^3 + x^26*y - 2*x^26*z0 + x^24*y*z0^2 + 2*x^24*z0^3 - 2*x^22*y*z0^4 - x^25*z0 + 2*x^23*y*z0^2 + x^23*z0^3 - 2*x^21*y*z0^4 + x^24*y + 2*x^20*y*z0^4 - 2*x^23*y + x^23*z0 - x^21*y*z0^2 + x^21*z0^3 - 2*x^19*y*z0^4 + x^22*z0 + 2*x^20*y*z0^2 - 2*x^20*z0^3 + 2*x^21*y + x^19*y*z0^2 - x^19*z0^3 - x^18*y*z0^2 + x^18*z0^3 - 2*x^16*y*z0^4 - 2*x^17*y*z0^2 - 2*x^17*z0^3 - 2*x^15*y*z0^4 + 2*x^16*y*z0^2 + x^16*z0^3 - 2*x^17*y + x^15*y*z0^2 - 2*x^16*y + x^16*z0 + 2*x^14*y*z0^2 - x^14*z0^3 - x^12*y*z0^4 - 2*x^15*y - x^13*y*z0^2 + 2*x^13*z0^3 + 2*x^11*y*z0^4 - 2*x^14*y - x^14*z0 - 2*x^12*z0^3 + 2*x^13*y + x^13*z0 - 2*x^11*y*z0^2 + x^11*z0^3 + x^9*y*z0^4 - x^12*z0 - 2*x^10*y*z0^2 - x^10*z0^3 - x^8*y*z0^4 - x^11*y + x^11*z0 + x^9*y*z0^2 + x^9*z0^3 - 2*x^7*y*z0^4 - 2*x^10*y - 2*x^10*z0 + x^8*y*z0^2 + 2*x^8*z0^3 - 2*x^6*y*z0^4 - x^9*y + x^9*z0 + x^7*y*z0^2 + x^7*z0^3 - x^5*y*z0^4 - 2*x^8*z0 + 2*x^6*y*z0^2 - x^6*z0^3 + x^4*y*z0^4 + 2*x^7*y + 2*x^7*z0 - 2*x^5*y*z0^2 - x^5*z0^3 + x^3*y*z0^4 + x^6*y + x^6*z0 - 2*x^4*z0^3 - x^2*y*z0^4 - x^5*y + x^5*z0 - 2*x^3*y*z0^2 - x^4*y + x^2*y*z0^2 + 2*x^2*z0^3 + x^3*z0)/y) * dx, - ((-2*x^61*z0^4 - x^60*z0^4 + 2*x^58*y^2*z0^4 + x^61*z0^2 + x^57*y^2*z0^4 - x^60*z0^2 - x^58*y^2*z0^2 + 2*x^58*z0^4 + 2*x^61 + x^57*y^2*z0^2 + x^57*z0^4 + 2*x^60 - 2*x^58*y^2 - x^58*z0^2 - 2*x^57*y^2 + x^57*z0^2 - 2*x^55*z0^4 - 2*x^58 - x^54*z0^4 - 2*x^57 + x^55*z0^2 - x^54*z0^2 + 2*x^52*z0^4 + 2*x^55 + x^51*z0^4 + 2*x^54 - x^52*z0^2 + x^51*z0^2 - 2*x^49*z0^4 - 2*x^52 - x^48*z0^4 - 2*x^51 + x^49*z0^2 - x^48*z0^2 + 2*x^46*z0^4 + 2*x^49 + x^45*z0^4 + 2*x^48 - x^46*z0^2 + x^45*z0^2 - 2*x^43*z0^4 - 2*x^46 - x^42*z0^4 - 2*x^45 + x^43*z0^2 - x^41*z0^4 - x^42*z0^2 - x^40*y*z0^3 + 2*x^40*z0^4 + 2*x^43 + x^41*z0^2 + x^39*y*z0^3 + 2*x^42 - 2*x^40*y*z0 + 2*x^40*z0^2 + x^38*y*z0^3 - 2*x^38*z0^4 - x^41 - x^37*y*z0^3 + x^37*z0^4 + 2*x^40 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - 2*x^36*z0^4 + x^39 - 2*x^37*y*z0 + x^37*z0^2 - 2*x^35*y*z0^3 - x^35*z0^4 - 2*x^38 + 2*x^36*y*z0 - x^34*y*z0^3 + x^37 + 2*x^35*y*z0 - 2*x^35*z0^2 - x^33*y*z0^3 + 2*x^33*z0^4 - x^34*y*z0 - 2*x^32*y*z0^3 + 2*x^32*z0^4 + 2*x^35 + x^33*y*z0 - x^33*z0^2 + x^31*y*z0^3 + 2*x^31*z0^4 - x^34 + x^32*y*z0 + 2*x^32*z0^2 + 2*x^33 - 2*x^31*y*z0 - x^31*z0^2 + x^29*y*z0^3 - x^29*z0^4 + 2*x^32 + 2*x^30*z0^2 - 2*x^28*y*z0^3 - x^28*z0^4 + x^31 - 2*x^29*z0^2 + x^27*y*z0^3 + x^27*z0^4 + 2*x^30 + 2*x^28*z0^2 + x^26*y^2*z0^2 + 2*x^26*y*z0^3 - 2*x^26*z0^4 + 2*x^27*y*z0 + x^27*z0^2 - x^25*y*z0^3 - x^25*z0^4 - x^28 + 2*x^26*y*z0 - 2*x^24*y*z0^3 + x^24*z0^4 - x^25*y*z0 + 2*x^25*z0^2 + x^23*y*z0^3 + 2*x^23*z0^4 + 2*x^26 + 2*x^24*y*z0 - 2*x^24*z0^2 + 2*x^22*y*z0^3 - x^25 - 2*x^23*y*z0 + x^23*z0^2 + x^21*z0^4 - 2*x^24 + 2*x^22*y*z0 - x^22*z0^2 - x^20*z0^4 + 2*x^23 - x^21*z0^2 + x^19*y*z0^3 - x^20*y*z0 - x^18*y*z0^3 + x^18*z0^4 + 2*x^21 + x^19*y*z0 - 2*x^19*z0^2 + x^17*y*z0^3 - x^17*z0^4 + 2*x^20 - 2*x^16*y*z0^3 + 2*x^16*z0^4 + x^19 - x^17*y*z0 + x^17*z0^2 - 2*x^15*y*z0^3 + 2*x^15*z0^4 - 2*x^18 - 2*x^16*y*z0 - 2*x^16*z0^2 + 2*x^14*y*z0^3 - x^14*z0^4 - x^17 + x^15*y*z0 + x^15*z0^2 + x^13*z0^4 + 2*x^14*y*z0 + 2*x^12*y*z0^3 - 2*x^12*z0^4 - 2*x^13*y*z0 + 2*x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 - 2*x^12*y*z0 - 2*x^12*z0^2 - 2*x^10*y*z0^3 - x^10*z0^4 + x^13 + x^11*y*z0 + x^11*z0^2 - 2*x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 + x^8*y*z0^3 + x^11 + x^9*z0^2 - 2*x^7*y*z0^3 + 2*x^7*z0^4 + x^10 - 2*x^8*y*z0 - 2*x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 + 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + 2*x^8 + 2*x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 + x^7 - x^5*z0^2 - 2*x^3*z0^4 + 2*x^4*y*z0 - x^4*z0^2 + x^5 - x^3*y*z0 + x^3*z0^2 - 2*x^2*y*z0 + x^2*z0^2 + x^3 + x^2)/y) * dx, - ((-x^61*z0^3 - 2*x^60*z0^3 + x^58*y^2*z0^3 + 2*x^57*y^2*z0^3 - 2*x^60*z0 + x^58*z0^3 + x^59*z0 + 2*x^57*y^2*z0 - x^56*y^2*z0 + 2*x^54*y^2*z0^3 + 2*x^57*z0 - x^55*z0^3 - x^56*z0 - 2*x^54*z0 + x^52*z0^3 + x^53*z0 + 2*x^51*z0 - x^49*z0^3 - x^50*z0 - 2*x^48*z0 + x^46*z0^3 + x^47*z0 + 2*x^45*z0 - x^43*z0^3 - x^44*z0 - x^41*z0^3 - x^39*y*z0^4 - 2*x^42*z0 + 2*x^40*y*z0^2 - 2*x^40*z0^3 + x^41*z0 + 2*x^39*z0^3 + 2*x^37*y*z0^4 - x^40*z0 - 2*x^38*y*z0^2 - 2*x^38*z0^3 + 2*x^36*y*z0^4 - 2*x^39*y - x^39*z0 + 2*x^37*y*z0^2 + 2*x^37*z0^3 - 2*x^35*y*z0^4 + x^38*y + 2*x^36*y*z0^2 - 2*x^36*z0^3 + 2*x^37*z0 + 2*x^35*y*z0^2 - x^33*y*z0^4 - x^36*y - x^36*z0 + 2*x^34*y*z0^2 - x^34*z0^3 + x^32*y*z0^4 - 2*x^35*z0 + 2*x^33*y*z0^2 - 2*x^33*z0^3 + 2*x^31*y*z0^4 - x^34*z0 - 2*x^32*y*z0^2 + x^32*z0^3 - x^30*y*z0^4 + 2*x^33*y + x^33*z0 + 2*x^31*y*z0^2 + x^29*y*z0^4 + 2*x^32*y + 2*x^32*z0 + 2*x^30*y*z0^2 - 2*x^30*z0^3 - x^28*y*z0^4 + x^31*y - 2*x^29*y*z0^2 - 2*x^29*z0^3 - x^30*y - x^30*z0 + x^26*y^2*z0^3 + x^29*y + 2*x^29*z0 - x^27*y*z0^2 - 2*x^27*z0^3 - x^28*y + 2*x^26*y*z0^2 - 2*x^26*z0^3 + 2*x^27*z0 - x^25*y*z0^2 - 2*x^25*z0^3 - x^23*y*z0^4 - x^26*y - x^26*z0 - 2*x^24*y*z0^2 - x^24*z0^3 - 2*x^22*y*z0^4 - 2*x^25*y + x^25*z0 - 2*x^23*y*z0^2 - 2*x^23*z0^3 - x^21*y*z0^4 - 2*x^22*y*z0^2 + 2*x^22*z0^3 + 2*x^23*y - x^21*y*z0^2 + 2*x^21*z0^3 - x^19*y*z0^4 - 2*x^22*y + x^22*z0 + 2*x^20*y*z0^2 + x^20*z0^3 + x^18*y*z0^4 + 2*x^21*y + x^21*z0 + 2*x^19*y*z0^2 - 2*x^19*z0^3 - x^17*y*z0^4 + x^20*y + 2*x^20*z0 + x^18*z0^3 + x^19*y - 2*x^19*z0 - 2*x^17*y*z0^2 - 2*x^15*y*z0^4 + 2*x^18*y + x^18*z0 + x^16*y*z0^2 + 2*x^16*z0^3 - x^14*y*z0^4 + 2*x^17*y - 2*x^17*z0 + 2*x^15*z0^3 + 2*x^13*y*z0^4 - 2*x^16*y + x^16*z0 + 2*x^14*y*z0^2 + x^14*z0^3 + 2*x^12*y*z0^4 + 2*x^15*y - 2*x^15*z0 + x^13*y*z0^2 + 2*x^13*z0^3 + x^11*y*z0^4 - 2*x^14*y + x^14*z0 + x^12*z0^3 + 2*x^10*y*z0^4 - x^13*y - 2*x^13*z0 + x^11*y*z0^2 + x^11*z0^3 + 2*x^9*y*z0^4 + 2*x^12*y - 2*x^12*z0 + 2*x^10*y*z0^2 - 2*x^10*z0^3 - 2*x^8*y*z0^4 + 2*x^11*z0 - x^9*z0^3 - 2*x^7*y*z0^4 - 2*x^10*y - x^10*z0 - 2*x^8*y*z0^2 - 2*x^8*z0^3 - x^6*y*z0^4 - 2*x^9*y - 2*x^9*z0 + x^7*y*z0^2 - 2*x^5*y*z0^4 + 2*x^8*y + x^8*z0 + 2*x^6*z0^3 + x^7*y + 2*x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^3*y*z0^4 + 2*x^6*z0 + x^4*y*z0^2 - x^2*y*z0^4 - x^5*y + 2*x^3*y*z0^2 + 2*x^3*z0^3 - x^4*y - x^4*z0 - 2*x^2*y*z0^2 - x^3*y - 2*x^3*z0 + 2*x^2*y)/y) * dx, - ((-2*x^61*z0^4 + x^60*z0^4 + 2*x^58*y^2*z0^4 + 2*x^61*z0^2 + x^59*z0^4 - x^57*y^2*z0^4 + x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^58*z0^4 - x^56*y^2*z0^4 - x^61 - x^57*y^2*z0^2 - x^57*z0^4 - x^60 + x^58*y^2 - 2*x^58*z0^2 - x^56*z0^4 + x^57*y^2 - x^57*z0^2 - 2*x^55*z0^4 + x^58 + x^54*z0^4 + x^57 + 2*x^55*z0^2 + x^53*z0^4 + x^54*z0^2 + 2*x^52*z0^4 - x^55 - x^51*z0^4 - x^54 - 2*x^52*z0^2 - x^50*z0^4 - x^51*z0^2 - 2*x^49*z0^4 + x^52 + x^48*z0^4 + x^51 + 2*x^49*z0^2 + x^47*z0^4 + x^48*z0^2 + 2*x^46*z0^4 - x^49 - x^45*z0^4 - x^48 - 2*x^46*z0^2 - x^44*z0^4 - x^45*z0^2 - 2*x^43*z0^4 + x^46 + x^42*z0^4 + x^45 + 2*x^43*z0^2 + x^41*z0^4 + x^42*z0^2 - x^40*y*z0^3 - 2*x^40*z0^4 - x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^39*z0^4 - x^42 + x^40*y*z0 - 2*x^40*z0^2 - x^38*y*z0^3 - 2*x^39*y*z0 + 2*x^39*z0^2 - x^40 + 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 + x^39 + 2*x^35*y*z0^3 - x^35*z0^4 + 2*x^38 - x^36*y*z0 - 2*x^36*z0^2 + x^34*y*z0^3 + 2*x^34*z0^4 + 2*x^37 - x^35*y*z0 + 2*x^35*z0^2 + 2*x^33*z0^4 - 2*x^36 + x^34*y*z0 + 2*x^32*y*z0^3 - x^32*z0^4 - x^35 - x^33*z0^2 + 2*x^31*y*z0^3 + 2*x^31*z0^4 + x^34 + x^32*y*z0 - x^32*z0^2 - x^30*y*z0^3 - 2*x^33 + 2*x^31*y*z0 + 2*x^31*z0^2 + 2*x^29*y*z0^3 - x^29*z0^4 + 2*x^30*y*z0 - 2*x^30*z0^2 - 2*x^28*y*z0^3 + x^28*z0^4 + x^26*y^2*z0^4 - x^31 + x^29*y*z0 - 2*x^29*z0^2 - x^27*y*z0^3 + 2*x^27*z0^4 - x^30 - x^26*y*z0^3 + x^29 + 2*x^27*y*z0 + 2*x^27*z0^2 + x^25*y*z0^3 + x^25*z0^4 + 2*x^28 + 2*x^26*y*z0 + x^26*z0^2 + 2*x^24*y*z0^3 - x^27 - 2*x^25*y*z0 + 2*x^23*y*z0^3 + x^26 + x^24*y*z0 + x^22*z0^4 - x^25 + x^23*y*z0 + 2*x^23*z0^2 + 2*x^21*y*z0^3 - x^21*z0^4 - x^24 + 2*x^22*y*z0 - x^22*z0^2 + 2*x^20*y*z0^3 + 2*x^21*y*z0 + x^21*z0^2 + 2*x^19*z0^4 - 2*x^22 - x^20*z0^2 + x^18*y*z0^3 - x^18*z0^4 + 2*x^21 + x^19*y*z0 - x^19*z0^2 - 2*x^17*z0^4 - 2*x^18*y*z0 - x^18*z0^2 + x^16*y*z0^3 + x^16*z0^4 - x^19 - 2*x^17*y*z0 + 2*x^17*z0^2 + x^15*y*z0^3 - 2*x^15*z0^4 - x^18 + 2*x^16*y*z0 - 2*x^16*z0^2 - 2*x^14*y*z0^3 - x^17 - x^15*y*z0 + 2*x^15*z0^2 - 2*x^13*y*z0^3 + x^13*z0^4 + 2*x^16 - 2*x^14*y*z0 - 2*x^14*z0^2 - 2*x^12*y*z0^3 - x^12*z0^4 - x^15 - x^13*y*z0 + 2*x^13*z0^2 - 2*x^11*y*z0^3 - 2*x^11*z0^4 - x^14 + 2*x^12*y*z0 - x^10*y*z0^3 - x^10*z0^4 + 2*x^13 - 2*x^11*z0^2 - x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 - x^8*y*z0^3 + 2*x^8*z0^4 - x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^8*y*z0 - 2*x^6*y*z0^3 - x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 + 2*x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 - x^4*y*z0^3 - 2*x^5*y*z0 + 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + x^6 - 2*x^4*y*z0 + x^4*z0^2 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-2*x^61*z0^4 + 2*x^58*y^2*z0^4 - x^61*z0^2 + x^58*y^2*z0^2 + 2*x^58*z0^4 - x^61 - x^60 + x^58*y^2 + x^58*z0^2 + x^57*y^2 - 2*x^55*z0^4 + x^58 + x^57 - x^55*z0^2 + 2*x^52*z0^4 - x^55 - x^54 + x^52*z0^2 - 2*x^49*z0^4 + x^52 + x^51 - x^49*z0^2 + 2*x^46*z0^4 - x^49 - x^48 + x^46*z0^2 - 2*x^43*z0^4 + x^46 + x^45 - x^43*z0^2 - x^40*y*z0^3 - x^43 - x^41*z0^2 - x^39*y*z0^3 + x^39*z0^4 - x^42 + 2*x^40*y*z0 - x^40*z0^2 + 2*x^38*y*z0^3 + x^39*z0^2 - 2*x^37*z0^4 + 2*x^40 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + 2*x^39 - 2*x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*z0^4 - x^36*z0^2 + 2*x^34*z0^4 + 2*x^37 - 2*x^35*y*z0 + 2*x^35*z0^2 + 2*x^33*y*z0^3 - x^33*z0^4 + 2*x^36 - x^34*y*z0 - 2*x^34*z0^2 - x^32*y*z0^3 - 2*x^32*z0^4 + x^35 + 2*x^33*y*z0 - 2*x^33*z0^2 - x^31*y*z0^3 - x^31*z0^4 + x^32*y*z0 + 2*x^32*z0^2 - 2*x^30*z0^4 - x^33 + 2*x^31*y*z0 - x^31*z0^2 + 2*x^29*y*z0^3 - x^32 - x^30*y*z0 - x^30*z0^2 - 2*x^31 - 2*x^29*y*z0 + x^29*z0^2 - 2*x^27*z0^4 + 2*x^28*y*z0 + x^28*z0^2 - 2*x^26*y*z0^3 + x^29 + x^27*y^2 + 2*x^27*z0^2 + x^25*y*z0^3 - 2*x^25*z0^4 + x^28 - x^26*y*z0 + x^26*z0^2 - 2*x^24*z0^4 + 2*x^27 - 2*x^25*y*z0 - x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 + 2*x^26 - 2*x^24*y*z0 - x^24*z0^2 - x^22*z0^4 - x^25 + x^23*y*z0 + 2*x^23*z0^2 - x^21*y*z0^3 + x^24 - 2*x^22*z0^2 + 2*x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^21*y*z0 + 2*x^21*z0^2 - 2*x^19*y*z0^3 + x^19*z0^4 + 2*x^20*y*z0 + x^20*z0^2 + x^18*y*z0^3 + 2*x^18*z0^4 - 2*x^21 - 2*x^19*y*z0 + x^19*z0^2 + x^17*y*z0^3 - x^17*z0^4 - 2*x^20 - x^18*y*z0 + 2*x^18*z0^2 + 2*x^16*y*z0^3 - 2*x^16*z0^4 + 2*x^19 + x^17*y*z0 - x^17*z0^2 + x^15*y*z0^3 - x^15*z0^4 + 2*x^18 + x^16*z0^2 - 2*x^14*y*z0^3 - 2*x^14*z0^4 + x^15*y*z0 - 2*x^15*z0^2 - x^13*y*z0^3 + 2*x^13*z0^4 - 2*x^16 + 2*x^14*y*z0 - x^14*z0^2 + x^12*z0^4 - x^15 - 2*x^13*y*z0 + 2*x^13*z0^2 + x^11*z0^4 + 2*x^14 + x^12*y*z0 - x^12*z0^2 - 2*x^10*y*z0^3 + x^10*z0^4 - 2*x^11*y*z0 + x^11*z0^2 - 2*x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 - 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 - x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 - x^8*y*z0 - 2*x^8*z0^2 - 2*x^6*y*z0^3 + x^6*z0^4 - x^7*y*z0 + x^7*z0^2 + 2*x^5*y*z0^3 + 2*x^5*z0^4 - x^8 + 2*x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^5*y*z0 - 2*x^5*z0^2 - x^3*y*z0^3 - 2*x^6 - x^2*y*z0^3 + 2*x^2*z0^4 - x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 + 2*x^2*z0^2 - x^3 + x^2)/y) * dx, - ((2*x^61*z0^3 + 2*x^60*z0^3 - 2*x^58*y^2*z0^3 + x^61*z0 - x^59*z0^3 - 2*x^57*y^2*z0^3 - x^58*y^2*z0 - x^58*z0^3 + x^56*y^2*z0^3 - 2*x^59*z0 + x^57*z0^3 - x^55*y^2*z0^3 - x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 + x^55*z0^3 + 2*x^56*z0 - x^54*z0^3 + x^55*z0 - x^53*z0^3 - x^52*z0^3 - 2*x^53*z0 + x^51*z0^3 - x^52*z0 + x^50*z0^3 + x^49*z0^3 + 2*x^50*z0 - x^48*z0^3 + x^49*z0 - x^47*z0^3 - x^46*z0^3 - 2*x^47*z0 + x^45*z0^3 - x^46*z0 + x^44*z0^3 + x^43*z0^3 + 2*x^44*z0 - x^42*z0^3 + x^43*z0 + x^41*z0^3 + 2*x^39*y*z0^4 + x^40*y*z0^2 - 2*x^38*y*z0^4 - x^41*z0 + x^39*y*z0^2 - 2*x^40*y - x^40*z0 + x^38*y*z0^2 - x^38*z0^3 - x^36*y*z0^4 - 2*x^39*y + 2*x^37*y*z0^2 + x^37*z0^3 + x^35*y*z0^4 - 2*x^38*y + 2*x^38*z0 - x^36*y*z0^2 + 2*x^36*z0^3 + x^37*y + x^37*z0 + x^35*y*z0^2 + 2*x^35*z0^3 + x^36*y - x^36*z0 + 2*x^34*y*z0^2 - 2*x^34*z0^3 - x^35*y + 2*x^35*z0 - 2*x^33*y*z0^2 - 2*x^33*z0^3 + 2*x^31*y*z0^4 - 2*x^34*y + 2*x^34*z0 - 2*x^32*y*z0^2 - 2*x^32*z0^3 - 2*x^33*y - x^33*z0 + x^31*y*z0^2 + x^31*z0^3 - x^29*y*z0^4 - 2*x^32*y + x^32*z0 - 2*x^30*y*z0^2 - 2*x^31*z0 - x^29*y*z0^2 + x^29*z0^3 - 2*x^27*y*z0^4 + x^30*y - 2*x^30*z0 + x^28*z0^3 + 2*x^26*y*z0^4 - 2*x^29*y - 2*x^29*z0 + x^27*y^2*z0 + 2*x^27*y*z0^2 - x^25*y*z0^4 + 2*x^28*z0 + 2*x^26*y*z0^2 + x^26*z0^3 + x^24*y*z0^4 + 2*x^27*z0 + x^25*y*z0^2 - 2*x^23*y*z0^4 - x^26*y - 2*x^26*z0 + x^24*y*z0^2 - x^24*z0^3 + x^22*y*z0^4 + 2*x^25*y - x^25*z0 - x^23*y*z0^2 - 2*x^23*z0^3 - 2*x^21*y*z0^4 + x^24*y - 2*x^24*z0 - x^22*z0^3 + x^20*y*z0^4 - 2*x^23*y - x^23*z0 + 2*x^21*y*z0^2 + x^21*z0^3 + 2*x^22*y - 2*x^20*y*z0^2 + x^20*z0^3 + 2*x^21*y + x^21*z0 - x^19*y*z0^2 + 2*x^19*z0^3 + x^20*y - x^20*z0 - 2*x^18*y*z0^2 + 2*x^16*y*z0^4 + x^19*y + 2*x^19*z0 + x^17*y*z0^2 - 2*x^17*z0^3 + 2*x^15*y*z0^4 + x^18*y + x^18*z0 - 2*x^16*z0^3 + x^14*y*z0^4 - 2*x^17*y - x^17*z0 + x^15*y*z0^2 - 2*x^16*y + x^16*z0 - 2*x^14*y*z0^2 - x^14*z0^3 + 2*x^12*y*z0^4 + 2*x^15*y + x^13*z0^3 + x^11*y*z0^4 + x^14*y - 2*x^14*z0 + x^12*y*z0^2 - x^12*z0^3 - 2*x^13*z0 - x^11*y*z0^2 - x^11*z0^3 - 2*x^12*y - 2*x^12*z0 - 2*x^10*y*z0^2 + x^10*z0^3 + 2*x^8*y*z0^4 - 2*x^11*y - x^11*z0 - x^9*y*z0^2 + x^10*y + x^10*z0 + 2*x^8*y*z0^2 + x^8*z0^3 + x^9*y + x^7*z0^3 - 2*x^8*y - 2*x^8*z0 - x^6*z0^3 + x^4*y*z0^4 + x^7*y + 2*x^7*z0 + 2*x^5*y*z0^2 + x^5*z0^3 - 2*x^6*y + 2*x^6*z0 - 2*x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^2*y*z0^4 + x^5*y - 2*x^5*z0 - x^3*z0^3 - 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^3*y - 2*x^3*z0 + 2*x^2*y)/y) * dx, - ((-2*x^60*z0^4 + x^59*z0^4 + 2*x^57*y^2*z0^4 - x^60*z0^2 - x^56*y^2*z0^4 - 2*x^61 + x^57*y^2*z0^2 + 2*x^57*z0^4 - 2*x^60 + 2*x^58*y^2 - x^56*z0^4 + 2*x^57*y^2 + x^57*z0^2 + 2*x^58 - 2*x^54*z0^4 + 2*x^57 + x^53*z0^4 - x^54*z0^2 - 2*x^55 + 2*x^51*z0^4 - 2*x^54 - x^50*z0^4 + x^51*z0^2 + 2*x^52 - 2*x^48*z0^4 + 2*x^51 + x^47*z0^4 - x^48*z0^2 - 2*x^49 + 2*x^45*z0^4 - 2*x^48 - x^44*z0^4 + x^45*z0^2 + 2*x^46 - 2*x^42*z0^4 + 2*x^45 - x^42*z0^2 - 2*x^40*z0^4 - 2*x^43 + 2*x^39*z0^4 - 2*x^42 - 2*x^40*z0^2 - x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + 2*x^39*y*z0 + x^39*z0^2 + 2*x^37*y*z0^3 + x^37*z0^4 - 2*x^38*y*z0 - 2*x^36*z0^4 - x^39 - 2*x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 + x^35*z0^4 + 2*x^36*y*z0 - x^36*z0^2 - x^34*y*z0^3 - 2*x^34*z0^4 - x^37 + x^35*y*z0 - x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 + x^36 + x^34*y*z0 - 2*x^34*z0^2 + x^35 + 2*x^33*y*z0 - 2*x^33*z0^2 + 2*x^34 - 2*x^32*y*z0 + x^30*z0^4 - x^33 + 2*x^31*y*z0 - x^31*z0^2 - x^29*y*z0^3 + 2*x^32 - x^30*y*z0 - 2*x^30*z0^2 + x^28*y*z0^3 + x^28*z0^4 - x^31 - 2*x^29*y*z0 - x^29*z0^2 + x^27*y^2*z0^2 + x^27*z0^4 - 2*x^30 - x^28*y*z0 - x^26*y*z0^3 - x^26*z0^4 - x^29 + x^27*y*z0 + 2*x^25*y*z0^3 + x^25*z0^4 - x^28 + x^26*y*z0 - x^26*z0^2 - 2*x^24*y*z0^3 + x^24*z0^4 + 2*x^27 + x^23*y*z0^3 + x^23*z0^4 - 2*x^24*y*z0 + 2*x^24*z0^2 + x^22*y*z0^3 + 2*x^22*z0^4 - 2*x^23*y*z0 + x^23*z0^2 - 2*x^21*y*z0^3 - x^21*z0^4 + x^24 + 2*x^22*z0^2 + x^20*z0^4 - 2*x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 + 2*x^19*z0^4 + x^22 - 2*x^20*y*z0 - 2*x^20*z0^2 + x^18*y*z0^3 - x^18*z0^4 + x^21 - 2*x^19*y*z0 - x^19*z0^2 + x^17*y*z0^3 + 2*x^17*z0^4 + x^20 + 2*x^18*y*z0 - x^18*z0^2 + 2*x^19 + 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^15*z0^4 - x^18 + x^16*y*z0 + x^16*z0^2 - 2*x^14*y*z0^3 + x^14*z0^4 - x^17 + x^15*y*z0 + 2*x^13*z0^4 - 2*x^16 + x^14*z0^2 + 2*x^12*y*z0^3 - 2*x^12*z0^4 - x^15 + x^13*y*z0 + 2*x^13*z0^2 - x^11*y*z0^3 + 2*x^11*z0^4 + 2*x^14 - x^12*y*z0 + 2*x^10*y*z0^3 - x^10*z0^4 + 2*x^13 - x^11*z0^2 - 2*x^9*y*z0^3 + x^9*z0^4 + x^10*y*z0 + x^10*z0^2 - x^11 - 2*x^9*y*z0 - x^9*z0^2 + 2*x^7*y*z0^3 - 2*x^7*z0^4 - 2*x^10 - 2*x^8*z0^2 + x^6*z0^4 - x^9 + x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 + 2*x^5*z0^4 - x^8 - x^6*y*z0 + x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 - 2*x^5*y*z0 - x^3*y*z0^3 + 2*x^4*y*z0 + 2*x^2*y*z0^3 + 2*x^2*z0^4 + x^5 + x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*z0^2 - x^3)/y) * dx, - ((x^61*z0^3 - x^58*y^2*z0^3 - 2*x^61*z0 + x^59*z0^3 - x^60*z0 + 2*x^58*y^2*z0 - x^56*y^2*z0^3 - 2*x^59*z0 + x^57*y^2*z0 - 2*x^57*z0^3 - x^55*y^2*z0^3 + 2*x^58*z0 + 2*x^56*y^2*z0 - x^56*z0^3 + 2*x^54*y^2*z0^3 + x^57*z0 + 2*x^56*z0 + 2*x^54*z0^3 - 2*x^55*z0 + x^53*z0^3 - x^54*z0 - 2*x^53*z0 - 2*x^51*z0^3 + 2*x^52*z0 - x^50*z0^3 + x^51*z0 + 2*x^50*z0 + 2*x^48*z0^3 - 2*x^49*z0 + x^47*z0^3 - x^48*z0 - 2*x^47*z0 - 2*x^45*z0^3 + 2*x^46*z0 - x^44*z0^3 + x^45*z0 + 2*x^44*z0 + 2*x^42*z0^3 - 2*x^43*z0 + 2*x^41*z0^3 + x^39*y*z0^4 - x^42*z0 - 2*x^40*y*z0^2 - 2*x^40*z0^3 - x^38*y*z0^4 + x^41*z0 - 2*x^39*y*z0^2 + 2*x^39*z0^3 + 2*x^37*y*z0^4 - x^40*y - x^40*z0 + x^38*y*z0^2 + 2*x^38*z0^3 + x^39*y - x^39*z0 - 2*x^37*y*z0^2 + x^37*z0^3 + 2*x^35*y*z0^4 + x^38*y + x^38*z0 + x^36*z0^3 + x^34*y*z0^4 - 2*x^37*y - x^37*z0 + x^35*y*z0^2 - x^35*z0^3 + x^33*y*z0^4 - x^36*y + x^34*y*z0^2 - 2*x^34*z0^3 + 2*x^35*y + 2*x^35*z0 + x^33*y*z0^2 - x^33*z0^3 + 2*x^31*y*z0^4 - x^34*y - x^34*z0 - 2*x^32*y*z0^2 + 2*x^32*z0^3 + 2*x^30*y*z0^4 + 2*x^33*y - x^33*z0 - 2*x^31*y*z0^2 + 2*x^31*z0^3 - x^29*y*z0^4 - 2*x^32*z0 + 2*x^30*y*z0^2 - x^28*y*z0^4 + x^31*y + x^31*z0 + 2*x^29*z0^3 + x^27*y^2*z0^3 - x^27*y*z0^4 + x^30*y - x^28*y*z0^2 - x^28*z0^3 + x^29*y - 2*x^29*z0 + 2*x^27*y*z0^2 - 2*x^27*z0^3 - x^25*y*z0^4 + 2*x^28*y - 2*x^28*z0 + x^26*y*z0^2 + 2*x^26*z0^3 + x^24*y*z0^4 + x^27*z0 - x^25*z0^3 - 2*x^23*y*z0^4 - 2*x^26*y - x^24*y*z0^2 + x^24*z0^3 - 2*x^22*y*z0^4 - x^25*y + 2*x^23*y*z0^2 + 2*x^23*z0^3 - x^24*y + 2*x^24*z0 - x^22*y*z0^2 + x^22*z0^3 + 2*x^20*y*z0^4 + x^23*z0 + x^21*y*z0^2 + x^21*z0^3 + 2*x^19*y*z0^4 + 2*x^22*z0 + x^20*z0^3 + x^18*y*z0^4 + 2*x^21*y + 2*x^21*z0 + x^17*y*z0^4 - 2*x^20*y + 2*x^20*z0 - 2*x^18*y*z0^2 - x^16*y*z0^4 - 2*x^19*y - x^19*z0 - 2*x^17*y*z0^2 - 2*x^17*z0^3 - 2*x^15*y*z0^4 - 2*x^18*y + 2*x^18*z0 - x^16*y*z0^2 - x^16*z0^3 + x^14*y*z0^4 - 2*x^17*y + 2*x^17*z0 - 2*x^15*y*z0^2 + x^15*z0^3 - 2*x^13*y*z0^4 + 2*x^16*y - x^16*z0 + x^14*y*z0^2 + x^14*z0^3 - 2*x^15*z0 + x^13*y*z0^2 + x^13*z0^3 - 2*x^11*y*z0^4 + 2*x^14*z0 - x^12*y*z0^2 + 2*x^12*z0^3 - x^13*y - x^11*z0^3 + 2*x^9*y*z0^4 + 2*x^12*y - 2*x^12*z0 - x^10*z0^3 - 2*x^8*y*z0^4 + x^11*z0 + x^9*y*z0^2 - 2*x^7*y*z0^4 - x^10*y - x^10*z0 - x^8*y*z0^2 - x^8*z0^3 + 2*x^6*y*z0^4 - x^9*y - x^7*y*z0^2 + 2*x^7*z0^3 - x^8*y - x^8*z0 - 2*x^6*y*z0^2 + x^6*z0^3 + 2*x^4*y*z0^4 - 2*x^7*y - 2*x^7*z0 + 2*x^5*y*z0^2 - x^5*z0^3 - x^3*y*z0^4 - 2*x^6*y + 2*x^6*z0 - 2*x^4*y*z0^2 + 2*x^2*y*z0^4 - x^3*y*z0^2 - 2*x^3*z0^3 + 2*x^4*y + x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + x^3*y - x^2*y + 2*x^2*z0)/y) * dx, - ((2*x^61*z0^4 + x^60*z0^4 - 2*x^58*y^2*z0^4 + 2*x^61*z0^2 - x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 - 2*x^58*z0^4 - 2*x^61 + x^57*y^2*z0^2 - x^57*z0^4 + 2*x^58*y^2 - 2*x^58*z0^2 + x^57*z0^2 + 2*x^55*z0^4 + 2*x^58 + x^54*z0^4 + 2*x^55*z0^2 - x^54*z0^2 - 2*x^52*z0^4 - 2*x^55 - x^51*z0^4 - 2*x^52*z0^2 + x^51*z0^2 + 2*x^49*z0^4 + 2*x^52 + x^48*z0^4 + 2*x^49*z0^2 - x^48*z0^2 - 2*x^46*z0^4 - 2*x^49 - x^45*z0^4 - 2*x^46*z0^2 + x^45*z0^2 + 2*x^43*z0^4 + 2*x^46 + x^42*z0^4 + 2*x^43*z0^2 + x^41*z0^4 - x^42*z0^2 + x^40*y*z0^3 - 2*x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 + x^40*y*z0 + x^40*z0^2 + x^38*y*z0^3 + 2*x^38*z0^4 + x^41 - x^39*z0^2 + x^37*y*z0^3 - x^37*z0^4 - 2*x^40 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + x^36*z0^4 - 2*x^39 - x^37*y*z0 + 2*x^37*z0^2 + 2*x^35*z0^4 + 2*x^38 - 2*x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 + 2*x^34*z0^4 + x^37 - x^35*y*z0 + 2*x^33*y*z0^3 - 2*x^33*z0^4 - 2*x^36 - 2*x^34*y*z0 + 2*x^34*z0^2 + 2*x^32*y*z0^3 + x^32*z0^4 + x^35 - 2*x^33*z0^2 + 2*x^31*y*z0^3 - 2*x^34 + 2*x^32*y*z0 + 2*x^30*y*z0^3 - 2*x^30*z0^4 - 2*x^33 - 2*x^31*y*z0 + 2*x^31*z0^2 + x^27*y^2*z0^4 + x^32 + x^30*z0^2 + x^28*z0^4 + 2*x^31 - 2*x^29*y*z0 - x^29*z0^2 + x^27*y*z0^3 - 2*x^27*z0^4 - 2*x^30 + x^28*y*z0 + x^28*z0^2 + x^26*y*z0^3 - x^27*y*z0 + 2*x^27*z0^2 - 2*x^25*y*z0^3 + x^25*z0^4 + x^28 - x^26*y*z0 - x^26*z0^2 - 2*x^24*y*z0^3 + x^24*z0^4 - x^27 - x^25*y*z0 - 2*x^25*z0^2 - x^23*y*z0^3 + 2*x^26 + 2*x^24*y*z0 + x^22*y*z0^3 - x^25 + 2*x^23*y*z0 + 2*x^23*z0^2 - 2*x^21*y*z0^3 + x^21*z0^4 - 2*x^22*y*z0 + x^22*z0^2 + 2*x^20*y*z0^3 - 2*x^20*z0^4 + 2*x^23 - x^19*y*z0^3 + 2*x^19*z0^4 + x^22 + 2*x^20*z0^2 - 2*x^18*z0^4 - x^19*y*z0 - 2*x^19*z0^2 - 2*x^20 - x^18*y*z0 + x^18*z0^2 + x^16*y*z0^3 + 2*x^16*z0^4 + x^19 - 2*x^17*y*z0 + 2*x^17*z0^2 + 2*x^15*y*z0^3 - 2*x^15*z0^4 - x^16*y*z0 + 2*x^16*z0^2 - x^14*y*z0^3 + 2*x^15*y*z0 + x^13*y*z0^3 + x^13*z0^4 - x^16 - 2*x^14*y*z0 - 2*x^14*z0^2 - 2*x^12*y*z0^3 + x^12*z0^4 + 2*x^15 + 2*x^13*y*z0 + x^13*z0^2 + x^11*y*z0^3 + 2*x^11*z0^4 + 2*x^14 - x^12*y*z0 - x^12*z0^2 - x^10*y*z0^3 + 2*x^10*z0^4 - x^13 - x^11*y*z0 - x^11*z0^2 + x^9*y*z0^3 - x^12 - 2*x^10*y*z0 + 2*x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^11 + x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 + 2*x^7*z0^4 - x^10 - 2*x^8*y*z0 - x^8*z0^2 - 2*x^6*z0^4 + 2*x^9 + x^7*y*z0 + x^7*z0^2 + 2*x^5*y*z0^3 - 2*x^5*z0^4 + x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 - x^4*y*z0^3 - x^4*z0^4 - x^7 - x^5*y*z0 - x^5*z0^2 + x^3*z0^4 - 2*x^6 + x^4*z0^2 - 2*x^2*y*z0^3 - x^2*z0^4 + x^5 - x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 + x^61*z0^2 + 2*x^59*z0^4 + x^60*z0^2 - x^58*y^2*z0^2 - x^58*z0^4 - 2*x^56*y^2*z0^4 + x^61 - x^57*y^2*z0^2 + x^60 - x^58*y^2 - x^58*z0^2 - 2*x^56*z0^4 - x^57*y^2 - x^57*z0^2 + x^55*z0^4 - x^58 - x^57 + x^55*z0^2 + 2*x^53*z0^4 + x^54*z0^2 - x^52*z0^4 + x^55 + x^54 - x^52*z0^2 - 2*x^50*z0^4 - x^51*z0^2 + x^49*z0^4 - x^52 - x^51 + x^49*z0^2 + 2*x^47*z0^4 + x^48*z0^2 - x^46*z0^4 + x^49 + x^48 - x^46*z0^2 - 2*x^44*z0^4 - x^45*z0^2 + x^43*z0^4 - x^46 - x^45 + x^43*z0^2 + x^41*z0^4 + x^42*z0^2 - 2*x^40*y*z0^3 + x^40*z0^4 + x^43 + x^41*z0^2 + x^39*y*z0^3 - x^39*z0^4 + x^42 - 2*x^40*y*z0 - 2*x^40*z0^2 + 2*x^38*y*z0^3 - 2*x^38*z0^4 - x^41 - 2*x^39*y*z0 - 2*x^39*z0^2 - x^37*y*z0^3 + 2*x^37*z0^4 + x^40 + 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 + x^36*z0^4 - x^39 - 2*x^37*y*z0 - 2*x^37*z0^2 - x^35*y*z0^3 + 2*x^35*z0^4 + 2*x^38 - 2*x^36*y*z0 + 2*x^36*z0^2 + x^34*y*z0^3 - x^34*z0^4 + 2*x^37 - x^35*y*z0 - x^33*z0^4 - x^34*y*z0 - 2*x^34*z0^2 + 2*x^32*y*z0^3 - x^35 + x^33*z0^2 + 2*x^31*z0^4 + 2*x^34 - x^32*y*z0 - 2*x^32*z0^2 - 2*x^30*y*z0^3 + x^31*y*z0 + 2*x^31*z0^2 + x^29*y*z0^3 - x^32 + x^30*z0^2 - x^28*y*z0^3 + 2*x^28*z0^4 - 2*x^31 - x^29*y*z0 - 2*x^29*z0^2 + x^27*y*z0^3 + x^27*z0^4 - 2*x^30 + x^28*y^2 + 2*x^28*y*z0 - 2*x^28*z0^2 + 2*x^26*y*z0^3 + 2*x^26*z0^4 + x^29 + x^27*y*z0 + x^27*z0^2 - 2*x^25*y*z0^3 - x^25*z0^4 - x^28 + 2*x^26*y*z0 + 2*x^24*y*z0^3 + x^27 - 2*x^25*z0^2 + x^23*y*z0^3 + 2*x^23*z0^4 - x^24*y*z0 + 2*x^24*z0^2 - x^22*y*z0^3 + 2*x^25 + 2*x^23*y*z0 + 2*x^21*y*z0^3 - 2*x^22*y*z0 - 2*x^22*z0^2 + 2*x^20*y*z0^3 + x^20*z0^4 - x^23 + x^21*y*z0 + 2*x^21*z0^2 + 2*x^19*y*z0^3 + 2*x^19*z0^4 - x^22 + x^20*y*z0 - x^20*z0^2 - 2*x^18*y*z0^3 + x^18*z0^4 - x^21 + x^19*y*z0 - x^19*z0^2 + x^17*y*z0^3 + 2*x^17*z0^4 - 2*x^20 - x^18*y*z0 - x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^16*z0^4 - x^19 - 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*z0^4 + 2*x^18 - 2*x^16*y*z0 - x^16*z0^2 + 2*x^14*y*z0^3 - 2*x^14*z0^4 + x^17 - 2*x^15*y*z0 + 2*x^15*z0^2 + x^13*z0^4 - x^16 - x^14*y*z0 - 2*x^14*z0^2 + x^12*z0^4 + x^15 - 2*x^13*y*z0 - x^13*z0^2 + 2*x^11*y*z0^3 + x^10*y*z0^3 + x^9*y*z0^3 + 2*x^9*z0^4 + x^12 - x^10*z0^2 + x^8*z0^4 + x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 + x^7*z0^4 + x^10 + 2*x^8*y*z0 - x^8*z0^2 - 2*x^6*y*z0^3 + 2*x^6*z0^4 - x^9 - x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*z0^4 - 2*x^8 - x^6*z0^2 - x^4*y*z0^3 - x^4*z0^4 - 2*x^7 - 2*x^5*y*z0 + 2*x^5*z0^2 + x^3*z0^4 + 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 - x^5 - 2*x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 - x^3 - 2*x^2)/y) * dx, - ((-2*x^61*z0^3 + 2*x^60*z0^3 + 2*x^58*y^2*z0^3 - x^61*z0 - 2*x^57*y^2*z0^3 + x^58*y^2*z0 - 2*x^58*z0^3 - x^57*z0^3 - x^55*y^2*z0^3 + x^58*z0 - x^54*y^2*z0^3 + 2*x^55*z0^3 + x^54*z0^3 - x^55*z0 - 2*x^52*z0^3 - x^51*z0^3 + x^52*z0 + 2*x^49*z0^3 + x^48*z0^3 - x^49*z0 - 2*x^46*z0^3 - x^45*z0^3 + x^46*z0 + 2*x^43*z0^3 + x^42*z0^3 - x^43*z0 - 2*x^41*z0^3 - 2*x^39*y*z0^4 - x^40*y*z0^2 - x^41*z0 - x^39*y*z0^2 + x^39*z0^3 - 2*x^37*y*z0^4 + 2*x^40*y - x^38*y*z0^2 + x^38*z0^3 - x^36*y*z0^4 - x^39*y + x^39*z0 + 2*x^37*z0^3 - 2*x^35*y*z0^4 + x^38*y - 2*x^38*z0 + 2*x^36*y*z0^2 - x^36*z0^3 + x^34*y*z0^4 - x^37*y + x^37*z0 - x^35*z0^3 + 2*x^33*y*z0^4 - x^36*z0 - x^34*z0^3 + x^32*y*z0^4 - x^35*y - x^35*z0 + 2*x^33*y*z0^2 + x^33*z0^3 - x^31*y*z0^4 + 2*x^34*y - 2*x^32*y*z0^2 - 2*x^30*y*z0^4 - x^33*z0 - 2*x^31*z0^3 - 2*x^29*y*z0^4 - 2*x^32*y - 2*x^30*z0^3 - x^28*y*z0^4 - x^31*y + 2*x^31*z0 - x^27*y*z0^4 - x^30*y + 2*x^30*z0 + x^28*y^2*z0 - x^28*y*z0^2 - 2*x^28*z0^3 + 2*x^26*y*z0^4 + x^29*y - 2*x^27*y*z0^2 + x^27*z0^3 + 2*x^28*y - 2*x^28*z0 - x^26*z0^3 + 2*x^24*y*z0^4 - 2*x^27*y - x^27*z0 + x^25*z0^3 - 2*x^23*y*z0^4 + x^26*y - x^26*z0 - 2*x^24*z0^3 - x^22*y*z0^4 + 2*x^25*y - 2*x^25*z0 - 2*x^23*y*z0^2 + x^23*z0^3 + 2*x^21*y*z0^4 - x^24*z0 - x^22*z0^3 - x^20*y*z0^4 - x^23*y + 2*x^23*z0 + 2*x^21*y*z0^2 - x^21*z0^3 + x^22*y - 2*x^22*z0 - 2*x^20*y*z0^2 + x^18*y*z0^4 - 2*x^21*y - x^19*y*z0^2 - 2*x^19*z0^3 - x^17*y*z0^4 - x^20*y - x^20*z0 + x^18*y*z0^2 + x^18*z0^3 - 2*x^16*y*z0^4 - 2*x^19*y - 2*x^17*y*z0^2 - 2*x^17*z0^3 - x^15*y*z0^4 + 2*x^18*y - x^18*z0 + 2*x^16*z0^3 + 2*x^14*y*z0^4 - x^17*y - 2*x^17*z0 + 2*x^16*y - 2*x^16*z0 - 2*x^14*y*z0^2 + x^12*y*z0^4 - 2*x^15*y - x^15*z0 + x^13*z0^3 + x^11*y*z0^4 - 2*x^14*y - 2*x^14*z0 + x^12*y*z0^2 + 2*x^12*z0^3 - x^13*y + x^13*z0 - 2*x^11*y*z0^2 + x^9*y*z0^4 + x^12*y - x^12*z0 - 2*x^8*y*z0^4 - 2*x^11*y + 2*x^11*z0 + 2*x^9*y*z0^2 - 2*x^7*y*z0^4 + x^10*y + 2*x^10*z0 - x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 - 2*x^9*y - 2*x^9*z0 - x^7*y*z0^2 + x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y + x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^4*y*z0^4 + x^7*z0 - x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - x^6*y - 2*x^6*z0 + x^4*y*z0^2 + 2*x^2*y*z0^4 + x^5*y + 2*x^5*z0 - 2*x^4*y - x^4*z0 - 2*x^2*z0^3 - x^3*y + x^3*z0 - 2*x^2*y + 2*x^2*z0)/y) * dx, - ((-2*x^61*z0^4 - 2*x^60*z0^4 + 2*x^58*y^2*z0^4 - x^61*z0^2 + 2*x^59*z0^4 + 2*x^57*y^2*z0^4 - 2*x^60*z0^2 + x^58*y^2*z0^2 + 2*x^58*z0^4 - 2*x^56*y^2*z0^4 - 2*x^61 + 2*x^57*y^2*z0^2 + 2*x^57*z0^4 - 2*x^60 + 2*x^58*y^2 + x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 + 2*x^57*z0^2 - 2*x^55*z0^4 + 2*x^58 - 2*x^54*z0^4 + 2*x^57 - x^55*z0^2 + 2*x^53*z0^4 - 2*x^54*z0^2 + 2*x^52*z0^4 - 2*x^55 + 2*x^51*z0^4 - 2*x^54 + x^52*z0^2 - 2*x^50*z0^4 + 2*x^51*z0^2 - 2*x^49*z0^4 + 2*x^52 - 2*x^48*z0^4 + 2*x^51 - x^49*z0^2 + 2*x^47*z0^4 - 2*x^48*z0^2 + 2*x^46*z0^4 - 2*x^49 + 2*x^45*z0^4 - 2*x^48 + x^46*z0^2 - 2*x^44*z0^4 + 2*x^45*z0^2 - 2*x^43*z0^4 + 2*x^46 - 2*x^42*z0^4 + 2*x^45 - x^43*z0^2 - x^41*z0^4 - 2*x^42*z0^2 - x^40*y*z0^3 - 2*x^43 - x^41*z0^2 - x^39*y*z0^3 + x^39*z0^4 - 2*x^42 + 2*x^40*y*z0 - x^40*z0^2 + x^38*y*z0^3 - x^38*z0^4 + 2*x^41 - 2*x^39*y*z0 - 2*x^39*z0^2 - x^37*y*z0^3 + 2*x^37*z0^4 - 2*x^40 + x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^37*y*z0 + x^37*z0^2 - x^35*y*z0^3 - x^35*z0^4 - 2*x^38 + 2*x^36*y*z0 + 2*x^36*z0^2 - 2*x^34*y*z0^3 + x^34*z0^4 + x^37 + 2*x^35*y*z0 + x^35*z0^2 + 2*x^33*y*z0^3 - 2*x^33*z0^4 - x^36 + x^34*z0^2 + 2*x^32*z0^4 + 2*x^35 - x^33*y*z0 - x^33*z0^2 + x^31*y*z0^3 + x^31*z0^4 - x^34 + 2*x^32*y*z0 - 2*x^32*z0^2 + 2*x^30*z0^4 + 2*x^33 + 2*x^31*y*z0 + x^31*z0^2 + 2*x^29*y*z0^3 + x^29*z0^4 + x^32 + x^28*y^2*z0^2 - 2*x^28*z0^4 + 2*x^31 - 2*x^29*y*z0 - 2*x^29*z0^2 + x^27*y*z0^3 + 2*x^27*z0^4 + x^30 + 2*x^28*y*z0 + x^26*z0^4 + 2*x^29 + x^27*y*z0 - 2*x^27*z0^2 - 2*x^25*y*z0^3 - 2*x^25*z0^4 - 2*x^26*y*z0 + 2*x^26*z0^2 + x^24*y*z0^3 - 2*x^24*z0^4 + 2*x^27 - 2*x^25*z0^2 + x^23*y*z0^3 + x^23*z0^4 - x^26 - x^24*y*z0 + x^24*z0^2 + 2*x^22*y*z0^3 - x^22*z0^4 - x^25 + 2*x^23*y*z0 + 2*x^23*z0^2 + x^21*y*z0^3 - 2*x^21*z0^4 + 2*x^24 + x^22*z0^2 - x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^23 + x^21*z0^2 - 2*x^19*y*z0^3 + 2*x^19*z0^4 - 2*x^22 + x^20*y*z0 - x^20*z0^2 - x^18*y*z0^3 - x^18*z0^4 - 2*x^21 + x^19*y*z0 - x^17*y*z0^3 - x^17*z0^4 - x^20 - 2*x^18*y*z0 - 2*x^16*y*z0^3 - 2*x^19 - 2*x^17*y*z0 - x^17*z0^2 - x^15*y*z0^3 - 2*x^15*z0^4 - 2*x^18 - x^16*z0^2 - x^14*y*z0^3 + 2*x^17 - x^15*y*z0 + x^15*z0^2 + x^13*y*z0^3 + x^13*z0^4 + 2*x^16 - x^14*y*z0 + 2*x^14*z0^2 + x^12*y*z0^3 - x^12*z0^4 - x^15 + 2*x^13*y*z0 + x^11*y*z0^3 - 2*x^11*z0^4 - 2*x^14 - 2*x^12*y*z0 - 2*x^10*y*z0^3 + x^10*z0^4 - x^13 + 2*x^11*y*z0 - 2*x^9*y*z0^3 + 2*x^12 - x^10*y*z0 + x^10*z0^2 - 2*x^8*z0^4 - 2*x^11 + x^9*y*z0 + x^7*y*z0^3 - x^7*z0^4 + 2*x^10 + x^8*y*z0 + x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 - x^5*y*z0^3 + 2*x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 - 2*x^4*z0^4 + 2*x^7 + 2*x^5*y*z0 + x^5*z0^2 + 2*x^6 - x^4*z0^2 - 2*x^2*y*z0^3 + 2*x^2*z0^4 + x^5 - x^3*y*z0 + x^3*z0^2 - 2*x^2*y*z0 + x^2*z0^2 + x^2)/y) * dx, - ((x^61*z0^3 + 2*x^60*z0^3 - x^58*y^2*z0^3 + x^61*z0 - x^59*z0^3 - 2*x^57*y^2*z0^3 + 2*x^60*z0 - x^58*y^2*z0 + x^56*y^2*z0^3 - 2*x^59*z0 - 2*x^57*y^2*z0 - x^55*y^2*z0^3 - x^58*z0 + 2*x^56*y^2*z0 + x^56*z0^3 - 2*x^54*y^2*z0^3 - 2*x^57*z0 + 2*x^56*z0 + x^55*z0 - x^53*z0^3 + 2*x^54*z0 - 2*x^53*z0 - x^52*z0 + x^50*z0^3 - 2*x^51*z0 + 2*x^50*z0 + x^49*z0 - x^47*z0^3 + 2*x^48*z0 - 2*x^47*z0 - x^46*z0 + x^44*z0^3 - 2*x^45*z0 + 2*x^44*z0 + x^43*z0 + x^39*y*z0^4 + 2*x^42*z0 - 2*x^40*y*z0^2 - x^40*z0^3 - x^38*y*z0^4 - x^41*z0 + x^39*y*z0^2 + 2*x^37*y*z0^4 - 2*x^40*y - 2*x^40*z0 + 2*x^38*y*z0^2 + 2*x^38*z0^3 + x^36*y*z0^4 + 2*x^39*y - 2*x^39*z0 - 2*x^37*z0^3 - x^35*y*z0^4 + 2*x^38*y + 2*x^38*z0 - x^36*y*z0^2 + 2*x^36*z0^3 + x^34*y*z0^4 + x^37*y - 2*x^35*y*z0^2 + 2*x^35*z0^3 + x^33*y*z0^4 + x^36*y + x^36*z0 - x^34*y*z0^2 - 2*x^32*y*z0^4 - 2*x^35*y + x^35*z0 - 2*x^33*z0^3 - x^31*y*z0^4 - 2*x^34*z0 - x^32*y*z0^2 - x^32*z0^3 + x^30*y*z0^4 - 2*x^33*z0 - x^31*y*z0^2 - 2*x^31*z0^3 + 2*x^32*y + x^32*z0 + 2*x^30*y*z0^2 + x^30*z0^3 + x^28*y^2*z0^3 + 2*x^28*y*z0^4 + 2*x^31*y - x^31*z0 - 2*x^29*y*z0^2 - x^29*z0^3 - 2*x^30*y + x^30*z0 - 2*x^28*y*z0^2 - x^26*y*z0^4 + x^29*z0 + 2*x^27*z0^3 + x^25*y*z0^4 - 2*x^28*z0 - 2*x^26*y*z0^2 - 2*x^26*z0^3 - 2*x^24*y*z0^4 + x^27*y + 2*x^27*z0 + x^25*y*z0^2 + 2*x^25*z0^3 + 2*x^23*y*z0^4 + 2*x^26*z0 + x^22*y*z0^4 + 2*x^25*z0 - x^21*y*z0^4 + x^24*y + 2*x^24*z0 + x^22*y*z0^2 + x^22*z0^3 + 2*x^23*y - x^23*z0 - 2*x^21*y*z0^2 + x^21*z0^3 + x^19*y*z0^4 - 2*x^22*y + 2*x^22*z0 + x^20*y*z0^2 + 2*x^20*z0^3 - x^18*y*z0^4 - x^21*y - x^21*z0 - 2*x^19*y*z0^2 - x^19*z0^3 - x^17*y*z0^4 - 2*x^20*y - 2*x^18*y*z0^2 - 2*x^18*z0^3 - x^16*y*z0^4 - x^19*y + 2*x^19*z0 - x^17*z0^3 + x^15*y*z0^4 - x^18*y + 2*x^16*y*z0^2 + x^16*z0^3 + x^14*y*z0^4 + x^17*z0 - x^15*y*z0^2 - x^15*z0^3 - 2*x^13*y*z0^4 + x^16*y + 2*x^16*z0 + x^14*y*z0^2 - x^14*z0^3 - 2*x^15*y - 2*x^15*z0 + 2*x^11*y*z0^4 + 2*x^14*y + 2*x^14*z0 - x^12*y*z0^2 - x^12*z0^3 - x^10*y*z0^4 - x^13*y + x^13*z0 - x^11*z0^3 + 2*x^9*y*z0^4 - x^12*y + x^10*z0^3 - 2*x^8*y*z0^4 - x^11*y - 2*x^11*z0 + x^9*y*z0^2 + 2*x^9*z0^3 + 2*x^7*y*z0^4 - x^10*z0 - x^8*y*z0^2 + x^8*z0^3 + 2*x^9*y - x^9*z0 + x^7*y*z0^2 - x^5*y*z0^4 + x^8*y + x^6*y*z0^2 - 2*x^6*z0^3 + x^4*y*z0^4 + x^7*y + x^7*z0 + 2*x^5*y*z0^2 + x^5*z0^3 - x^3*y*z0^4 - 2*x^6*y + 2*x^6*z0 + 2*x^4*y*z0^2 - x^4*z0^3 - 2*x^5*y + x^5*z0 + 2*x^3*y*z0^2 - 2*x^3*z0^3 - 2*x^4*y + x^4*z0 - x^2*y*z0^2 + 2*x^2*z0^3 + x^3*y - 2*x^3*z0 + 2*x^2*y - 2*x^2*z0)/y) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 - 2*x^61*z0^2 + x^59*z0^4 + 2*x^60*z0^2 + 2*x^58*y^2*z0^2 - x^58*z0^4 - x^56*y^2*z0^4 - 2*x^57*y^2*z0^2 + 2*x^58*z0^2 - x^56*z0^4 - 2*x^57*z0^2 + x^55*z0^4 - 2*x^55*z0^2 + x^53*z0^4 + 2*x^54*z0^2 - x^52*z0^4 + 2*x^52*z0^2 - x^50*z0^4 - 2*x^51*z0^2 + x^49*z0^4 - 2*x^49*z0^2 + x^47*z0^4 + 2*x^48*z0^2 - x^46*z0^4 + 2*x^46*z0^2 - x^44*z0^4 - 2*x^45*z0^2 + x^43*z0^4 - 2*x^43*z0^2 + 2*x^41*z0^4 + 2*x^42*z0^2 - 2*x^40*y*z0^3 + x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - x^40*y*z0 + 2*x^38*y*z0^3 + 2*x^38*z0^4 + x^41 + 2*x^39*y*z0 - 2*x^37*y*z0^3 - 2*x^40 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^37*y*z0 - 2*x^37*z0^2 - x^35*y*z0^3 + 2*x^35*z0^4 - x^38 - 2*x^36*y*z0 + 2*x^34*y*z0^3 + x^34*z0^4 + x^37 + 2*x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 - x^36 - x^34*y*z0 - 2*x^34*z0^2 + 2*x^32*y*z0^3 - 2*x^32*z0^4 - x^35 + x^33*z0^2 - x^31*y*z0^3 + x^31*z0^4 + x^34 + x^32*y*z0 - 2*x^32*z0^2 + 2*x^30*y*z0^3 + 2*x^30*z0^4 + x^28*y^2*z0^4 + x^33 + x^31*y*z0 - x^31*z0^2 - x^29*y*z0^3 + x^30*y*z0 + 2*x^28*z0^4 - 2*x^31 + 2*x^29*y*z0 + x^29*z0^2 - 2*x^27*y*z0^3 + x^27*z0^4 + x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y*z0 + 2*x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 - x^28 + 2*x^26*z0^2 - x^24*y*z0^3 - 2*x^24*z0^4 + x^23*y*z0^3 + 2*x^23*z0^4 + 2*x^26 + x^24*y*z0 - x^22*y*z0^3 + 2*x^22*z0^4 - 2*x^25 + 2*x^23*y*z0 + x^23*z0^2 + 2*x^21*y*z0^3 + 2*x^21*z0^4 + 2*x^22*y*z0 + 2*x^22*z0^2 - x^20*y*z0^3 - x^20*z0^4 + x^21*y*z0 - x^19*y*z0^3 - 2*x^19*z0^4 + 2*x^20*y*z0 + 2*x^18*y*z0^3 + x^18*z0^4 - x^21 - x^19*y*z0 + 2*x^17*z0^4 - x^20 - x^18*y*z0 - 2*x^18*z0^2 + 2*x^16*y*z0^3 - x^16*z0^4 - x^19 + 2*x^17*y*z0 + 2*x^17*z0^2 - x^15*y*z0^3 + 2*x^18 + 2*x^16*y*z0 + 2*x^16*z0^2 + 2*x^14*y*z0^3 - 2*x^17 + 2*x^15*y*z0 - x^15*z0^2 - x^13*y*z0^3 - 2*x^13*z0^4 + 2*x^16 - 2*x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 + 2*x^12*z0^4 + x^15 - 2*x^13*y*z0 - 2*x^11*y*z0^3 + x^11*z0^4 + x^14 - 2*x^12*z0^2 + x^10*y*z0^3 - 2*x^10*z0^4 - 2*x^11*y*z0 + x^11*z0^2 + 2*x^9*y*z0^3 + x^12 - 2*x^10*y*z0 + x^10*z0^2 - 2*x^8*y*z0^3 + x^8*z0^4 + x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 + 2*x^7*y*z0^3 - 2*x^7*z0^4 + 2*x^10 - x^8*y*z0 + 2*x^8*z0^2 + 2*x^7*y*z0 + x^7*z0^2 + 2*x^5*y*z0^3 + 2*x^5*z0^4 - 2*x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - x^7 + 2*x^5*z0^2 - 2*x^3*y*z0^3 + x^3*z0^4 - 2*x^6 - 2*x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 - x^2*z0^4 - x^5 + x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0 - x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 - x^60*z0^4 + x^58*y^2*z0^4 - x^61*z0^2 + x^59*z0^4 + x^57*y^2*z0^4 - 2*x^60*z0^2 + x^58*y^2*z0^2 + x^58*z0^4 - x^56*y^2*z0^4 + 2*x^61 + 2*x^57*y^2*z0^2 + x^57*z0^4 - 2*x^60 - 2*x^58*y^2 + x^58*z0^2 - x^56*z0^4 + 2*x^57*y^2 + 2*x^57*z0^2 - x^55*z0^4 - 2*x^58 - x^54*z0^4 + 2*x^57 - x^55*z0^2 + x^53*z0^4 - 2*x^54*z0^2 + x^52*z0^4 + 2*x^55 + x^51*z0^4 - 2*x^54 + x^52*z0^2 - x^50*z0^4 + 2*x^51*z0^2 - x^49*z0^4 - 2*x^52 - x^48*z0^4 + 2*x^51 - x^49*z0^2 + x^47*z0^4 - 2*x^48*z0^2 + x^46*z0^4 + 2*x^49 + x^45*z0^4 - 2*x^48 + x^46*z0^2 - x^44*z0^4 + 2*x^45*z0^2 - x^43*z0^4 - 2*x^46 - x^42*z0^4 + 2*x^45 - x^43*z0^2 + x^41*z0^4 - 2*x^42*z0^2 + 2*x^40*y*z0^3 - x^40*z0^4 + 2*x^43 - x^41*z0^2 - x^39*y*z0^3 - 2*x^39*z0^4 - 2*x^42 + 2*x^40*y*z0 - x^40*z0^2 + 2*x^39*y*z0 - 2*x^39*z0^2 + x^37*y*z0^3 - 2*x^40 + 2*x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 - 2*x^37*y*z0 - 2*x^37*z0^2 - x^35*y*z0^3 + 2*x^38 + 2*x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 - x^37 + x^35*y*z0 + x^35*z0^2 - 2*x^33*y*z0^3 - 2*x^33*z0^4 - 2*x^36 - x^34*y*z0 - 2*x^34*z0^2 - 2*x^32*y*z0^3 - 2*x^32*z0^4 - x^35 - x^33*z0^2 + x^31*y*z0^3 - x^31*z0^4 - x^34 - x^32*y*z0 + 2*x^30*y*z0^3 + x^30*z0^4 - 2*x^33 - x^31*y*z0 - x^31*z0^2 - 2*x^29*y*z0^3 + 2*x^29*z0^4 + 2*x^28*y*z0^3 + x^28*z0^4 - 2*x^31 + x^29*y^2 + 2*x^29*y*z0 - x^29*z0^2 + x^27*y*z0^3 + 2*x^27*z0^4 + x^30 + 2*x^28*z0^2 + 2*x^26*y*z0^3 - x^29 - x^27*y*z0 - x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 + 2*x^28 - 2*x^26*y*z0 - x^26*z0^2 + x^24*y*z0^3 - 2*x^24*z0^4 + 2*x^23*y*z0^3 + x^23*z0^4 + 2*x^26 + 2*x^24*z0^2 - 2*x^22*y*z0^3 - 2*x^22*z0^4 + x^25 - x^23*y*z0 - 2*x^23*z0^2 - 2*x^21*y*z0^3 - 2*x^21*z0^4 + x^24 + 2*x^22*z0^2 + x^20*y*z0^3 + 2*x^21*y*z0 + x^19*y*z0^3 + x^19*z0^4 - 2*x^22 - x^20*y*z0 + 2*x^20*z0^2 + x^18*z0^4 - x^21 - x^19*y*z0 - x^19*z0^2 + 2*x^17*y*z0^3 + 2*x^20 - 2*x^18*y*z0 - x^16*y*z0^3 - 2*x^16*z0^4 + 2*x^17*y*z0 - x^17*z0^2 - x^15*y*z0^3 - x^15*z0^4 + 2*x^18 - 2*x^16*y*z0 + 2*x^16*z0^2 + x^14*y*z0^3 + 2*x^14*z0^4 + x^17 + x^15*y*z0 - 2*x^13*y*z0^3 - x^13*z0^4 - x^14*y*z0 + 2*x^14*z0^2 - 2*x^12*y*z0^3 + x^15 - x^13*z0^2 - x^11*y*z0^3 - 2*x^11*z0^4 - x^14 - x^12*y*z0 - x^10*z0^4 - 2*x^13 + 2*x^11*y*z0 - x^11*z0^2 - 2*x^9*z0^4 - 2*x^12 + x^10*y*z0 + x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*y*z0^3 + x^7*z0^4 + x^10 + x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 + 2*x^9 + 2*x^7*y*z0 - x^5*y*z0^3 - 2*x^5*z0^4 - x^8 - 2*x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 - x^7 + 2*x^5*y*z0 - x^5*z0^2 - x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^6 - 2*x^4*y*z0 + x^4*z0^2 - x^2*z0^4 - x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 + 2*x^2*z0^2)/y) * dx, - ((-x^60*z0^3 - x^59*z0^3 + x^57*y^2*z0^3 - x^60*z0 - 2*x^58*z0^3 + x^56*y^2*z0^3 + 2*x^59*z0 + x^57*y^2*z0 + x^57*z0^3 + 2*x^55*y^2*z0^3 - 2*x^56*y^2*z0 + x^56*z0^3 + x^57*z0 + 2*x^55*z0^3 - 2*x^56*z0 - x^54*z0^3 - x^53*z0^3 - x^54*z0 - 2*x^52*z0^3 + 2*x^53*z0 + x^51*z0^3 + x^50*z0^3 + x^51*z0 + 2*x^49*z0^3 - 2*x^50*z0 - x^48*z0^3 - x^47*z0^3 - x^48*z0 - 2*x^46*z0^3 + 2*x^47*z0 + x^45*z0^3 + x^44*z0^3 + x^45*z0 + 2*x^43*z0^3 - 2*x^44*z0 - x^42*z0^3 - x^41*z0^3 - x^42*z0 - 2*x^40*z0^3 + 2*x^41*z0 + x^39*z0^3 - x^37*y*z0^4 + 2*x^40*z0 - 2*x^38*y*z0^2 - 2*x^36*y*z0^4 + 2*x^39*y - 2*x^37*y*z0^2 - 2*x^37*z0^3 - x^35*y*z0^4 + 2*x^38*y - x^36*y*z0^2 + x^36*z0^3 - x^37*z0 + x^35*z0^3 + x^33*y*z0^4 - 2*x^36*y + x^36*z0 + 2*x^34*y*z0^2 + 2*x^35*y + 2*x^35*z0 + x^33*y*z0^2 + x^33*z0^3 - x^31*y*z0^4 - 2*x^34*y - x^34*z0 + 2*x^32*y*z0^2 - x^32*z0^3 - 2*x^30*y*z0^4 - 2*x^33*y + x^31*z0^3 + x^29*y*z0^4 + 2*x^32*y - x^32*z0 - 2*x^30*z0^3 + 2*x^28*y*z0^4 + 2*x^31*y + x^29*y^2*z0 + x^29*y*z0^2 + 2*x^29*z0^3 - x^27*y*z0^4 - 2*x^30*y + x^30*z0 + 2*x^28*z0^3 - x^26*y*z0^4 + 2*x^29*z0 - 2*x^27*y*z0^2 + 2*x^27*z0^3 - x^25*y*z0^4 - 2*x^28*y - x^28*z0 + 2*x^26*y*z0^2 + 2*x^26*z0^3 + x^24*y*z0^4 + 2*x^27*y + 2*x^27*z0 + 2*x^25*y*z0^2 + 2*x^25*z0^3 - x^26*y + 2*x^26*z0 + 2*x^24*y*z0^2 - x^24*z0^3 + 2*x^22*y*z0^4 + 2*x^25*y + x^23*y*z0^2 + 2*x^23*z0^3 - 2*x^21*y*z0^4 + x^24*y - x^24*z0 + x^22*y*z0^2 - 2*x^22*z0^3 + x^20*y*z0^4 - 2*x^23*y - 2*x^23*z0 - x^21*z0^3 + x^22*y + x^22*z0 + 2*x^20*y*z0^2 + 2*x^21*z0 - 2*x^19*y*z0^2 + 2*x^19*z0^3 - 2*x^17*y*z0^4 + 2*x^18*y*z0^2 - 2*x^19*y - 2*x^17*y*z0^2 - x^17*z0^3 + x^15*y*z0^4 + x^18*y + 2*x^16*y*z0^2 - 2*x^16*z0^3 - x^14*y*z0^4 - 2*x^17*z0 - 2*x^15*y*z0^2 + x^13*y*z0^4 + x^16*y + 2*x^16*z0 + x^14*y*z0^2 - x^14*z0^3 + x^12*y*z0^4 - x^15*y + x^15*z0 + x^13*y*z0^2 - x^13*z0^3 + x^14*y + x^14*z0 + x^12*y*z0^2 - x^12*z0^3 + x^10*y*z0^4 + 2*x^13*y + x^13*z0 - x^11*y*z0^2 - 2*x^11*z0^3 + x^9*y*z0^4 - 2*x^12*y - 2*x^12*z0 + 2*x^10*z0^3 + x^11*y + 2*x^11*z0 + x^9*z0^3 - x^7*y*z0^4 + 2*x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^7*y*z0^2 + x^5*y*z0^4 - 2*x^8*y + x^8*z0 + x^6*z0^3 + 2*x^7*y - x^7*z0 + 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y + 2*x^6*z0 + 2*x^4*y*z0^2 - x^2*y*z0^4 - x^5*y - x^5*z0 + 2*x^3*y*z0^2 + 2*x^4*y - 2*x^4*z0 + x^2*y*z0^2 - 2*x^2*z0^3 - 2*x^3*y + x^3*z0 - x^2*z0)/y) * dx, - ((2*x^61*z0^4 + 2*x^60*z0^4 - 2*x^58*y^2*z0^4 + 2*x^61*z0^2 - x^59*z0^4 - 2*x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 - 2*x^61 + x^57*y^2*z0^2 - 2*x^57*z0^4 + 2*x^58*y^2 - 2*x^58*z0^2 + x^56*z0^4 + x^57*z0^2 + 2*x^55*z0^4 + 2*x^58 + 2*x^54*z0^4 + 2*x^55*z0^2 - x^53*z0^4 - x^54*z0^2 - 2*x^52*z0^4 - 2*x^55 - 2*x^51*z0^4 - 2*x^52*z0^2 + x^50*z0^4 + x^51*z0^2 + 2*x^49*z0^4 + 2*x^52 + 2*x^48*z0^4 + 2*x^49*z0^2 - x^47*z0^4 - x^48*z0^2 - 2*x^46*z0^4 - 2*x^49 - 2*x^45*z0^4 - 2*x^46*z0^2 + x^44*z0^4 + x^45*z0^2 + 2*x^43*z0^4 + 2*x^46 + 2*x^42*z0^4 + 2*x^43*z0^2 - x^42*z0^2 + x^40*y*z0^3 + 2*x^40*z0^4 - 2*x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + x^39*z0^4 + x^40*y*z0 + 2*x^40*z0^2 + x^38*y*z0^3 + 2*x^38*z0^4 + x^41 - 2*x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 - x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + x^36*z0^4 - 2*x^39 - x^37*y*z0 + 2*x^37*z0^2 - x^35*y*z0^3 + 2*x^35*z0^4 - 2*x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 - x^34*z0^4 + 2*x^37 - 2*x^35*y*z0 - 2*x^33*y*z0^3 - x^33*z0^4 + 2*x^34*y*z0 + x^34*z0^2 - 2*x^32*z0^4 + x^35 + 2*x^33*y*z0 - 2*x^33*z0^2 - 2*x^31*y*z0^3 + x^31*z0^4 - x^34 - x^32*y*z0 - 2*x^32*z0^2 - 2*x^30*y*z0^3 + 2*x^33 - x^31*y*z0 + 2*x^31*z0^2 + x^29*y^2*z0^2 + x^29*y*z0^3 - 2*x^29*z0^4 + x^32 - x^30*y*z0 - x^30*z0^2 + 2*x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 + 2*x^29*y*z0 - 2*x^29*z0^2 - x^27*y*z0^3 + x^27*z0^4 + 2*x^30 + x^28*y*z0 + x^28*z0^2 + 2*x^26*z0^4 - x^29 - x^27*y*z0 - x^27*z0^2 + x^25*y*z0^3 + x^25*z0^4 - x^28 - 2*x^26*z0^2 - 2*x^24*y*z0^3 + 2*x^24*z0^4 - 2*x^27 - 2*x^25*y*z0 - x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 - 2*x^26 - 2*x^24*y*z0 - x^24*z0^2 + x^22*y*z0^3 - x^25 - 2*x^23*y*z0 + 2*x^23*z0^2 + 2*x^21*y*z0^3 + x^21*z0^4 + x^24 + x^22*y*z0 + x^22*z0^2 + x^20*y*z0^3 + x^20*z0^4 - 2*x^19*z0^4 + x^22 + 2*x^20*y*z0 + x^18*y*z0^3 + x^18*z0^4 - x^21 + x^19*y*z0 - x^19*z0^2 - 2*x^17*y*z0^3 + x^18*y*z0 + 2*x^18*z0^2 + x^16*y*z0^3 - 2*x^16*z0^4 + 2*x^17*z0^2 + 2*x^15*y*z0^3 + 2*x^15*z0^4 - 2*x^16*y*z0 - x^16*z0^2 + 2*x^14*y*z0^3 + 2*x^14*z0^4 - 2*x^15*z0^2 + x^13*y*z0^3 - 2*x^13*z0^4 - 2*x^16 + 2*x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 - 2*x^15 - 2*x^13*y*z0 + x^13*z0^2 + x^11*z0^4 - 2*x^14 - x^12*y*z0 - x^12*z0^2 + 2*x^10*y*z0^3 + x^10*z0^4 + 2*x^13 + x^11*z0^2 - 2*x^9*y*z0^3 + 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 + x^8*z0^4 - x^11 - x^9*z0^2 + 2*x^7*y*z0^3 - x^7*z0^4 + 2*x^10 - 2*x^8*y*z0 - x^8*z0^2 + 2*x^6*z0^4 - x^9 + x^7*y*z0 + 2*x^7*z0^2 + x^5*y*z0^3 + x^5*z0^4 + x^6*y*z0 + x^6*z0^2 + 2*x^4*z0^4 - 2*x^7 + 2*x^5*y*z0 - 2*x^5*z0^2 + x^3*y*z0^3 + x^3*z0^4 - 2*x^6 - x^4*z0^2 - x^2*y*z0^3 + x^2*z0^4 - x^3*z0^2 - 2*x^2*y*z0 - x^3 + x^2)/y) * dx, - ((2*x^61*z0^3 + x^60*z0^3 - 2*x^58*y^2*z0^3 + 2*x^61*z0 + 2*x^59*z0^3 - x^57*y^2*z0^3 - x^60*z0 - 2*x^58*y^2*z0 + 2*x^58*z0^3 - 2*x^56*y^2*z0^3 - 2*x^59*z0 + x^57*y^2*z0 + x^57*z0^3 + x^55*y^2*z0^3 - 2*x^58*z0 + 2*x^56*y^2*z0 - 2*x^56*z0^3 - 2*x^54*y^2*z0^3 + x^57*z0 - 2*x^55*z0^3 + 2*x^56*z0 - x^54*z0^3 + 2*x^55*z0 + 2*x^53*z0^3 - x^54*z0 + 2*x^52*z0^3 - 2*x^53*z0 + x^51*z0^3 - 2*x^52*z0 - 2*x^50*z0^3 + x^51*z0 - 2*x^49*z0^3 + 2*x^50*z0 - x^48*z0^3 + 2*x^49*z0 + 2*x^47*z0^3 - x^48*z0 + 2*x^46*z0^3 - 2*x^47*z0 + x^45*z0^3 - 2*x^46*z0 - 2*x^44*z0^3 + x^45*z0 - 2*x^43*z0^3 + 2*x^44*z0 - x^42*z0^3 + 2*x^43*z0 - x^41*z0^3 + 2*x^39*y*z0^4 - x^42*z0 + x^40*y*z0^2 - x^40*z0^3 + 2*x^38*y*z0^4 + 2*x^39*y*z0^2 + x^39*z0^3 - x^37*y*z0^4 + x^40*y - 2*x^40*z0 - x^38*y*z0^2 - x^38*z0^3 + 2*x^37*z0^3 + x^35*y*z0^4 - 2*x^38*y - x^38*z0 + 2*x^36*y*z0^2 + 2*x^34*y*z0^4 + 2*x^37*y - x^37*z0 - x^35*y*z0^2 - 2*x^35*z0^3 - x^33*y*z0^4 + 2*x^36*y - x^36*z0 + x^34*y*z0^2 + 2*x^32*y*z0^4 + x^35*z0 + x^33*y*z0^2 - x^33*z0^3 + 2*x^31*y*z0^4 - 2*x^34*y + x^34*z0 + 2*x^32*z0^3 + x^30*y*z0^4 + 2*x^33*y - x^33*z0 + x^31*y*z0^2 - x^31*z0^3 + x^29*y^2*z0^3 + x^29*y*z0^4 - x^32*y - 2*x^32*z0 - 2*x^30*y*z0^2 + x^30*z0^3 - 2*x^28*y*z0^4 - 2*x^31*y - 2*x^29*y*z0^2 + 2*x^29*z0^3 - 2*x^27*y*z0^4 + 2*x^30*y + x^30*z0 - 2*x^28*y*z0^2 - 2*x^28*z0^3 + x^26*y*z0^4 - 2*x^29*z0 + 2*x^27*y*z0^2 + x^25*y*z0^4 + 2*x^28*y + x^28*z0 + 2*x^26*y*z0^2 + 2*x^26*z0^3 + 2*x^24*y*z0^4 - 2*x^27*y + 2*x^25*y*z0^2 - x^25*z0^3 + 2*x^23*y*z0^4 - 2*x^26*z0 - x^24*y*z0^2 + 2*x^24*z0^3 - x^22*y*z0^4 + 2*x^25*y - 2*x^25*z0 - 2*x^23*y*z0^2 - x^23*z0^3 - 2*x^21*y*z0^4 - 2*x^24*y - x^22*y*z0^2 + x^22*z0^3 + x^20*y*z0^4 + 2*x^23*y - 2*x^23*z0 + x^21*y*z0^2 - x^21*z0^3 - x^19*y*z0^4 - 2*x^22*y + x^22*z0 - 2*x^20*y*z0^2 + 2*x^20*z0^3 + 2*x^18*y*z0^4 - x^17*y*z0^4 - 2*x^20*y + x^20*z0 - 2*x^18*z0^3 - 2*x^16*y*z0^4 + x^19*y - 2*x^17*y*z0^2 + 2*x^15*y*z0^4 - x^18*y - x^16*y*z0^2 - x^16*z0^3 + 2*x^17*y - x^17*z0 - x^15*y*z0^2 - 2*x^15*z0^3 - x^13*y*z0^4 - 2*x^16*y - 2*x^16*z0 + x^14*z0^3 + 2*x^12*y*z0^4 - 2*x^15*y - x^13*y*z0^2 - 2*x^13*z0^3 + x^11*y*z0^4 - x^14*y - x^14*z0 - 2*x^12*z0^3 + x^10*y*z0^4 - x^11*y*z0^2 + 2*x^11*z0^3 + x^9*y*z0^4 - x^12*y + x^12*z0 - x^10*y*z0^2 - x^10*z0^3 - x^8*y*z0^4 + x^11*y - x^11*z0 + x^9*z0^3 - x^7*y*z0^4 - x^10*y + x^10*z0 + x^6*y*z0^4 - 2*x^9*y + x^9*z0 + 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y + x^6*y*z0^2 - x^6*z0^3 + x^4*y*z0^4 - x^5*y*z0^2 + 2*x^5*z0^3 - x^6*y + x^4*y*z0^2 - 2*x^4*z0^3 - x^2*y*z0^4 - x^5*y - x^5*z0 - 2*x^3*z0^3 + x^4*y - 2*x^2*y*z0^2 + x^2*z0)/y) * dx, - ((2*x^61*z0^4 - x^60*z0^4 - 2*x^58*y^2*z0^4 - 2*x^61*z0^2 - x^59*z0^4 + x^57*y^2*z0^4 + 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 - x^61 + x^57*z0^4 - 2*x^60 + x^58*y^2 + 2*x^58*z0^2 + x^56*z0^4 + 2*x^57*y^2 + 2*x^55*z0^4 + x^58 - x^54*z0^4 + 2*x^57 - 2*x^55*z0^2 - x^53*z0^4 - 2*x^52*z0^4 - x^55 + x^51*z0^4 - 2*x^54 + 2*x^52*z0^2 + x^50*z0^4 + 2*x^49*z0^4 + x^52 - x^48*z0^4 + 2*x^51 - 2*x^49*z0^2 - x^47*z0^4 - 2*x^46*z0^4 - x^49 + x^45*z0^4 - 2*x^48 + 2*x^46*z0^2 + x^44*z0^4 + 2*x^43*z0^4 + x^46 - x^42*z0^4 + 2*x^45 - 2*x^43*z0^2 - 2*x^41*z0^4 + x^40*y*z0^3 - x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - x^39*z0^4 - 2*x^42 - x^40*y*z0 - 2*x^40*z0^2 + x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + 2*x^39*z0^2 + 2*x^37*y*z0^3 + 2*x^37*z0^4 - x^40 + 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 - 2*x^39 - 2*x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 - 2*x^35*z0^4 + x^38 - 2*x^36*z0^2 - x^37 + 2*x^35*y*z0 - x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 + x^34*y*z0 - 2*x^34*z0^2 - x^32*y*z0^3 + x^35 + 2*x^33*y*z0 + x^31*y*z0^3 - 2*x^31*z0^4 + x^29*y^2*z0^4 + 2*x^34 - x^32*y*z0 - 2*x^32*z0^2 - 2*x^30*y*z0^3 + x^30*z0^4 - x^33 - x^31*y*z0 - 2*x^31*z0^2 + x^29*y*z0^3 - x^29*z0^4 - 2*x^32 + 2*x^30*y*z0 + 2*x^30*z0^2 + x^28*y*z0^3 - x^28*z0^4 + 2*x^31 - x^29*y*z0 + 2*x^29*z0^2 + x^27*y*z0^3 + x^30 - 2*x^26*y*z0^3 - x^29 + x^27*y*z0 - x^27*z0^2 - 2*x^25*y*z0^3 - x^25*z0^4 - 2*x^28 - x^26*y*z0 + x^26*z0^2 + 2*x^24*z0^4 - x^25*z0^2 - 2*x^23*z0^4 - 2*x^26 - 2*x^24*y*z0 + 2*x^24*z0^2 + 2*x^22*y*z0^3 + 2*x^22*z0^4 + 2*x^25 + x^23*y*z0 + x^23*z0^2 + 2*x^21*y*z0^3 + 2*x^21*z0^4 + 2*x^20*y*z0^3 - 2*x^23 + 2*x^21*y*z0 - x^21*z0^2 + x^19*y*z0^3 - x^19*z0^4 + 2*x^22 - 2*x^20*y*z0 - 2*x^20*z0^2 + x^18*y*z0^3 - x^18*z0^4 + x^21 - x^19*y*z0 + 2*x^19*z0^2 + 2*x^17*y*z0^3 - x^20 - 2*x^18*y*z0 + x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 - x^19 - x^17*z0^2 - x^15*y*z0^3 + x^15*z0^4 - x^18 - 2*x^16*y*z0 + 2*x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 + x^17 + 2*x^15*z0^2 - x^13*y*z0^3 - 2*x^13*z0^4 - 2*x^16 + 2*x^14*y*z0 + x^14*z0^2 + 2*x^12*z0^4 - x^15 - x^13*y*z0 + 2*x^11*z0^4 - 2*x^10*y*z0^3 + 2*x^10*z0^4 + 2*x^13 - 2*x^11*y*z0 - 2*x^11*z0^2 + 2*x^9*y*z0^3 - 2*x^12 - x^10*y*z0 - x^10*z0^2 + x^8*y*z0^3 - 2*x^11 - x^9*z0^2 - x^10 - 2*x^8*y*z0 + 2*x^6*y*z0^3 + x^6*z0^4 - x^7*y*z0 - 2*x^7*z0^2 + x^5*z0^4 + 2*x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 + x^4*z0^4 - x^7 - x^5*y*z0 + x^5*z0^2 + 2*x^3*y*z0^3 - x^3*z0^4 - x^6 + 2*x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - x^5 + x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-2*x^61*z0^4 - 2*x^60*z0^4 + 2*x^58*y^2*z0^4 - x^61*z0^2 + x^59*z0^4 + 2*x^57*y^2*z0^4 + x^58*y^2*z0^2 + 2*x^58*z0^4 - x^56*y^2*z0^4 - x^61 + 2*x^57*z0^4 + x^60 + x^58*y^2 + x^58*z0^2 - x^56*z0^4 - x^57*y^2 - 2*x^55*z0^4 + x^58 - 2*x^54*z0^4 - x^57 - x^55*z0^2 + x^53*z0^4 + 2*x^52*z0^4 - x^55 + 2*x^51*z0^4 + x^54 + x^52*z0^2 - x^50*z0^4 - 2*x^49*z0^4 + x^52 - 2*x^48*z0^4 - x^51 - x^49*z0^2 + x^47*z0^4 + 2*x^46*z0^4 - x^49 + 2*x^45*z0^4 + x^48 + x^46*z0^2 - x^44*z0^4 - 2*x^43*z0^4 + x^46 - 2*x^42*z0^4 - x^45 - x^43*z0^2 + x^41*z0^4 - x^40*y*z0^3 + x^40*z0^4 - x^43 - x^41*z0^2 - x^39*y*z0^3 - x^39*z0^4 + x^42 + 2*x^40*y*z0 - 2*x^40*z0^2 - 2*x^38*y*z0^3 - x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 + x^37*z0^4 + 2*x^40 + x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 - 2*x^36*z0^4 - x^39 + 2*x^37*z0^2 + x^35*z0^4 + 2*x^38 - 2*x^36*y*z0 - x^36*z0^2 + 2*x^37 + 2*x^35*y*z0 + x^35*z0^2 + x^33*z0^4 - x^36 - x^34*y*z0 - 2*x^34*z0^2 + x^32*y*z0^3 + x^32*z0^4 + x^33*y*z0 + x^33*z0^2 + 2*x^31*y*z0^3 - x^31*z0^4 - 2*x^34 + x^32*y*z0 - 2*x^30*y*z0^3 + 2*x^30*z0^4 - 2*x^31*y*z0 - x^31*z0^2 + x^29*y*z0^3 + 2*x^32 + x^30*y^2 - 2*x^30*y*z0 + x^30*z0^2 + x^28*y*z0^3 + 2*x^28*z0^4 + x^29*y*z0 - x^29*z0^2 + 2*x^27*y*z0^3 + 2*x^27*z0^4 - x^30 + x^28*y*z0 - x^26*z0^4 - 2*x^29 - 2*x^27*y*z0 + x^27*z0^2 - x^25*z0^4 - x^28 + x^26*z0^2 + x^24*z0^4 - 2*x^27 + x^25*y*z0 - 2*x^25*z0^2 - 2*x^23*y*z0^3 + x^23*z0^4 + 2*x^26 - x^24*y*z0 - x^24*z0^2 + x^22*y*z0^3 + 2*x^25 + x^23*y*z0 - x^21*y*z0^3 - 2*x^21*z0^4 - 2*x^24 - x^22*y*z0 + 2*x^22*z0^2 + x^20*z0^4 - x^23 - 2*x^21*y*z0 + x^21*z0^2 + 2*x^19*y*z0^3 - x^19*z0^4 - x^22 - x^18*y*z0^3 + 2*x^18*z0^4 + 2*x^21 + x^17*y*z0^3 + 2*x^17*z0^4 + 2*x^20 - x^18*y*z0 - x^18*z0^2 + 2*x^16*y*z0^3 - 2*x^16*z0^4 + x^19 + x^17*y*z0 + x^17*z0^2 - x^15*y*z0^3 - x^15*z0^4 + 2*x^18 - x^16*y*z0 - x^16*z0^2 + x^14*y*z0^3 + 2*x^17 + x^15*y*z0 - 2*x^15*z0^2 + x^13*y*z0^3 - x^13*z0^4 - x^16 + x^14*y*z0 - 2*x^14*z0^2 - 2*x^12*y*z0^3 - 2*x^12*z0^4 - 2*x^15 - x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 - x^14 - x^12*y*z0 + 2*x^12*z0^2 + 2*x^10*z0^4 - x^11*y*z0 - x^9*z0^4 + 2*x^12 + x^10*y*z0 - 2*x^10*z0^2 + x^8*y*z0^3 + 2*x^8*z0^4 - x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 - x^7*z0^4 - 2*x^8*y*z0 + 2*x^8*z0^2 - x^6*y*z0^3 + 2*x^6*z0^4 - x^9 - 2*x^7*y*z0 + x^7*z0^2 - 2*x^5*z0^4 - x^8 + x^6*y*z0 - x^6*z0^2 + x^7 - x^5*y*z0 - x^5*z0^2 + 2*x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^6 - x^4*y*z0 + 2*x^4*z0^2 - x^2*y*z0^3 + x^2*z0^4 + 2*x^3*y*z0 + x^3*z0^2 + x^2*y*z0 - 2*x^2*z0^2 + x^2)/y) * dx, - ((2*x^61*z0^3 - 2*x^60*z0^3 - 2*x^58*y^2*z0^3 + 2*x^59*z0^3 + 2*x^57*y^2*z0^3 + x^60*z0 + x^58*z0^3 - 2*x^56*y^2*z0^3 - x^57*y^2*z0 + x^57*z0^3 + 2*x^55*y^2*z0^3 - 2*x^56*z0^3 + x^54*y^2*z0^3 - x^57*z0 - x^55*z0^3 - x^54*z0^3 + 2*x^53*z0^3 + x^54*z0 + x^52*z0^3 + x^51*z0^3 - 2*x^50*z0^3 - x^51*z0 - x^49*z0^3 - x^48*z0^3 + 2*x^47*z0^3 + x^48*z0 + x^46*z0^3 + x^45*z0^3 - 2*x^44*z0^3 - x^45*z0 - x^43*z0^3 - x^42*z0^3 - x^41*z0^3 + 2*x^39*y*z0^4 + x^42*z0 + x^40*y*z0^2 + x^40*z0^3 - x^38*y*z0^4 - 2*x^39*z0^3 + x^37*y*z0^4 - 2*x^38*y*z0^2 - x^38*z0^3 + x^39*y - x^39*z0 + 2*x^37*y*z0^2 + x^35*y*z0^4 - x^38*y - 2*x^36*z0^3 + 2*x^34*y*z0^4 - 2*x^37*z0 + 2*x^35*y*z0^2 - 2*x^35*z0^3 - 2*x^33*y*z0^4 + x^36*z0 + x^34*y*z0^2 + 2*x^34*z0^3 + x^32*y*z0^4 + 2*x^35*z0 + x^31*y*z0^4 - 2*x^34*y - 2*x^30*y*z0^4 + x^33*y + x^31*z0^3 + 2*x^29*y*z0^4 + x^32*y + x^30*y^2*z0 + 2*x^30*z0^3 + 2*x^28*y*z0^4 + x^31*y + x^31*z0 + x^29*y*z0^2 + x^27*y*z0^4 - x^28*y*z0^2 + x^28*z0^3 + 2*x^26*y*z0^4 - x^29*y - 2*x^29*z0 + 2*x^27*y*z0^2 - x^27*z0^3 + 2*x^25*y*z0^4 - x^26*y*z0^2 - x^26*z0^3 + 2*x^24*y*z0^4 - x^27*y + 2*x^25*y*z0^2 - 2*x^25*z0^3 + x^23*y*z0^4 + 2*x^26*z0 + 2*x^24*y*z0^2 - x^24*z0^3 + 2*x^22*y*z0^4 - 2*x^25*y + 2*x^25*z0 + 2*x^23*y*z0^2 - 2*x^23*z0^3 + x^21*y*z0^4 - 2*x^24*y - 2*x^24*z0 - x^22*y*z0^2 - 2*x^22*z0^3 - 2*x^20*y*z0^4 - 2*x^23*y - x^21*y*z0^2 - 2*x^21*z0^3 - 2*x^19*y*z0^4 - 2*x^22*y + x^22*z0 + 2*x^18*y*z0^4 - x^21*y + 2*x^21*z0 + x^19*y*z0^2 + x^19*z0^3 - x^17*y*z0^4 - 2*x^20*y - x^18*y*z0^2 + 2*x^18*z0^3 + x^16*y*z0^4 + x^19*y - 2*x^17*z0^3 - 2*x^15*y*z0^4 - x^18*y + x^18*z0 - x^16*y*z0^2 + x^16*z0^3 + 2*x^14*y*z0^4 + x^17*y - 2*x^17*z0 - x^15*y*z0^2 - x^15*z0^3 - x^16*y + 2*x^14*y*z0^2 + 2*x^14*z0^3 - 2*x^12*y*z0^4 + 2*x^15*y + 2*x^15*z0 - x^13*y*z0^2 - 2*x^13*z0^3 + 2*x^14*y + 2*x^10*y*z0^4 + x^11*z0^3 + 2*x^9*y*z0^4 - 2*x^12*y + x^12*z0 + 2*x^10*y*z0^2 + 2*x^10*z0^3 + 2*x^8*y*z0^4 + x^11*y - 2*x^11*z0 + x^9*y*z0^2 + x^7*y*z0^4 + 2*x^10*y + x^10*z0 + x^8*y*z0^2 + 2*x^8*z0^3 + x^9*y + x^9*z0 - x^5*y*z0^4 - x^8*y + 2*x^8*z0 + x^6*y*z0^2 + x^4*y*z0^4 + 2*x^7*y + 2*x^7*z0 - 2*x^5*y*z0^2 + x^5*z0^3 + x^3*y*z0^4 - x^6*y - 2*x^6*z0 - x^4*y*z0^2 - 2*x^4*z0^3 + 2*x^2*y*z0^4 + x^5*y + 2*x^5*z0 - 2*x^3*y*z0^2 + x^3*z0^3 - 2*x^4*y + 2*x^4*z0 + 2*x^3*y + x^3*z0 + 2*x^2*z0)/y) * dx, - ((x^61*z0^4 - 2*x^60*z0^4 - x^58*y^2*z0^4 - x^61*z0^2 + x^59*z0^4 + 2*x^57*y^2*z0^4 + x^58*y^2*z0^2 - x^58*z0^4 - x^56*y^2*z0^4 + x^61 + 2*x^57*z0^4 - 2*x^60 - x^58*y^2 + x^58*z0^2 - x^56*z0^4 + 2*x^57*y^2 + x^55*z0^4 - x^58 - 2*x^54*z0^4 + 2*x^57 - x^55*z0^2 + x^53*z0^4 - x^52*z0^4 + x^55 + 2*x^51*z0^4 - 2*x^54 + x^52*z0^2 - x^50*z0^4 + x^49*z0^4 - x^52 - 2*x^48*z0^4 + 2*x^51 - x^49*z0^2 + x^47*z0^4 - x^46*z0^4 + x^49 + 2*x^45*z0^4 - 2*x^48 + x^46*z0^2 - x^44*z0^4 + x^43*z0^4 - x^46 - 2*x^42*z0^4 + 2*x^45 - x^43*z0^2 - 2*x^40*y*z0^3 + 2*x^40*z0^4 + x^43 - x^41*z0^2 - x^39*y*z0^3 - 2*x^39*z0^4 - 2*x^42 + 2*x^40*y*z0 + x^40*z0^2 + x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + 2*x^39*y*z0 + x^39*z0^2 + 2*x^37*y*z0^3 + 2*x^37*z0^4 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + 2*x^36*z0^4 + 2*x^39 - x^37*y*z0 + 2*x^37*z0^2 - x^35*z0^4 + 2*x^36*y*z0 - x^36*z0^2 - 2*x^34*z0^4 - 2*x^35*y*z0 + x^33*y*z0^3 - x^33*z0^4 - 2*x^36 + x^34*y*z0 + 2*x^32*y*z0^3 - 2*x^33*y*z0 + x^33*z0^2 - x^31*y*z0^3 + x^31*z0^4 - 2*x^34 + x^32*y*z0 + x^32*z0^2 + x^30*y^2*z0^2 - 2*x^30*z0^4 + 2*x^33 + 2*x^31*y*z0 + 2*x^31*z0^2 - 2*x^29*y*z0^3 + x^29*z0^4 - x^32 - x^30*y*z0 + x^30*z0^2 - x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 - 2*x^29*y*z0 + x^27*y*z0^3 - x^27*z0^4 - 2*x^30 + x^28*z0^2 - x^25*y*z0^3 + 2*x^25*z0^4 + x^28 - x^26*y*z0 + 2*x^26*z0^2 + 2*x^24*z0^4 - x^27 - 2*x^25*y*z0 - 2*x^25*z0^2 - x^26 - 2*x^24*y*z0 + 2*x^24*z0^2 - 2*x^22*y*z0^3 + x^22*z0^4 + x^25 + 2*x^23*y*z0 + 2*x^23*z0^2 - 2*x^21*z0^4 + x^24 - 2*x^22*z0^2 + x^20*y*z0^3 + 2*x^20*z0^4 - 2*x^23 - x^21*y*z0 - 2*x^21*z0^2 - x^19*y*z0^3 - 2*x^19*z0^4 + x^22 - x^20*y*z0 + 2*x^20*z0^2 - x^21 + x^19*y*z0 + 2*x^19*z0^2 - 2*x^17*y*z0^3 - x^17*z0^4 - 2*x^18*y*z0 + 2*x^18*z0^2 + x^16*y*z0^3 - x^16*z0^4 - x^17*z0^2 + x^15*y*z0^3 + 2*x^18 - 2*x^16*y*z0 - x^16*z0^2 + 2*x^14*y*z0^3 - x^17 + x^15*y*z0 - 2*x^15*z0^2 + x^13*y*z0^3 + x^13*z0^4 - x^16 - x^14*y*z0 + 2*x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 - 2*x^15 - x^13*y*z0 - 2*x^11*y*z0^3 + x^14 + x^12*y*z0 - 2*x^12*z0^2 - 2*x^10*y*z0^3 - 2*x^10*z0^4 + x^11*y*z0 + x^11*z0^2 - 2*x^9*y*z0^3 - x^12 + 2*x^10*y*z0 - x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 + x^9*y*z0 + 2*x^9*z0^2 - x^7*y*z0^3 + x^10 - x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 - x^6*z0^4 + 2*x^9 - 2*x^7*y*z0 - x^7*z0^2 - 2*x^5*y*z0^3 + x^5*z0^4 + x^8 + 2*x^6*z0^2 + 2*x^7 + 2*x^5*y*z0 - x^5*z0^2 + 2*x^3*y*z0^3 + x^3*z0^4 + x^2*z0^4 + 2*x^5 - x^3*y*z0 + x^2*y*z0 - x^2*z0^2 - x^3 - x^2)/y) * dx, - ((2*x^61*z0^3 - x^60*z0^3 - 2*x^58*y^2*z0^3 + 2*x^59*z0^3 + x^57*y^2*z0^3 + 2*x^60*z0 + 2*x^58*z0^3 - 2*x^56*y^2*z0^3 - 2*x^59*z0 - 2*x^57*y^2*z0 - 2*x^57*z0^3 + x^55*y^2*z0^3 + 2*x^56*y^2*z0 - 2*x^56*z0^3 - 2*x^54*y^2*z0^3 - 2*x^57*z0 - 2*x^55*z0^3 + 2*x^56*z0 + 2*x^54*z0^3 + 2*x^53*z0^3 + 2*x^54*z0 + 2*x^52*z0^3 - 2*x^53*z0 - 2*x^51*z0^3 - 2*x^50*z0^3 - 2*x^51*z0 - 2*x^49*z0^3 + 2*x^50*z0 + 2*x^48*z0^3 + 2*x^47*z0^3 + 2*x^48*z0 + 2*x^46*z0^3 - 2*x^47*z0 - 2*x^45*z0^3 - 2*x^44*z0^3 - 2*x^45*z0 - 2*x^43*z0^3 + 2*x^44*z0 + 2*x^42*z0^3 - x^41*z0^3 + 2*x^39*y*z0^4 + 2*x^42*z0 + x^40*y*z0^2 + 2*x^40*z0^3 - x^38*y*z0^4 - 2*x^41*z0 - 2*x^39*z0^3 - 2*x^40*z0 - x^38*z0^3 - x^39*y - x^39*z0 + x^35*y*z0^4 + x^38*y + x^36*y*z0^2 - 2*x^36*z0^3 - 2*x^37*z0 - x^35*y*z0^2 - 2*x^33*y*z0^4 - 2*x^36*y - x^34*y*z0^2 - 2*x^34*z0^3 + x^32*y*z0^4 - x^35*y + 2*x^33*y*z0^2 + x^33*z0^3 + x^31*y*z0^4 - x^34*y + 2*x^34*z0 + 2*x^32*y*z0^2 + x^30*y^2*z0^3 - 2*x^30*y*z0^4 + x^33*y - x^33*z0 + 2*x^31*y*z0^2 + 2*x^29*y*z0^4 + 2*x^32*y - 2*x^32*z0 + x^30*y*z0^2 + x^28*y*z0^4 + x^31*y - 2*x^29*y*z0^2 + 2*x^30*y - 2*x^28*y*z0^2 + 2*x^28*z0^3 - 2*x^26*y*z0^4 + 2*x^29*z0 + x^27*z0^3 + x^25*y*z0^4 - 2*x^28*y + x^28*z0 - x^26*y*z0^2 - 2*x^26*z0^3 - 2*x^24*y*z0^4 - x^27*y + x^27*z0 + x^25*y*z0^2 + x^25*z0^3 - x^23*y*z0^4 + 2*x^26*y + x^26*z0 - x^24*z0^3 - 2*x^22*y*z0^4 + 2*x^25*y - 2*x^25*z0 - x^23*y*z0^2 + x^23*z0^3 - 2*x^21*y*z0^4 - 2*x^24*y - 2*x^24*z0 + 2*x^22*y*z0^2 + x^22*z0^3 - x^20*y*z0^4 - 2*x^23*y - 2*x^23*z0 + x^21*y*z0^2 - 2*x^21*z0^3 + x^19*y*z0^4 - 2*x^22*y - x^22*z0 - 2*x^20*y*z0^2 + x^18*y*z0^4 - x^21*z0 + 2*x^19*y*z0^2 + x^17*y*z0^4 + x^20*y - x^20*z0 - x^18*y*z0^2 - x^18*z0^3 - 2*x^19*y + x^19*z0 - x^17*y*z0^2 + x^17*z0^3 + 2*x^15*y*z0^4 - x^18*y + x^18*z0 + x^16*y*z0^2 + x^16*z0^3 - 2*x^17*y - 2*x^17*z0 + 2*x^15*y*z0^2 - x^15*z0^3 + x^13*y*z0^4 + 2*x^16*y - 2*x^16*z0 + x^14*y*z0^2 + 2*x^14*z0^3 + 2*x^12*y*z0^4 - 2*x^15*y - x^15*z0 + 2*x^13*y*z0^2 - 2*x^13*z0^3 - 2*x^11*y*z0^4 - x^14*y + x^14*z0 - 2*x^12*y*z0^2 - x^12*z0^3 + x^10*y*z0^4 + x^13*z0 + x^11*y*z0^2 - 2*x^11*z0^3 - x^12*y + x^12*z0 - 2*x^10*y*z0^2 - 2*x^10*z0^3 + x^8*y*z0^4 - x^11*y + 2*x^11*z0 + x^9*y*z0^2 - 2*x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y + 2*x^8*y*z0^2 - 2*x^6*y*z0^4 - 2*x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 - 2*x^5*y*z0^4 - x^8*z0 + 2*x^6*y*z0^2 - 2*x^6*z0^3 + x^7*y + 2*x^7*z0 - x^5*z0^3 - 2*x^3*y*z0^4 - 2*x^6*y - 2*x^6*z0 + 2*x^4*y*z0^2 + x^2*y*z0^4 - x^3*y*z0^2 + x^3*z0^3 - x^4*y - 2*x^4*z0 + x^2*y*z0^2 - 2*x^3*y + 2*x^3*z0 - x^2*z0)/y) * dx, - ((2*x^61*z0^4 + 2*x^60*z0^4 - 2*x^58*y^2*z0^4 + x^61*z0^2 + x^59*z0^4 - 2*x^57*y^2*z0^4 + 2*x^60*z0^2 - x^58*y^2*z0^2 - 2*x^58*z0^4 - x^56*y^2*z0^4 - 2*x^57*y^2*z0^2 - 2*x^57*z0^4 - 2*x^60 - x^58*z0^2 - x^56*z0^4 + 2*x^57*y^2 - 2*x^57*z0^2 + 2*x^55*z0^4 + 2*x^54*z0^4 + 2*x^57 + x^55*z0^2 + x^53*z0^4 + 2*x^54*z0^2 - 2*x^52*z0^4 - 2*x^51*z0^4 - 2*x^54 - x^52*z0^2 - x^50*z0^4 - 2*x^51*z0^2 + 2*x^49*z0^4 + 2*x^48*z0^4 + 2*x^51 + x^49*z0^2 + x^47*z0^4 + 2*x^48*z0^2 - 2*x^46*z0^4 - 2*x^45*z0^4 - 2*x^48 - x^46*z0^2 - x^44*z0^4 - 2*x^45*z0^2 + 2*x^43*z0^4 + 2*x^42*z0^4 + 2*x^45 + x^43*z0^2 - 2*x^41*z0^4 + 2*x^42*z0^2 + x^40*y*z0^3 + x^41*z0^2 + x^39*y*z0^3 - x^39*z0^4 - 2*x^42 - 2*x^40*y*z0 + 2*x^40*z0^2 - x^38*y*z0^3 - x^38*z0^4 + 2*x^41 + 2*x^39*z0^2 - 2*x^37*y*z0^3 - 2*x^37*z0^4 - x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 + x^36*z0^4 - 2*x^39 - x^37*y*z0 + 2*x^35*y*z0^3 + 2*x^35*z0^4 + x^38 - 2*x^36*y*z0 - 2*x^36*z0^2 + 2*x^34*y*z0^3 + x^34*z0^4 + x^37 + x^35*z0^2 - x^33*y*z0^3 + x^36 - 2*x^34*y*z0 + 2*x^32*y*z0^3 + x^32*z0^4 + x^30*y^2*z0^4 - 2*x^35 + 2*x^33*y*z0 - 2*x^33*z0^2 - x^31*y*z0^3 + 2*x^31*z0^4 - x^34 - x^32*z0^2 - 2*x^30*y*z0^3 - 2*x^30*z0^4 - x^31*y*z0 - 2*x^31*z0^2 + 2*x^29*y*z0^3 - 2*x^29*z0^4 - x^32 - 2*x^30*y*z0 - x^30*z0^2 - x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 + 2*x^29*y*z0 + x^29*z0^2 + x^27*y*z0^3 - x^27*z0^4 + x^28*y*z0 + x^26*y*z0^3 - 2*x^29 - 2*x^27*z0^2 - x^25*y*z0^3 - x^25*z0^4 + x^28 - x^26*y*z0 + x^26*z0^2 - x^24*y*z0^3 - 2*x^24*z0^4 + x^27 - 2*x^25*y*z0 - 2*x^25*z0^2 - 2*x^23*z0^4 - x^26 + x^24*y*z0 - x^24*z0^2 + 2*x^22*y*z0^3 + x^22*z0^4 - 2*x^25 - x^23*y*z0 + 2*x^23*z0^2 - x^21*y*z0^3 - x^21*z0^4 + 2*x^24 - x^22*y*z0 - x^22*z0^2 - x^20*y*z0^3 - x^23 + x^21*y*z0 - 2*x^21*z0^2 + x^19*y*z0^3 - 2*x^19*z0^4 - x^22 + x^20*y*z0 - 2*x^20*z0^2 - 2*x^18*z0^4 - x^21 + x^19*y*z0 - 2*x^19*z0^2 - x^17*z0^4 - 2*x^20 - x^18*y*z0 + 2*x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^16*z0^4 - x^19 + 2*x^17*y*z0 + 2*x^17*z0^2 - x^15*y*z0^3 + x^15*z0^4 + x^18 - 2*x^16*y*z0 + x^16*z0^2 + x^14*y*z0^3 + 2*x^15*z0^2 - x^13*y*z0^3 - x^13*z0^4 - x^16 - 2*x^14*y*z0 - x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 - x^15 - x^13*y*z0 + 2*x^13*z0^2 - x^11*z0^4 - 2*x^14 - 2*x^12*y*z0 + x^12*z0^2 - x^10*y*z0^3 - x^10*z0^4 - x^13 + 2*x^11*y*z0 - 2*x^11*z0^2 - x^9*y*z0^3 + x^12 + x^10*y*z0 + 2*x^8*y*z0^3 - x^8*z0^4 + x^9*z0^2 + 2*x^7*y*z0^3 - 2*x^8*y*z0 + x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 + x^7*z0^2 - 2*x^5*z0^4 - x^8 - x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - 2*x^4*z0^4 - x^7 + x^5*y*z0 + 2*x^5*z0^2 + 2*x^3*y*z0^3 + x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 - 2*x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + x^2*y*z0 + x^2*z0^2 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 - 2*x^60*z0^4 + x^58*y^2*z0^4 + x^59*z0^4 + 2*x^57*y^2*z0^4 - 2*x^60*z0^2 + x^58*z0^4 - x^56*y^2*z0^4 - 2*x^61 + 2*x^57*y^2*z0^2 + 2*x^57*z0^4 - 2*x^60 + 2*x^58*y^2 - x^56*z0^4 + 2*x^57*y^2 + 2*x^57*z0^2 - x^55*z0^4 + 2*x^58 - 2*x^54*z0^4 + 2*x^57 + x^53*z0^4 - 2*x^54*z0^2 + x^52*z0^4 - 2*x^55 + 2*x^51*z0^4 - 2*x^54 - x^50*z0^4 + 2*x^51*z0^2 - x^49*z0^4 + 2*x^52 - 2*x^48*z0^4 + 2*x^51 + x^47*z0^4 - 2*x^48*z0^2 + x^46*z0^4 - 2*x^49 + 2*x^45*z0^4 - 2*x^48 - x^44*z0^4 + 2*x^45*z0^2 - x^43*z0^4 + 2*x^46 - 2*x^42*z0^4 + 2*x^45 - x^41*z0^4 - 2*x^42*z0^2 + 2*x^40*y*z0^3 - 2*x^40*z0^4 - 2*x^43 - 2*x^39*z0^4 - 2*x^42 + x^40*z0^2 - x^38*y*z0^3 + x^38*z0^4 - 2*x^41 + 2*x^39*z0^2 - x^37*y*z0^3 + 2*x^37*z0^4 + 2*x^40 - 2*x^38*y*z0 + 2*x^36*z0^4 + x^39 - 2*x^37*z0^2 + x^35*y*z0^3 - 2*x^35*z0^4 - 2*x^38 + x^36*y*z0 - 2*x^36*z0^2 - 2*x^34*y*z0^3 - x^34*z0^4 + 2*x^37 - x^35*y*z0 + 2*x^35*z0^2 + x^33*y*z0^3 - x^36 + x^34*y*z0 - 2*x^34*z0^2 + x^32*z0^4 + x^33*y*z0 - 2*x^31*y*z0^3 + x^31*z0^4 + 2*x^34 - x^32*y*z0 - x^32*z0^2 + 2*x^30*y*z0^3 - x^30*z0^4 - 2*x^33 + x^31*y^2 + 2*x^31*y*z0 + x^31*z0^2 - 2*x^29*y*z0^3 + x^29*z0^4 - x^32 + x^30*y*z0 - x^28*y*z0^3 + 2*x^28*z0^4 + x^31 - x^29*y*z0 - x^29*z0^2 - 2*x^27*y*z0^3 - 2*x^27*z0^4 + x^28*y*z0 + 2*x^26*z0^4 - x^29 + x^27*y*z0 - x^25*y*z0^3 + x^28 - x^26*y*z0 + 2*x^26*z0^2 + x^24*y*z0^3 + 2*x^24*z0^4 - x^27 - 2*x^25*y*z0 + x^25*z0^2 - 2*x^23*y*z0^3 - 2*x^23*z0^4 - 2*x^24*y*z0 + 2*x^24*z0^2 - x^22*y*z0^3 - 2*x^25 - x^23*y*z0 + x^23*z0^2 + x^21*y*z0^3 + 2*x^21*z0^4 - x^24 + 2*x^22*y*z0 + x^20*y*z0^3 + 2*x^23 + x^21*y*z0 + x^19*y*z0^3 - 2*x^19*z0^4 - 2*x^20*y*z0 - x^20*z0^2 + 2*x^18*y*z0^3 - x^18*z0^4 + 2*x^21 - 2*x^19*y*z0 + x^19*z0^2 + x^17*y*z0^3 - x^17*z0^4 - 2*x^20 - x^18*y*z0 + 2*x^18*z0^2 + x^16*y*z0^3 + x^16*z0^4 - x^19 + x^17*y*z0 - 2*x^15*y*z0^3 - 2*x^15*z0^4 + 2*x^18 + 2*x^16*y*z0 + 2*x^16*z0^2 - 2*x^14*y*z0^3 + x^14*z0^4 - x^17 + 2*x^15*y*z0 - x^15*z0^2 - 2*x^13*y*z0^3 + 2*x^13*z0^4 + x^16 + x^14*y*z0 - x^14*z0^2 + 2*x^12*y*z0^3 - x^13*y*z0 + 2*x^13*z0^2 - x^11*y*z0^3 - x^11*z0^4 + 2*x^12*y*z0 - 2*x^10*y*z0^3 - 2*x^13 + 2*x^11*y*z0 - 2*x^12 - x^10*y*z0 - x^10*z0^2 - x^8*y*z0^3 - x^8*z0^4 + x^11 + x^9*y*z0 + x^7*z0^4 + 2*x^10 - x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + 2*x^9 + x^7*y*z0 - 2*x^7*z0^2 - 2*x^5*y*z0^3 + x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^5*y*z0 - x^5*z0^2 + 2*x^3*y*z0^3 - 2*x^6 + 2*x^4*y*z0 - 2*x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 - x^3*z0^2 - x^2*y*z0 + 2*x^2*z0^2 - x^3 + x^2)/y) * dx, - ((x^61*z0^3 + 2*x^60*z0^3 - x^58*y^2*z0^3 - x^61*z0 - x^59*z0^3 - 2*x^57*y^2*z0^3 - x^60*z0 + x^58*y^2*z0 + x^56*y^2*z0^3 + 2*x^59*z0 + x^57*y^2*z0 + x^57*z0^3 - x^55*y^2*z0^3 + x^58*z0 - 2*x^56*y^2*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 + x^57*z0 - 2*x^56*z0 - x^54*z0^3 - x^55*z0 - x^53*z0^3 - x^54*z0 + 2*x^53*z0 + x^51*z0^3 + x^52*z0 + x^50*z0^3 + x^51*z0 - 2*x^50*z0 - x^48*z0^3 - x^49*z0 - x^47*z0^3 - x^48*z0 + 2*x^47*z0 + x^45*z0^3 + x^46*z0 + x^44*z0^3 + x^45*z0 - 2*x^44*z0 - x^42*z0^3 - x^43*z0 + x^39*y*z0^4 - x^42*z0 - 2*x^40*y*z0^2 - 2*x^40*z0^3 + 2*x^38*y*z0^4 + x^41*z0 - x^39*y*z0^2 - 2*x^37*y*z0^4 + 2*x^40*y - 2*x^40*z0 + x^38*y*z0^2 + 2*x^38*z0^3 + x^36*y*z0^4 + 2*x^39*y + x^39*z0 + x^37*y*z0^2 + x^37*z0^3 - x^35*y*z0^4 - 2*x^38*y - 2*x^38*z0 + x^36*y*z0^2 + 2*x^36*z0^3 - x^37*y + x^37*z0 - 2*x^35*y*z0^2 - x^35*z0^3 + 2*x^33*y*z0^4 - 2*x^36*y + 2*x^34*y*z0^2 + x^34*z0^3 - x^32*y*z0^4 + x^35*y + x^35*z0 + x^33*y*z0^2 - 2*x^33*z0^3 - 2*x^31*y*z0^4 - 2*x^34*y - x^32*y*z0^2 + x^32*z0^3 - x^33*y + x^33*z0 + x^31*y^2*z0 + x^31*y*z0^2 - 2*x^31*z0^3 + x^29*y*z0^4 + 2*x^32*y - x^32*z0 + 2*x^30*y*z0^2 + 2*x^30*z0^3 - 2*x^28*y*z0^4 + x^31*y + x^31*z0 - x^29*y*z0^2 + 2*x^29*z0^3 - x^27*y*z0^4 + x^30*y - 2*x^30*z0 + x^28*y*z0^2 + x^28*z0^3 - 2*x^26*y*z0^4 + x^29*y + x^29*z0 + 2*x^27*y*z0^2 - 2*x^27*z0^3 - 2*x^25*y*z0^4 + 2*x^28*y - 2*x^28*z0 - x^26*y*z0^2 - 2*x^26*z0^3 + x^24*y*z0^4 - 2*x^27*y + 2*x^27*z0 + x^25*y*z0^2 - x^23*y*z0^4 - x^26*y + 2*x^24*y*z0^2 - 2*x^24*z0^3 + 2*x^22*y*z0^4 - x^23*y*z0^2 + x^23*z0^3 + x^21*y*z0^4 + x^24*y - 2*x^24*z0 + 2*x^22*y*z0^2 - x^22*z0^3 + 2*x^20*y*z0^4 - x^23*z0 - x^21*z0^3 + x^22*y + 2*x^20*y*z0^2 + x^18*y*z0^4 - x^21*y + x^21*z0 + 2*x^19*y*z0^2 + x^17*y*z0^4 + 2*x^20*y + 2*x^20*z0 + 2*x^18*y*z0^2 - 2*x^16*y*z0^4 - 2*x^19*y + x^19*z0 + 2*x^17*y*z0^2 + x^17*z0^3 + 2*x^15*y*z0^4 - 2*x^18*z0 + 2*x^16*z0^3 + 2*x^14*y*z0^4 + x^17*y - x^17*z0 - 2*x^15*z0^3 + x^13*y*z0^4 + x^16*z0 - 2*x^14*y*z0^2 + 2*x^14*z0^3 - 2*x^12*y*z0^4 + 2*x^15*y - 2*x^15*z0 + 2*x^13*y*z0^2 - x^13*z0^3 - x^11*y*z0^4 - 2*x^12*y*z0^2 + 2*x^12*z0^3 - 2*x^10*y*z0^4 - x^13*y - 2*x^11*y*z0^2 + x^11*z0^3 + x^9*y*z0^4 - 2*x^12*y + 2*x^12*z0 - x^10*y*z0^2 - x^10*z0^3 + x^8*y*z0^4 - x^11*y + 2*x^11*z0 - x^9*z0^3 - x^7*y*z0^4 - 2*x^10*z0 - x^8*y*z0^2 + x^8*z0^3 - 2*x^9*y + x^9*z0 + x^7*y*z0^2 - x^7*z0^3 + 2*x^8*z0 - 2*x^6*z0^3 + 2*x^4*y*z0^4 + x^7*y - x^7*z0 + x^5*y*z0^2 - x^5*z0^3 + 2*x^3*y*z0^4 - 2*x^6*y - 2*x^6*z0 - 2*x^4*z0^3 + 2*x^5*y + 2*x^5*z0 - x^3*y*z0^2 + x^3*z0^3 - 2*x^4*y + x^4*z0 - 2*x^2*y*z0^2 - 2*x^2*z0^3 + x^3*y - x^3*z0 - 2*x^2*y + 2*x^2*z0)/y) * dx, - ((-x^60*z0^4 - x^61*z0^2 + x^57*y^2*z0^4 - 2*x^60*z0^2 + x^58*y^2*z0^2 - 2*x^61 + 2*x^57*y^2*z0^2 + x^57*z0^4 + 2*x^58*y^2 + x^58*z0^2 + 2*x^57*z0^2 + 2*x^58 - x^54*z0^4 - x^55*z0^2 - 2*x^54*z0^2 - 2*x^55 + x^51*z0^4 + x^52*z0^2 + 2*x^51*z0^2 + 2*x^52 - x^48*z0^4 - x^49*z0^2 - 2*x^48*z0^2 - 2*x^49 + x^45*z0^4 + x^46*z0^2 + 2*x^45*z0^2 + 2*x^46 - x^42*z0^4 - x^43*z0^2 - x^41*z0^4 - 2*x^42*z0^2 + x^40*z0^4 - 2*x^43 - x^41*z0^2 - x^39*y*z0^3 - 2*x^39*z0^4 + 2*x^40*y*z0 + x^40*z0^2 - 2*x^38*y*z0^3 - 2*x^38*z0^4 - x^41 - 2*x^39*z0^2 - 2*x^37*y*z0^3 + 2*x^37*z0^4 - x^40 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - x^35*z0^4 - 2*x^38 + 2*x^36*y*z0 + 2*x^36*z0^2 - 2*x^34*y*z0^3 + 2*x^37 + x^35*y*z0 - 2*x^33*y*z0^3 + x^33*z0^4 + x^36 + 2*x^34*y*z0 + x^34*z0^2 + x^32*y*z0^3 + 2*x^32*z0^4 + 2*x^35 + 2*x^33*y*z0 + 2*x^33*z0^2 + x^31*y^2*z0^2 - 2*x^34 - x^32*y*z0 + x^32*z0^2 - x^30*y*z0^3 - 2*x^33 - x^31*y*z0 - x^31*z0^2 - x^29*y*z0^3 + x^29*z0^4 + 2*x^32 + 2*x^30*y*z0 + x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^29*y*z0 + 2*x^29*z0^2 - 2*x^27*y*z0^3 + x^27*z0^4 - 2*x^30 + 2*x^28*y*z0 - x^28*z0^2 + x^29 - 2*x^27*y*z0 - x^27*z0^2 - 2*x^25*y*z0^3 + x^25*z0^4 + 2*x^28 + x^26*y*z0 - 2*x^26*z0^2 + x^24*y*z0^3 - 2*x^24*z0^4 + 2*x^27 + 2*x^25*z0^2 - 2*x^23*y*z0^3 - x^23*z0^4 + 2*x^26 - 2*x^24*y*z0 - x^24*z0^2 + 2*x^22*y*z0^3 - x^22*z0^4 - 2*x^25 - 2*x^23*y*z0 + 2*x^21*y*z0^3 + 2*x^21*z0^4 + x^24 - 2*x^22*y*z0 + x^22*z0^2 + x^20*y*z0^3 + 2*x^20*z0^4 - 2*x^21*y*z0 - 2*x^21*z0^2 - 2*x^19*y*z0^3 - x^19*z0^4 + 2*x^18*y*z0^3 + x^21 - x^19*y*z0 + 2*x^19*z0^2 - 2*x^17*y*z0^3 + x^17*z0^4 - x^20 + x^18*y*z0 - x^18*z0^2 - 2*x^16*z0^4 + 2*x^19 - x^17*y*z0 - x^17*z0^2 + 2*x^15*y*z0^3 - 2*x^15*z0^4 + 2*x^16*y*z0 - x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 + 2*x^15*y*z0 - x^15*z0^2 + 2*x^13*z0^4 - 2*x^16 - x^14*y*z0 + 2*x^14*z0^2 - x^12*y*z0^3 - 2*x^12*z0^4 - x^15 + x^13*y*z0 + 2*x^11*z0^4 - 2*x^14 - x^12*y*z0 - 2*x^12*z0^2 + 2*x^10*y*z0^3 - x^10*z0^4 + x^13 + x^11*y*z0 - 2*x^11*z0^2 - 2*x^9*y*z0^3 + 2*x^9*z0^4 - x^10*y*z0 - 2*x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^9*z0^2 - 2*x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 + x^6*y*z0^3 + 2*x^6*z0^4 - x^9 + x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 + 2*x^5*z0^4 - x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 - 2*x^4*y*z0^3 - x^7 - 2*x^5*y*z0 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 - x^6 - 2*x^4*z0^2 + x^2*y*z0^3 - x^2*z0^4 + x^2*z0^2 + 2*x^3 - 2*x^2)/y) * dx, - ((-2*x^61*z0^3 - x^60*z0^3 + 2*x^58*y^2*z0^3 + 2*x^59*z0^3 + x^57*y^2*z0^3 - x^60*z0 - 2*x^56*y^2*z0^3 + x^57*y^2*z0 + 2*x^55*y^2*z0^3 - 2*x^56*z0^3 + x^54*y^2*z0^3 + x^57*z0 + 2*x^53*z0^3 - x^54*z0 - 2*x^50*z0^3 + x^51*z0 + 2*x^47*z0^3 - x^48*z0 - 2*x^44*z0^3 + x^45*z0 - 2*x^39*y*z0^4 - x^42*z0 - x^40*y*z0^2 - x^40*z0^3 + x^39*z0^3 + x^37*y*z0^4 + 2*x^40*z0 + 2*x^38*y*z0^2 + x^38*z0^3 - 2*x^36*y*z0^4 + x^39*z0 - x^37*y*z0^2 - x^37*z0^3 + x^35*y*z0^4 - 2*x^34*y*z0^4 + x^37*z0 + x^35*y*z0^2 + 2*x^35*z0^3 + 2*x^33*y*z0^4 - x^36*z0 - x^34*y*z0^2 + x^34*z0^3 - 2*x^32*y*z0^4 + x^35*y - 2*x^35*z0 + 2*x^33*y*z0^2 + x^33*z0^3 + x^31*y^2*z0^3 + 2*x^31*y*z0^4 + x^32*y*z0^2 - 2*x^32*z0^3 + x^33*y - 2*x^33*z0 - x^31*y*z0^2 - 2*x^31*z0^3 - 2*x^29*y*z0^4 - 2*x^32*y + x^30*y*z0^2 - x^30*z0^3 - x^28*y*z0^4 + x^31*y + x^31*z0 + x^29*y*z0^2 + x^27*y*z0^4 + x^30*y + x^28*y*z0^2 + x^29*y + 2*x^29*z0 + x^27*z0^3 - x^25*y*z0^4 + 2*x^28*y + x^28*z0 - x^24*y*z0^4 - x^27*z0 + x^25*y*z0^2 - x^25*z0^3 - x^23*y*z0^4 - x^26*y + 2*x^26*z0 - 2*x^24*y*z0^2 + 2*x^24*z0^3 + x^22*y*z0^4 - x^25*y - x^25*z0 - 2*x^23*y*z0^2 - 2*x^23*z0^3 + x^21*y*z0^4 - 2*x^24*y + x^24*z0 - x^22*y*z0^2 + 2*x^22*z0^3 + x^20*y*z0^4 + x^23*y + x^23*z0 - x^21*y*z0^2 - 2*x^21*z0^3 + x^22*y - x^20*z0^3 - 2*x^18*y*z0^4 + 2*x^21*y - x^19*z0^3 - x^17*y*z0^4 + x^20*y + x^20*z0 + x^18*y*z0^2 - x^18*z0^3 + 2*x^16*y*z0^4 - 2*x^19*y + 2*x^19*z0 + 2*x^17*y*z0^2 + x^17*z0^3 + x^15*y*z0^4 + x^18*y - x^16*y*z0^2 + 2*x^17*y - x^17*z0 - x^15*z0^3 - 2*x^16*y + 2*x^16*z0 + 2*x^12*y*z0^4 + x^15*y - 2*x^15*z0 + 2*x^13*y*z0^2 + x^13*z0^3 - 2*x^14*y - x^14*z0 + x^12*y*z0^2 - x^12*z0^3 - x^10*y*z0^4 - 2*x^13*y - x^13*z0 + 2*x^11*y*z0^2 + 2*x^11*z0^3 - x^9*y*z0^4 - 2*x^12*y - x^10*y*z0^2 + 2*x^8*y*z0^4 - 2*x^11*z0 + x^9*y*z0^2 + x^9*z0^3 - 2*x^7*y*z0^4 + 2*x^10*y - x^6*y*z0^4 + 2*x^9*y - 2*x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + x^8*z0 - 2*x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 + 2*x^7*y - 2*x^7*z0 + 2*x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 + 2*x^6*y - 2*x^6*z0 + 2*x^4*y*z0^2 - 2*x^2*y*z0^4 - 2*x^5*y + x^5*z0 + 2*x^3*y*z0^2 + 2*x^3*z0^3 - 2*x^4*y + 2*x^4*z0 - 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y - x^2*y + 2*x^2*z0)/y) * dx, - ((-2*x^61*z0^4 - 2*x^60*z0^4 + 2*x^58*y^2*z0^4 + x^59*z0^4 + 2*x^57*y^2*z0^4 - x^60*z0^2 + 2*x^58*z0^4 - x^56*y^2*z0^4 - x^61 + x^57*y^2*z0^2 + 2*x^57*z0^4 - x^60 + x^58*y^2 - x^56*z0^4 + x^57*y^2 + x^57*z0^2 - 2*x^55*z0^4 + x^58 - 2*x^54*z0^4 + x^57 + x^53*z0^4 - x^54*z0^2 + 2*x^52*z0^4 - x^55 + 2*x^51*z0^4 - x^54 - x^50*z0^4 + x^51*z0^2 - 2*x^49*z0^4 + x^52 - 2*x^48*z0^4 + x^51 + x^47*z0^4 - x^48*z0^2 + 2*x^46*z0^4 - x^49 + 2*x^45*z0^4 - x^48 - x^44*z0^4 + x^45*z0^2 - 2*x^43*z0^4 + x^46 - 2*x^42*z0^4 + x^45 + x^41*z0^4 - x^42*z0^2 - x^40*y*z0^3 - x^40*z0^4 - x^43 - x^42 + 2*x^40*z0^2 - x^39*y*z0 + x^39*z0^2 + 2*x^37*z0^4 - x^40 - x^36*z0^4 + 2*x^37*y*z0 - x^37*z0^2 - x^35*y*z0^3 - x^35*z0^4 + 2*x^38 - 2*x^36*y*z0 - x^36*z0^2 - x^34*y*z0^3 + x^34*z0^4 - x^37 + x^35*z0^2 - x^33*y*z0^3 + 2*x^33*z0^4 + x^31*y^2*z0^4 + x^36 + 2*x^34*y*z0 + 2*x^34*z0^2 - 2*x^32*y*z0^3 - x^32*z0^4 - 2*x^35 - x^33*y*z0 + x^33*z0^2 + 2*x^31*y*z0^3 - x^31*z0^4 - 2*x^34 - x^32*z0^2 + 2*x^30*y*z0^3 + x^30*z0^4 + x^33 - x^32 - x^30*y*z0 - x^30*z0^2 - 2*x^28*y*z0^3 + 2*x^31 + 2*x^29*y*z0 + x^29*z0^2 - x^27*y*z0^3 - 2*x^27*z0^4 - x^30 - 2*x^28*y*z0 + 2*x^28*z0^2 + x^26*y*z0^3 + x^27*z0^2 - 2*x^25*y*z0^3 + x^26*y*z0 - x^26*z0^2 - 2*x^24*y*z0^3 - 2*x^24*z0^4 + 2*x^27 + x^25*y*z0 - 2*x^23*y*z0^3 - 2*x^23*z0^4 + x^26 + x^24*z0^2 + 2*x^22*z0^4 - x^25 + 2*x^23*y*z0 - 2*x^23*z0^2 - x^21*y*z0^3 - 2*x^22*y*z0 + x^22*z0^2 + 2*x^20*y*z0^3 - 2*x^20*z0^4 + 2*x^21*y*z0 - 2*x^21*z0^2 + x^19*y*z0^3 + 2*x^19*z0^4 - 2*x^22 - x^20*z0^2 - 2*x^18*y*z0^3 - 2*x^18*z0^4 - x^21 + x^19*y*z0 + x^19*z0^2 + 2*x^17*y*z0^3 + x^17*z0^4 - 2*x^18*y*z0 - x^18*z0^2 + x^16*y*z0^3 + 2*x^16*z0^4 - x^17*y*z0 - x^17*z0^2 + 2*x^15*y*z0^3 + 2*x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 + 2*x^17 - x^15*y*z0 - x^13*y*z0^3 + 2*x^13*z0^4 - x^16 + 2*x^14*y*z0 + x^12*y*z0^3 - 2*x^12*z0^4 - 2*x^15 - x^13*y*z0 - 2*x^13*z0^2 - 2*x^11*z0^4 + 2*x^14 - 2*x^12*z0^2 - x^10*y*z0^3 + x^10*z0^4 - x^13 + 2*x^11*y*z0 + x^11*z0^2 - 2*x^9*y*z0^3 - 2*x^9*z0^4 + x^12 - x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 - x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 + x^7*y*z0^3 + x^7*z0^4 - x^8*y*z0 + x^8*z0^2 - 2*x^6*y*z0^3 + 2*x^6*z0^4 - x^9 + x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 + 2*x^8 + 2*x^6*y*z0 + x^6*z0^2 - x^4*y*z0^3 - 2*x^7 - x^5*y*z0 + 2*x^5*z0^2 - 2*x^3*y*z0^3 + 2*x^3*z0^4 + x^6 - 2*x^4*y*z0 + x^4*z0^2 - 2*x^2*z0^4 - x^5 + x^3*y*z0 + x^3*z0^2 + x^2*y*z0 - 2*x^2*z0^2 + x^3)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^4 + x^60*z0^4 - x^58*y^2*z0^4 - x^61*z0^2 + x^59*z0^4 - x^57*y^2*z0^4 + x^58*y^2*z0^2 - x^58*z0^4 - x^56*y^2*z0^4 + x^61 - x^57*z0^4 + x^60 - x^58*y^2 + x^58*z0^2 - x^56*z0^4 - x^57*y^2 + x^55*z0^4 - x^58 + x^54*z0^4 - x^57 - x^55*z0^2 + x^53*z0^4 - x^52*z0^4 + x^55 - x^51*z0^4 + x^54 + x^52*z0^2 - x^50*z0^4 + x^49*z0^4 - x^52 + x^48*z0^4 - x^51 - x^49*z0^2 + x^47*z0^4 - x^46*z0^4 + x^49 - x^45*z0^4 + x^48 + x^46*z0^2 - x^44*z0^4 + x^43*z0^4 - x^46 + x^42*z0^4 - x^45 - x^43*z0^2 - 2*x^40*y*z0^3 - 2*x^40*z0^4 + x^43 - x^41*z0^2 - x^39*y*z0^3 + x^39*z0^4 + x^42 + 2*x^40*y*z0 - 2*x^40*z0^2 - 2*x^38*z0^4 - x^41 + x^39*y*z0 + x^39*z0^2 + 2*x^37*y*z0^3 + 2*x^40 + 2*x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + x^36*z0^4 - x^39 + x^37*y*z0 - 2*x^37*z0^2 + 2*x^35*y*z0^3 - 2*x^36*y*z0 - x^36*z0^2 - x^34*z0^4 + x^37 + x^35*y*z0 + x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 - x^34*z0^2 - x^32*y*z0^3 - x^32*z0^4 + 2*x^31*y*z0^3 + 2*x^34 + x^32*y^2 - x^32*z0^2 + x^30*y*z0^3 + 2*x^30*z0^4 - x^33 - 2*x^31*y*z0 + x^31*z0^2 + 2*x^29*y*z0^3 + x^29*z0^4 + x^30*y*z0 + x^30*z0^2 + x^28*y*z0^3 + 2*x^28*z0^4 - x^31 + x^29*y*z0 + x^29*z0^2 + 2*x^27*y*z0^3 - 2*x^27*z0^4 - x^30 - 2*x^28*y*z0 - 2*x^28*z0^2 - x^26*y*z0^3 + 2*x^26*z0^4 - 2*x^29 + 2*x^27*y*z0 - x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 - 2*x^28 + 2*x^26*y*z0 + 2*x^26*z0^2 - x^27 - 2*x^25*z0^2 + x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + x^24*z0^2 - 2*x^22*y*z0^3 + x^22*z0^4 - 2*x^25 - 2*x^23*z0^2 + 2*x^21*y*z0^3 + 2*x^21*z0^4 - 2*x^24 - x^22*y*z0 + x^22*z0^2 - x^20*y*z0^3 + 2*x^20*z0^4 + x^23 - x^21*y*z0 - x^21*z0^2 + x^19*y*z0^3 + x^19*z0^4 - 2*x^22 + x^20*y*z0 - 2*x^20*z0^2 - x^21 - x^19*z0^2 - 2*x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^20 + 2*x^18*y*z0 + 2*x^18*z0^2 - 2*x^16*y*z0^3 + x^16*z0^4 + x^19 + x^17*z0^2 + x^15*y*z0^3 + x^15*z0^4 + x^18 - 2*x^16*y*z0 + 2*x^16*z0^2 + 2*x^14*y*z0^3 + x^14*z0^4 - 2*x^17 - 2*x^15*y*z0 - 2*x^15*z0^2 + 2*x^13*z0^4 + x^12*y*z0^3 - x^12*z0^4 + 2*x^15 - x^13*y*z0 - 2*x^13*z0^2 - 2*x^11*y*z0^3 + 2*x^11*z0^4 - 2*x^14 - 2*x^12*y*z0 + x^12*z0^2 - x^10*y*z0^3 - 2*x^10*z0^4 + 2*x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - 2*x^10*z0^2 - 2*x^8*y*z0^3 + x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 - 2*x^7*y*z0^3 - x^7*z0^4 - x^10 - x^8*y*z0 - x^6*y*z0^3 + x^6*z0^4 + x^9 + x^7*y*z0 + x^7*z0^2 + x^5*z0^4 + 2*x^8 + 2*x^6*y*z0 - 2*x^6*z0^2 - 2*x^4*y*z0^3 - x^7 + 2*x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*z0^4 + x^6 + 2*x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^3*y*z0 - 2*x^3*z0^2 - 2*x^2*z0^2 + 2*x^3 + 2*x^2)/y) * dx, - ((2*x^60*z0^3 - 2*x^61*z0 - x^59*z0^3 - 2*x^57*y^2*z0^3 + x^60*z0 + 2*x^58*y^2*z0 + x^56*y^2*z0^3 - x^57*y^2*z0 - x^57*z0^3 + 2*x^58*z0 + x^56*z0^3 - x^54*y^2*z0^3 - x^57*z0 + x^54*z0^3 - 2*x^55*z0 - x^53*z0^3 + x^54*z0 - x^51*z0^3 + 2*x^52*z0 + x^50*z0^3 - x^51*z0 + x^48*z0^3 - 2*x^49*z0 - x^47*z0^3 + x^48*z0 - x^45*z0^3 + 2*x^46*z0 + x^44*z0^3 - x^45*z0 + x^42*z0^3 - 2*x^43*z0 - x^41*z0^3 + x^42*z0 - x^38*y*z0^4 - 2*x^41*z0 - 2*x^39*y*z0^2 + 2*x^39*z0^3 + 2*x^37*y*z0^4 - x^40*y + 2*x^38*y*z0^2 - 2*x^36*y*z0^4 + x^39*y + x^39*z0 + 2*x^37*y*z0^2 - 2*x^37*z0^3 - 2*x^38*y + x^38*z0 - x^36*y*z0^2 + 2*x^34*y*z0^4 - 2*x^37*y - x^35*y*z0^2 + 2*x^35*z0^3 + x^33*y*z0^4 + x^36*y - x^36*z0 + x^34*y*z0^2 + 2*x^34*z0^3 + x^35*y - x^35*z0 + x^33*y*z0^2 - x^33*z0^3 - x^31*y*z0^4 + 2*x^34*y - x^34*z0 + x^32*y^2*z0 + 2*x^32*y*z0^2 + x^32*z0^3 + x^30*y*z0^4 - x^33*y - 2*x^31*y*z0^2 + x^31*z0^3 + 2*x^29*y*z0^4 - 2*x^32*y + x^32*z0 + x^30*y*z0^2 + x^30*z0^3 - x^28*y*z0^4 - 2*x^31*y + 2*x^31*z0 - 2*x^29*y*z0^2 - 2*x^29*z0^3 + 2*x^27*y*z0^4 - x^30*y + 2*x^30*z0 + 2*x^28*y*z0^2 + 2*x^28*z0^3 - 2*x^26*y*z0^4 - 2*x^29*y - x^27*y*z0^2 - 2*x^27*z0^3 - 2*x^25*y*z0^4 - 2*x^28*y + 2*x^28*z0 + 2*x^26*y*z0^2 + x^27*y + 2*x^25*y*z0^2 + 2*x^26*y + 2*x^26*z0 + 2*x^24*y*z0^2 - 2*x^24*z0^3 + x^22*y*z0^4 + 2*x^25*y - 2*x^25*z0 + x^23*y*z0^2 + x^21*y*z0^4 + x^24*y + 2*x^24*z0 - x^22*y*z0^2 + x^22*z0^3 + x^20*y*z0^4 - 2*x^23*y + x^23*z0 + x^21*z0^3 - x^19*y*z0^4 - x^22*y + 2*x^20*z0^3 + 2*x^18*y*z0^4 + 2*x^21*y - 2*x^21*z0 + x^19*y*z0^2 + x^19*z0^3 + x^17*y*z0^4 - x^20*y - 2*x^20*z0 + 2*x^18*z0^3 + 2*x^16*y*z0^4 - x^19*z0 - x^17*y*z0^2 - 2*x^17*z0^3 + 2*x^15*y*z0^4 - x^18*y - 2*x^18*z0 - 2*x^16*z0^3 + 2*x^14*y*z0^4 - x^17*y - 2*x^17*z0 - 2*x^15*y*z0^2 - 2*x^15*z0^3 + x^13*y*z0^4 + x^16*y - 2*x^16*z0 + 2*x^14*y*z0^2 - x^14*z0^3 + x^12*y*z0^4 + x^13*y*z0^2 - x^13*z0^3 - 2*x^11*y*z0^4 + x^14*y + 2*x^12*z0^3 + x^10*y*z0^4 - x^11*y*z0^2 + 2*x^11*z0^3 + 2*x^9*y*z0^4 - 2*x^12*y + 2*x^10*y*z0^2 - 2*x^10*z0^3 + x^8*y*z0^4 - x^11*z0 + 2*x^9*y*z0^2 - 2*x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y + 2*x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*z0 + x^7*y*z0^2 - x^7*z0^3 + x^5*y*z0^4 + 2*x^8*y + 2*x^8*z0 - x^6*y*z0^2 + x^6*z0^3 + x^4*y*z0^4 + x^7*y - 2*x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - 2*x^3*y*z0^4 - 2*x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^2*y*z0^4 + 2*x^5*z0 - 2*x^3*y*z0^2 - 2*x^3*z0^3 + x^2*y*z0^2 + x^2*z0^3 - 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((x^61*z0^4 + 2*x^60*z0^4 - x^58*y^2*z0^4 - x^61*z0^2 - 2*x^59*z0^4 - 2*x^57*y^2*z0^4 + x^58*y^2*z0^2 - x^58*z0^4 + 2*x^56*y^2*z0^4 - 2*x^61 - 2*x^57*z0^4 - x^60 + 2*x^58*y^2 + x^58*z0^2 + 2*x^56*z0^4 + x^57*y^2 + x^55*z0^4 + 2*x^58 + 2*x^54*z0^4 + x^57 - x^55*z0^2 - 2*x^53*z0^4 - x^52*z0^4 - 2*x^55 - 2*x^51*z0^4 - x^54 + x^52*z0^2 + 2*x^50*z0^4 + x^49*z0^4 + 2*x^52 + 2*x^48*z0^4 + x^51 - x^49*z0^2 - 2*x^47*z0^4 - x^46*z0^4 - 2*x^49 - 2*x^45*z0^4 - x^48 + x^46*z0^2 + 2*x^44*z0^4 + x^43*z0^4 + 2*x^46 + 2*x^42*z0^4 + x^45 - x^43*z0^2 - 2*x^41*z0^4 - 2*x^40*y*z0^3 - 2*x^43 - x^41*z0^2 - x^39*y*z0^3 - 2*x^39*z0^4 - x^42 + 2*x^40*y*z0 + 2*x^38*y*z0^3 + x^39*y*z0 + x^39*z0^2 + x^37*z0^4 - x^40 + 2*x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + 2*x^36*z0^4 + x^39 - x^37*y*z0 - 2*x^35*y*z0^3 + x^35*z0^4 + x^38 - x^36*z0^2 + x^34*z0^4 - x^37 - x^35*y*z0 + x^35*z0^2 - x^33*y*z0^3 - 2*x^33*z0^4 + 2*x^36 + 2*x^34*y*z0 - 2*x^34*z0^2 + x^32*y^2*z0^2 + 2*x^32*z0^4 - x^35 - 2*x^33*y*z0 - 2*x^33*z0^2 - 2*x^31*y*z0^3 - x^31*z0^4 - x^34 + x^32*y*z0 + 2*x^32*z0^2 + x^30*y*z0^3 - x^30*z0^4 + x^33 - 2*x^31*y*z0 + 2*x^31*z0^2 - x^29*y*z0^3 + 2*x^32 - x^30*y*z0 + x^30*z0^2 - 2*x^28*y*z0^3 + x^28*z0^4 + x^29*z0^2 - x^27*y*z0^3 - 2*x^30 + x^28*y*z0 + x^28*z0^2 + x^29 + 2*x^27*y*z0 + x^27*z0^2 - x^25*y*z0^3 + x^25*z0^4 + x^28 - x^26*y*z0 - 2*x^27 + 2*x^25*y*z0 + x^25*z0^2 - 2*x^23*y*z0^3 + 2*x^23*z0^4 + 2*x^26 + 2*x^22*z0^4 + 2*x^25 + 2*x^23*y*z0 - x^23*z0^2 - x^21*y*z0^3 - x^21*z0^4 - 2*x^24 - 2*x^22*y*z0 - 2*x^22*z0^2 - 2*x^23 - 2*x^21*y*z0 - x^21*z0^2 + 2*x^19*z0^4 - 2*x^22 + 2*x^20*y*z0 - x^20*z0^2 + x^18*z0^4 + 2*x^21 - 2*x^19*y*z0 - 2*x^19*z0^2 + 2*x^17*y*z0^3 - x^17*z0^4 - x^20 - 2*x^18*y*z0 + 2*x^18*z0^2 + 2*x^16*z0^4 + x^19 + 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^15*z0^4 + x^18 - 2*x^16*y*z0 - 2*x^14*y*z0^3 - x^14*z0^4 - x^17 + 2*x^15*z0^2 + x^13*y*z0^3 - 2*x^16 - x^12*y*z0^3 - 2*x^12*z0^4 - x^15 + x^13*y*z0 - x^13*z0^2 + 2*x^11*y*z0^3 + 2*x^11*z0^4 - 2*x^14 - 2*x^12*y*z0 + 2*x^12*z0^2 - 2*x^10*z0^4 - x^11*y*z0 + 2*x^11*z0^2 + 2*x^9*y*z0^3 + x^9*z0^4 + 2*x^12 + x^10*y*z0 - 2*x^10*z0^2 + 2*x^8*y*z0^3 + x^8*z0^4 - x^9*y*z0 + x^9*z0^2 + 2*x^7*y*z0^3 - x^7*z0^4 - x^10 - 2*x^8*y*z0 + 2*x^8*z0^2 - x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 + 2*x^7*z0^2 + x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 + 2*x^6*y*z0 + 2*x^6*z0^2 + x^4*z0^4 - 2*x^7 + x^5*y*z0 + x^5*z0^2 + 2*x^3*z0^4 + x^6 + 2*x^4*y*z0 - x^4*z0^2 - x^2*y*z0^3 - x^5 - x^3*y*z0 - x^3*z0^2 + x^2*z0^2 - x^3)/y) * dx, - ((-2*x^61*z0^3 - 2*x^60*z0^3 + 2*x^58*y^2*z0^3 - 2*x^61*z0 - x^59*z0^3 + 2*x^57*y^2*z0^3 - x^60*z0 + 2*x^58*y^2*z0 + x^56*y^2*z0^3 + x^57*y^2*z0 + 2*x^55*y^2*z0^3 + 2*x^58*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 + x^57*z0 - 2*x^55*z0 - x^53*z0^3 - x^54*z0 + 2*x^52*z0 + x^50*z0^3 + x^51*z0 - 2*x^49*z0 - x^47*z0^3 - x^48*z0 + 2*x^46*z0 + x^44*z0^3 + x^45*z0 - 2*x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 - x^42*z0 - x^40*y*z0^2 - 2*x^41*z0 - 2*x^39*y*z0^2 - 2*x^37*y*z0^4 - x^40*y + 2*x^40*z0 + 2*x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 + 2*x^39*y - 2*x^39*z0 + x^37*y*z0^2 + 2*x^37*z0^3 + x^35*y*z0^4 - x^38*y + x^38*z0 - x^36*y*z0^2 + 2*x^36*z0^3 + x^34*y*z0^4 - 2*x^37*y - x^37*z0 + x^35*y*z0^2 + x^33*y*z0^4 + x^36*y + 2*x^36*z0 - x^34*y*z0^2 + 2*x^34*z0^3 + x^32*y^2*z0^3 - x^32*y*z0^4 + 2*x^35*y + x^35*z0 - x^33*y*z0^2 - 2*x^31*y*z0^4 - 2*x^34*z0 + x^32*y*z0^2 + 2*x^32*z0^3 + 2*x^30*y*z0^4 + x^33*z0 - 2*x^31*y*z0^2 + 2*x^31*z0^3 - 2*x^29*y*z0^4 - x^32*y + x^32*z0 - 2*x^28*y*z0^4 + x^31*z0 - x^29*y*z0^2 - 2*x^27*y*z0^4 - x^30*y + x^30*z0 + 2*x^28*y*z0^2 - x^28*z0^3 - x^26*y*z0^4 - x^29*y + 2*x^29*z0 + 2*x^27*y*z0^2 - x^27*z0^3 + 2*x^28*z0 - 2*x^26*y*z0^2 - 2*x^26*z0^3 - 2*x^24*y*z0^4 + x^27*y + x^27*z0 + x^25*y*z0^2 + x^25*z0^3 - x^23*y*z0^4 + 2*x^26*y + 2*x^26*z0 - 2*x^24*y*z0^2 - x^24*z0^3 - 2*x^22*y*z0^4 + x^25*y - x^23*y*z0^2 - 2*x^23*z0^3 + x^21*y*z0^4 + x^24*y - 2*x^24*z0 - x^22*y*z0^2 - x^20*y*z0^4 - x^23*z0 - 2*x^21*y*z0^2 - x^19*y*z0^4 + 2*x^22*y + 2*x^22*z0 + x^20*y*z0^2 + 2*x^20*z0^3 - 2*x^18*y*z0^4 - x^21*y + 2*x^21*z0 - 2*x^19*y*z0^2 - 2*x^19*z0^3 + x^17*y*z0^4 - x^20*y - 2*x^20*z0 + x^16*y*z0^4 - x^19*z0 + x^17*y*z0^2 - x^18*y + 2*x^18*z0 - x^16*y*z0^2 - 2*x^16*z0^3 + 2*x^14*y*z0^4 + x^17*y - x^17*z0 + x^15*y*z0^2 + 2*x^14*y*z0^2 - x^15*y + 2*x^15*z0 - 2*x^13*y*z0^2 - x^11*y*z0^4 - x^14*z0 + 2*x^12*z0^3 + x^10*y*z0^4 - 2*x^13*y + 2*x^13*z0 - x^11*y*z0^2 - x^11*z0^3 - x^9*y*z0^4 + 2*x^12*z0 + 2*x^10*y*z0^2 + x^10*z0^3 + 2*x^8*y*z0^4 - x^11*y - x^11*z0 + x^9*y*z0^2 + x^9*z0^3 + 2*x^7*y*z0^4 - x^10*y - 2*x^10*z0 - x^8*y*z0^2 - 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*z0 + x^7*y*z0^2 + x^7*z0^3 + x^5*y*z0^4 + x^8*y + x^8*z0 - 2*x^6*y*z0^2 - 2*x^6*z0^3 + x^7*y - x^5*y*z0^2 + x^6*y + 2*x^6*z0 + 2*x^4*y*z0^2 + 2*x^4*z0^3 + 2*x^2*y*z0^4 - x^5*z0 + x^3*z0^3 - 2*x^4*z0 - 2*x^2*y*z0^2 - 2*x^2*z0^3 - 2*x^3*y - 2*x^3*z0 + x^2*y)/y) * dx, - ((-2*x^61*z0^4 + 2*x^58*y^2*z0^4 - x^60*z0^2 + 2*x^58*z0^4 + 2*x^61 + x^57*y^2*z0^2 - 2*x^58*y^2 + x^57*z0^2 - 2*x^55*z0^4 - 2*x^58 - x^54*z0^2 + 2*x^52*z0^4 + 2*x^55 + x^51*z0^2 - 2*x^49*z0^4 - 2*x^52 - x^48*z0^2 + 2*x^46*z0^4 + 2*x^49 + x^45*z0^2 - 2*x^43*z0^4 - 2*x^46 - x^41*z0^4 - x^42*z0^2 - x^40*y*z0^3 - 2*x^40*z0^4 + 2*x^43 - 2*x^38*z0^4 - x^41 - 2*x^39*y*z0 + x^39*z0^2 + x^37*y*z0^3 - x^37*z0^4 + x^40 - x^39 - 2*x^38 - x^36*y*z0 - x^36*z0^2 - x^34*y*z0^3 + x^34*z0^4 + x^32*y^2*z0^4 - 2*x^37 + 2*x^35*y*z0 - 2*x^35*z0^2 - x^33*z0^4 + x^36 + x^34*z0^2 + 2*x^32*z0^4 - 2*x^35 + 2*x^33*z0^2 - x^31*y*z0^3 + 2*x^34 - x^32*y*z0 + 2*x^32*z0^2 - x^30*y*z0^3 + x^33 + 2*x^31*y*z0 + x^31*z0^2 - x^29*y*z0^3 + 2*x^29*z0^4 + x^32 - 2*x^30*y*z0 - x^30*z0^2 + 2*x^28*z0^4 + 2*x^31 - 2*x^29*y*z0 + 2*x^27*y*z0^3 - x^27*z0^4 - x^30 - x^28*y*z0 - 2*x^26*y*z0^3 + 2*x^26*z0^4 + x^29 + x^27*y*z0 + x^27*z0^2 - 2*x^25*y*z0^3 - 2*x^25*z0^4 + 2*x^26*y*z0 + 2*x^26*z0^2 - 2*x^24*y*z0^3 + 2*x^24*z0^4 - x^27 + x^25*y*z0 + x^25*z0^2 - x^23*y*z0^3 - 2*x^23*z0^4 - x^26 - 2*x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^22*z0^4 + x^25 - 2*x^23*y*z0 - x^21*y*z0^3 - x^21*z0^4 - 2*x^22*y*z0 - 2*x^22*z0^2 + x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^23 - 2*x^21*y*z0 - 2*x^21*z0^2 + 2*x^19*y*z0^3 - 2*x^19*z0^4 - x^22 - 2*x^20*y*z0 - 2*x^20*z0^2 + 2*x^18*y*z0^3 + 2*x^21 - 2*x^19*y*z0 + 2*x^19*z0^2 + x^17*z0^4 - 2*x^20 + 2*x^18*y*z0 + x^18*z0^2 + 2*x^16*z0^4 - x^19 - 2*x^17*z0^2 + 2*x^15*y*z0^3 + 2*x^15*z0^4 + 2*x^18 + x^16*y*z0 + x^16*z0^2 + 2*x^14*y*z0^3 + 2*x^14*z0^4 + 2*x^17 - x^15*z0^2 + 2*x^13*z0^4 - 2*x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 - x^12*z0^4 - x^13*y*z0 + x^13*z0^2 + 2*x^11*y*z0^3 - x^11*z0^4 - x^12*y*z0 - x^12*z0^2 + 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^11*y*z0 - x^11*z0^2 - x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 - x^10*z0^2 - x^8*y*z0^3 - x^11 + x^7*y*z0^3 + x^7*z0^4 - 2*x^10 - x^8*z0^2 - x^6*y*z0^3 - 2*x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + x^8 - x^6*y*z0 - x^6*z0^2 + x^4*y*z0^3 - 2*x^4*z0^4 - x^7 + x^5*y*z0 - x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^6 + x^4*y*z0 + 2*x^4*z0^2 - 2*x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 + 2*x^3*z0^2 + 2*x^2*y*z0 + 2*x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((2*x^60*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 - 2*x^57*y^2*z0^4 - x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^56*y^2*z0^4 + 2*x^61 + x^57*y^2*z0^2 - 2*x^57*z0^4 - 2*x^60 - 2*x^58*y^2 + 2*x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 + x^57*z0^2 - 2*x^58 + 2*x^54*z0^4 + 2*x^57 - 2*x^55*z0^2 + 2*x^53*z0^4 - x^54*z0^2 + 2*x^55 - 2*x^51*z0^4 - 2*x^54 + 2*x^52*z0^2 - 2*x^50*z0^4 + x^51*z0^2 - 2*x^52 + 2*x^48*z0^4 + 2*x^51 - 2*x^49*z0^2 + 2*x^47*z0^4 - x^48*z0^2 + 2*x^49 - 2*x^45*z0^4 - 2*x^48 + 2*x^46*z0^2 - 2*x^44*z0^4 + x^45*z0^2 - 2*x^46 + 2*x^42*z0^4 + 2*x^45 - 2*x^43*z0^2 - 2*x^41*z0^4 - x^42*z0^2 - x^40*z0^4 + 2*x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - 2*x^42 - x^40*y*z0 + 2*x^40*z0^2 + 2*x^38*z0^4 + x^41 - 2*x^39*y*z0 - 2*x^39*z0^2 - x^37*z0^4 - 2*x^40 + x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - x^39 - 2*x^37*y*z0 + 2*x^37*z0^2 - 2*x^35*y*z0^3 + x^35*z0^4 + x^38 - x^36*y*z0 + 2*x^36*z0^2 - x^34*y*z0^3 - 2*x^34*z0^4 + 2*x^37 - x^35*y*z0 + 2*x^35*z0^2 + x^33*z0^4 - 2*x^36 + 2*x^34*y*z0 + x^32*y*z0^3 + 2*x^32*z0^4 + x^33*y^2 - 2*x^31*y*z0^3 + x^31*z0^4 - 2*x^32*y*z0 - x^32*z0^2 + 2*x^30*y*z0^3 + 2*x^33 + 2*x^31*z0^2 - x^29*y*z0^3 + x^29*z0^4 + 2*x^32 + 2*x^28*y*z0^3 + x^28*z0^4 - 2*x^31 + 2*x^29*y*z0 + 2*x^29*z0^2 - 2*x^27*y*z0^3 + x^27*z0^4 + x^30 + x^28*z0^2 - x^26*y*z0^3 + x^29 + x^27*y*z0 + x^25*z0^4 - x^28 + x^26*y*z0 - x^26*z0^2 - 2*x^24*y*z0^3 - 2*x^24*z0^4 + 2*x^25*z0^2 + 2*x^23*y*z0^3 - 2*x^26 + 2*x^24*y*z0 + x^24*z0^2 - x^22*y*z0^3 - x^25 + x^23*y*z0 + x^21*y*z0^3 + 2*x^21*z0^4 + x^22*z0^2 - x^20*y*z0^3 - x^20*z0^4 - x^23 + 2*x^21*y*z0 - x^21*z0^2 - 2*x^19*y*z0^3 - 2*x^22 + 2*x^20*z0^2 - 2*x^18*y*z0^3 - x^18*z0^4 - x^19*y*z0 - x^19*z0^2 + 2*x^17*y*z0^3 - 2*x^17*z0^4 - x^18*z0^2 - x^16*y*z0^3 - x^19 - 2*x^17*y*z0 + x^17*z0^2 + 2*x^15*z0^4 - x^18 - 2*x^16*z0^2 + x^14*y*z0^3 + x^14*z0^4 - x^17 - x^15*y*z0 - 2*x^15*z0^2 + x^13*y*z0^3 + x^13*z0^4 + x^16 - 2*x^14*y*z0 - 2*x^12*z0^4 + 2*x^15 + 2*x^13*y*z0 + x^11*y*z0^3 + x^11*z0^4 + x^14 + x^12*y*z0 - x^12*z0^2 + 2*x^10*z0^4 - x^13 - 2*x^11*y*z0 - x^11*z0^2 - x^12 + 2*x^10*z0^2 + x^8*y*z0^3 - x^8*z0^4 - x^9*y*z0 + x^7*y*z0^3 - x^7*z0^4 - x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 - 2*x^5*z0^4 + 2*x^8 + x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 - x^4*z0^4 + x^7 + x^5*z0^2 - x^6 - 2*x^4*y*z0 + 2*x^4*z0^2 - x^2*y*z0^3 + x^2*z0^4 - x^3*y*z0 + 2*x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3)/y) * dx, - ((-x^61*z0^3 + x^58*y^2*z0^3 + 2*x^61*z0 - x^59*z0^3 - 2*x^60*z0 - 2*x^58*y^2*z0 + 2*x^58*z0^3 + x^56*y^2*z0^3 - x^59*z0 + 2*x^57*y^2*z0 + x^57*z0^3 - x^55*y^2*z0^3 - 2*x^58*z0 + x^56*y^2*z0 + x^56*z0^3 - x^54*y^2*z0^3 + 2*x^57*z0 - 2*x^55*z0^3 + x^56*z0 - x^54*z0^3 + 2*x^55*z0 - x^53*z0^3 - 2*x^54*z0 + 2*x^52*z0^3 - x^53*z0 + x^51*z0^3 - 2*x^52*z0 + x^50*z0^3 + 2*x^51*z0 - 2*x^49*z0^3 + x^50*z0 - x^48*z0^3 + 2*x^49*z0 - x^47*z0^3 - 2*x^48*z0 + 2*x^46*z0^3 - x^47*z0 + x^45*z0^3 - 2*x^46*z0 + x^44*z0^3 + 2*x^45*z0 - 2*x^43*z0^3 + x^44*z0 - x^42*z0^3 + 2*x^43*z0 - 2*x^41*z0^3 - x^39*y*z0^4 - 2*x^42*z0 + 2*x^40*y*z0^2 + 2*x^38*y*z0^4 + x^41*z0 + 2*x^39*y*z0^2 - x^39*z0^3 + x^37*y*z0^4 + x^40*y - 2*x^38*y*z0^2 - 2*x^38*z0^3 - x^39*y - 2*x^39*z0 + 2*x^37*z0^3 + 2*x^35*y*z0^4 - 2*x^38*y - x^38*z0 - x^36*y*z0^2 - 2*x^36*z0^3 + 2*x^37*y - 2*x^35*y*z0^2 - x^33*y*z0^4 - x^36*y - 2*x^36*z0 - x^34*y*z0^2 + x^34*z0^3 + x^35*z0 + x^33*y^2*z0 - 2*x^33*z0^3 - 2*x^31*y*z0^4 - 2*x^34*y + 2*x^34*z0 - x^32*y*z0^2 - x^32*z0^3 - 2*x^30*y*z0^4 + 2*x^33*y - 2*x^31*y*z0^2 + x^31*z0^3 + x^29*y*z0^4 - 2*x^32*z0 - x^30*y*z0^2 + 2*x^30*z0^3 + x^28*y*z0^4 - 2*x^31*y - x^29*y*z0^2 + 2*x^29*z0^3 + x^27*y*z0^4 - x^30*y + x^30*z0 + x^28*y*z0^2 - 2*x^28*z0^3 + x^26*y*z0^4 - x^29*y + x^29*z0 - x^27*y*z0^2 - x^27*z0^3 + 2*x^25*y*z0^4 - 2*x^28*y - 2*x^28*z0 + x^26*y*z0^2 + x^24*y*z0^4 + x^27*y + 2*x^27*z0 + 2*x^25*y*z0^2 + x^25*z0^3 - x^23*y*z0^4 - 2*x^26*y - 2*x^26*z0 - x^24*y*z0^2 + 2*x^24*z0^3 - x^22*y*z0^4 - 2*x^25*y + x^25*z0 + 2*x^23*y*z0^2 - x^23*z0^3 + 2*x^21*y*z0^4 + x^24*y - 2*x^24*z0 + 2*x^22*y*z0^2 - x^22*z0^3 - x^20*y*z0^4 - x^23*y + x^23*z0 - x^21*y*z0^2 + 2*x^21*z0^3 - 2*x^19*y*z0^4 + 2*x^22*y + x^18*y*z0^4 - 2*x^21*y - 2*x^21*z0 - 2*x^19*y*z0^2 - 2*x^17*y*z0^4 - 2*x^20*z0 - x^18*y*z0^2 - 2*x^18*z0^3 + 2*x^16*y*z0^4 + 2*x^19*y - x^19*z0 + x^17*y*z0^2 - 2*x^17*z0^3 - x^18*y - x^18*z0 + 2*x^16*y*z0^2 + 2*x^16*z0^3 - x^14*y*z0^4 + x^17*z0 + x^15*z0^3 + 2*x^16*y + x^16*z0 - x^14*y*z0^2 - x^14*z0^3 + x^15*y - 2*x^15*z0 - x^13*y*z0^2 + 2*x^13*z0^3 - 2*x^11*y*z0^4 + x^14*y - x^14*z0 - x^12*y*z0^2 + x^10*y*z0^4 + 2*x^13*y - 2*x^13*z0 - 2*x^11*z0^3 + x^9*y*z0^4 + x^12*y + 2*x^12*z0 + 2*x^10*y*z0^2 + 2*x^8*y*z0^4 + 2*x^11*y - 2*x^11*z0 - 2*x^9*y*z0^2 + x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y - x^10*z0 + x^8*y*z0^2 + 2*x^8*z0^3 - x^9*y - 2*x^7*y*z0^2 + x^7*z0^3 - x^5*y*z0^4 + x^8*y + x^8*z0 + x^6*y*z0^2 + 2*x^6*z0^3 + 2*x^4*y*z0^4 - 2*x^7*z0 + x^5*y*z0^2 - 2*x^3*y*z0^4 - 2*x^6*y + x^4*y*z0^2 - 2*x^4*z0^3 - 2*x^2*y*z0^4 - x^5*y + x^5*z0 - x^3*y*z0^2 + x^3*z0^3 + x^4*y - x^4*z0 - x^2*y*z0^2 - x^2*z0^3 - x^3*y + 2*x^2*y)/y) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 - 2*x^61*z0^2 - x^59*z0^4 + 2*x^58*y^2*z0^2 - x^58*z0^4 + x^56*y^2*z0^4 + x^60 + 2*x^58*z0^2 + x^56*z0^4 - x^57*y^2 + x^55*z0^4 - x^57 - 2*x^55*z0^2 - x^53*z0^4 - x^52*z0^4 + x^54 + 2*x^52*z0^2 + x^50*z0^4 + x^49*z0^4 - x^51 - 2*x^49*z0^2 - x^47*z0^4 - x^46*z0^4 + x^48 + 2*x^46*z0^2 + x^44*z0^4 + x^43*z0^4 - x^45 - 2*x^43*z0^2 - 2*x^40*y*z0^3 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - x^39*z0^4 + x^42 - x^40*y*z0 - x^40*z0^2 + x^38*y*z0^3 + 2*x^38*z0^4 + x^41 + 2*x^39*y*z0 + 2*x^39*z0^2 + x^37*y*z0^3 + x^37*z0^4 - x^40 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - 2*x^37*z0^2 + x^35*y*z0^3 - x^35*z0^4 - x^36*y*z0 + 2*x^36*z0^2 + x^37 - x^35*y*z0 + x^33*y^2*z0^2 + 2*x^33*y*z0^3 - x^36 + 2*x^34*y*z0 + x^34*z0^2 - x^32*y*z0^3 + 2*x^32*z0^4 + 2*x^33*y*z0 - 2*x^33*z0^2 - 2*x^31*y*z0^3 - x^34 + 2*x^32*y*z0 - 2*x^32*z0^2 - 2*x^30*y*z0^3 - 2*x^30*z0^4 + x^33 + x^31*y*z0 + x^31*z0^2 + x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^30*y*z0 - x^30*z0^2 - 2*x^28*y*z0^3 - x^28*z0^4 - x^31 + 2*x^29*y*z0 - 2*x^29*z0^2 - x^27*y*z0^3 + x^27*z0^4 - x^30 - 2*x^28*y*z0 - 2*x^28*z0^2 - x^26*y*z0^3 - 2*x^26*z0^4 + x^29 + x^25*y*z0^3 + 2*x^25*z0^4 - 2*x^28 - 2*x^26*y*z0 - x^26*z0^2 - x^24*z0^4 - x^27 + 2*x^25*y*z0 - x^25*z0^2 + 2*x^23*z0^4 - x^26 + x^24*y*z0 + 2*x^22*z0^4 + 2*x^25 - x^23*y*z0 + 2*x^23*z0^2 - x^21*z0^4 + x^24 + x^22*y*z0 - x^22*z0^2 + 2*x^20*y*z0^3 + x^20*z0^4 - 2*x^23 + 2*x^21*z0^2 - x^19*y*z0^3 + 2*x^19*z0^4 - 2*x^22 + 2*x^20*y*z0 + x^20*z0^2 + 2*x^18*y*z0^3 + 2*x^18*z0^4 - x^21 - x^19*y*z0 - x^17*y*z0^3 + x^20 - 2*x^18*y*z0 - 2*x^18*z0^2 + 2*x^16*y*z0^3 - x^16*z0^4 - 2*x^19 + x^17*y*z0 + 2*x^17*z0^2 + x^15*y*z0^3 - x^15*z0^4 + 2*x^18 + x^16*y*z0 - x^16*z0^2 - 2*x^14*y*z0^3 - x^14*z0^4 + x^17 + x^15*z0^2 - 2*x^13*z0^4 - x^16 - 2*x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 + 2*x^15 + x^13*y*z0 - 2*x^13*z0^2 - 2*x^11*y*z0^3 - x^11*z0^4 + x^14 - 2*x^12*z0^2 - 2*x^10*y*z0^3 - 2*x^13 + x^11*y*z0 + x^11*z0^2 + 2*x^9*y*z0^3 + x^9*z0^4 - 2*x^12 + x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + x^11 - x^9*y*z0 - x^9*z0^2 - 2*x^7*y*z0^3 + x^10 - x^8*y*z0 - x^8*z0^2 - x^6*z0^4 - x^9 + x^7*y*z0 - x^5*y*z0^3 + x^8 + x^6*y*z0 + x^6*z0^2 + x^4*z0^4 - 2*x^7 + x^5*z0^2 - x^3*y*z0^3 + x^3*z0^4 + 2*x^6 - x^4*y*z0 + 2*x^2*y*z0^3 + x^2*z0^4 + x^5 + 2*x^3*y*z0 + x^3*z0^2 + x^2*y*z0 + x^2*z0^2 - x^3 - x^2)/y) * dx, - ((-x^60*z0^3 + x^61*z0 + x^57*y^2*z0^3 + 2*x^60*z0 - x^58*y^2*z0 - 2*x^58*z0^3 - 2*x^57*y^2*z0 + 2*x^57*z0^3 + 2*x^55*y^2*z0^3 - x^58*z0 - x^54*y^2*z0^3 - 2*x^57*z0 + 2*x^55*z0^3 - 2*x^54*z0^3 + x^55*z0 + 2*x^54*z0 - 2*x^52*z0^3 + 2*x^51*z0^3 - x^52*z0 - 2*x^51*z0 + 2*x^49*z0^3 - 2*x^48*z0^3 + x^49*z0 + 2*x^48*z0 - 2*x^46*z0^3 + 2*x^45*z0^3 - x^46*z0 - 2*x^45*z0 + 2*x^43*z0^3 - 2*x^42*z0^3 + x^43*z0 + 2*x^42*z0 - 2*x^40*z0^3 - 2*x^38*y*z0^4 + x^41*z0 + x^39*y*z0^2 + 2*x^39*z0^3 - 2*x^37*y*z0^4 - 2*x^40*y - x^38*y*z0^2 + 2*x^39*y + 2*x^39*z0 + 2*x^37*y*z0^2 + 2*x^37*z0^3 - 2*x^35*y*z0^4 - 2*x^38*y + 2*x^38*z0 - 2*x^36*y*z0^2 + 2*x^36*z0^3 - 2*x^34*y*z0^4 + x^37*y + 2*x^37*z0 - x^35*y*z0^2 + 2*x^35*z0^3 + x^33*y^2*z0^3 + 2*x^33*y*z0^4 - 2*x^36*z0 + 2*x^34*y*z0^2 - 2*x^34*z0^3 + 2*x^32*y*z0^4 + x^33*y*z0^2 - x^33*z0^3 - x^31*y*z0^4 + x^34*y - x^34*z0 + x^32*y*z0^2 - x^32*z0^3 + 2*x^30*y*z0^4 - x^33*z0 + 2*x^31*y*z0^2 + x^31*z0^3 - 2*x^29*y*z0^4 + 2*x^30*z0^3 + x^28*y*z0^4 + x^31*y - 2*x^31*z0 + 2*x^29*z0^3 + x^27*y*z0^4 - 2*x^30*z0 - x^28*y*z0^2 + x^28*z0^3 + x^26*y*z0^4 + 2*x^29*y + x^29*z0 + x^27*y*z0^2 + x^27*z0^3 + 2*x^25*y*z0^4 + x^28*y - x^28*z0 + x^26*y*z0^2 - 2*x^26*z0^3 + x^24*y*z0^4 - 2*x^27*y - 2*x^27*z0 + x^25*y*z0^2 - x^25*z0^3 + x^23*y*z0^4 + 2*x^26*y - x^26*z0 - x^24*y*z0^2 + x^22*y*z0^4 - x^25*z0 + 2*x^23*y*z0^2 + 2*x^23*z0^3 - 2*x^21*y*z0^4 + x^24*z0 - x^22*y*z0^2 + 2*x^22*z0^3 + x^20*y*z0^4 - 2*x^23*z0 + x^21*y*z0^2 + 2*x^21*z0^3 - 2*x^19*y*z0^4 + 2*x^22*y + 2*x^22*z0 - 2*x^20*z0^3 + 2*x^21*y - 2*x^21*z0 - x^19*y*z0^2 + x^17*y*z0^4 + 2*x^20*y - x^20*z0 - 2*x^18*y*z0^2 + 2*x^19*y - 2*x^19*z0 + 2*x^17*z0^3 - 2*x^18*y + x^18*z0 + 2*x^16*y*z0^2 - 2*x^16*z0^3 - x^14*y*z0^4 + 2*x^17*y + x^17*z0 - 2*x^15*z0^3 + 2*x^16*y - 2*x^16*z0 + x^14*y*z0^2 - x^14*z0^3 + 2*x^12*y*z0^4 + x^15*y + 2*x^15*z0 - 2*x^13*y*z0^2 + 2*x^14*y + 2*x^12*y*z0^2 + 2*x^12*z0^3 + 2*x^10*y*z0^4 + 2*x^13*y + 2*x^13*z0 + x^11*y*z0^2 + 2*x^12*y - x^12*z0 + x^10*y*z0^2 + 2*x^10*z0^3 - x^8*y*z0^4 + x^11*y - 2*x^11*z0 + 2*x^9*y*z0^2 - 2*x^9*z0^3 + x^10*y + 2*x^10*z0 - x^8*y*z0^2 - x^9*y + x^9*z0 - 2*x^7*y*z0^2 - 2*x^7*z0^3 - 2*x^5*y*z0^4 + 2*x^8*y - x^8*z0 - 2*x^4*y*z0^4 - x^7*y + 2*x^5*y*z0^2 + 2*x^5*z0^3 - 2*x^3*y*z0^4 - 2*x^6*y + x^6*z0 + 2*x^4*z0^3 - x^2*y*z0^4 + 2*x^5*z0 - x^3*y*z0^2 + 2*x^3*z0^3 - 2*x^4*y - x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - x^3*y + 2*x^3*z0 - 2*x^2*y - x^2*z0)/y) * dx, - ((-x^61*z0^4 + 2*x^60*z0^4 + x^58*y^2*z0^4 + 2*x^61*z0^2 - 2*x^57*y^2*z0^4 + 2*x^60*z0^2 - 2*x^58*y^2*z0^2 + x^58*z0^4 + 2*x^61 - 2*x^57*y^2*z0^2 - 2*x^57*z0^4 + 2*x^60 - 2*x^58*y^2 - 2*x^58*z0^2 - 2*x^57*y^2 - 2*x^57*z0^2 - x^55*z0^4 - 2*x^58 + 2*x^54*z0^4 - 2*x^57 + 2*x^55*z0^2 + 2*x^54*z0^2 + x^52*z0^4 + 2*x^55 - 2*x^51*z0^4 + 2*x^54 - 2*x^52*z0^2 - 2*x^51*z0^2 - x^49*z0^4 - 2*x^52 + 2*x^48*z0^4 - 2*x^51 + 2*x^49*z0^2 + 2*x^48*z0^2 + x^46*z0^4 + 2*x^49 - 2*x^45*z0^4 + 2*x^48 - 2*x^46*z0^2 - 2*x^45*z0^2 - x^43*z0^4 - 2*x^46 + 2*x^42*z0^4 - 2*x^45 + 2*x^43*z0^2 + 2*x^42*z0^2 + 2*x^40*y*z0^3 + 2*x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + x^39*z0^4 + 2*x^42 + x^40*y*z0 - 2*x^40*z0^2 + x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 + x^40 - x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + x^36*z0^4 - 2*x^37*y*z0 + x^37*z0^2 + 2*x^35*y*z0^3 + 2*x^35*z0^4 + x^33*y^2*z0^4 - x^36*y*z0 - x^36*z0^2 + 2*x^34*y*z0^3 - x^37 + x^35*y*z0 - x^36 - 2*x^34*y*z0 - 2*x^34*z0^2 - x^32*y*z0^3 - x^35 - 2*x^33*y*z0 + x^33*z0^2 - x^31*z0^4 - 2*x^34 + x^32*y*z0 - 2*x^30*y*z0^3 + x^31*y*z0 + x^31*z0^2 + 2*x^29*y*z0^3 - 2*x^32 + 2*x^30*y*z0 + 2*x^30*z0^2 - 2*x^29*y*z0 - 2*x^29*z0^2 - x^27*y*z0^3 - 2*x^30 - 2*x^28*y*z0 + 2*x^28*z0^2 + x^26*y*z0^3 - 2*x^26*z0^4 - 2*x^29 + x^27*y*z0 + 2*x^27*z0^2 + x^25*y*z0^3 + 2*x^25*z0^4 + 2*x^26*y*z0 + x^26*z0^2 - x^24*y*z0^3 + x^27 + 2*x^25*y*z0 + x^23*z0^4 - 2*x^24*y*z0 + 2*x^24*z0^2 + x^22*y*z0^3 - 2*x^22*z0^4 + 2*x^25 + 2*x^23*y*z0 + x^23*z0^2 - 2*x^21*y*z0^3 + 2*x^24 + 2*x^22*y*z0 + 2*x^22*z0^2 + 2*x^20*y*z0^3 - 2*x^23 - 2*x^21*z0^2 - x^19*y*z0^3 + 2*x^19*z0^4 - 2*x^22 - 2*x^20*y*z0 - 2*x^18*y*z0^3 + 2*x^18*z0^4 - x^21 + 2*x^19*y*z0 - 2*x^19*z0^2 + x^17*y*z0^3 + x^17*z0^4 + 2*x^20 + 2*x^18*y*z0 + 2*x^18*z0^2 - x^16*y*z0^3 - x^16*z0^4 + 2*x^17*y*z0 - x^15*y*z0^3 - x^15*z0^4 + x^18 + x^16*z0^2 - 2*x^14*z0^4 + x^17 + 2*x^15*y*z0 + x^13*z0^4 - 2*x^16 + 2*x^14*y*z0 + 2*x^14*z0^2 - x^12*y*z0^3 - 2*x^12*z0^4 - x^15 - x^13*y*z0 + 2*x^13*z0^2 - x^11*z0^4 + 2*x^14 + x^12*y*z0 + 2*x^12*z0^2 + x^10*y*z0^3 + 2*x^10*z0^4 + 2*x^13 + 2*x^11*y*z0 + 2*x^11*z0^2 + x^9*y*z0^3 - 2*x^12 - 2*x^10*y*z0 + x^10*z0^2 + x^8*z0^4 + x^11 + x^7*y*z0^3 - 2*x^7*z0^4 - x^10 - x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 + x^6*z0^4 - 2*x^7*y*z0 + x^7*z0^2 + 2*x^5*y*z0^3 - x^5*z0^4 - 2*x^8 - 2*x^6*y*z0 + 2*x^6*z0^2 + x^4*y*z0^3 - 2*x^4*z0^4 - x^7 + x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^6 - 2*x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 - x^2*z0^4 - x^5 + 2*x^3*y*z0 - 2*x^2*y*z0 - x^2*z0^2 + x^3 + 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 + 2*x^60*z0^4 + x^58*y^2*z0^4 - x^61*z0^2 - 2*x^59*z0^4 - 2*x^57*y^2*z0^4 + x^60*z0^2 + x^58*y^2*z0^2 + x^58*z0^4 + 2*x^56*y^2*z0^4 - x^61 - x^57*y^2*z0^2 - 2*x^57*z0^4 + 2*x^60 + x^58*y^2 + x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 - x^57*z0^2 - x^55*z0^4 + x^58 + 2*x^54*z0^4 - 2*x^57 - x^55*z0^2 - 2*x^53*z0^4 + x^54*z0^2 + x^52*z0^4 - x^55 - 2*x^51*z0^4 + 2*x^54 + x^52*z0^2 + 2*x^50*z0^4 - x^51*z0^2 - x^49*z0^4 + x^52 + 2*x^48*z0^4 - 2*x^51 - x^49*z0^2 - 2*x^47*z0^4 + x^48*z0^2 + x^46*z0^4 - x^49 - 2*x^45*z0^4 + 2*x^48 + x^46*z0^2 + 2*x^44*z0^4 - x^45*z0^2 - x^43*z0^4 + x^46 + 2*x^42*z0^4 - 2*x^45 - x^43*z0^2 - x^41*z0^4 + x^42*z0^2 + 2*x^40*y*z0^3 - x^40*z0^4 - x^43 - x^41*z0^2 - x^39*y*z0^3 + 2*x^42 + 2*x^40*y*z0 + 2*x^40*z0^2 + x^38*y*z0^3 + 2*x^38*z0^4 + x^41 - 2*x^39*y*z0 - x^37*z0^4 - 2*x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + 2*x^36*z0^4 + x^39 + 2*x^37*y*z0 + x^35*y*z0^3 + x^35*z0^4 - 2*x^38 + x^36*y*z0 + x^34*y*z0^3 + 2*x^34*z0^4 - 2*x^37 + 2*x^35*y*z0 - 2*x^33*y*z0^3 + 2*x^33*z0^4 + x^34*y^2 - 2*x^34*z0^2 - x^32*y*z0^3 - x^32*z0^4 - 2*x^35 + 2*x^33*y*z0 - 2*x^31*y*z0^3 - x^31*z0^4 - x^34 - x^32*y*z0 - x^32*z0^2 + x^30*y*z0^3 - 2*x^33 - 2*x^31*y*z0 - 2*x^29*y*z0^3 - 2*x^29*z0^4 + 2*x^30*y*z0 + x^30*z0^2 - 2*x^28*y*z0^3 + 2*x^31 - 2*x^29*y*z0 - x^28*z0^2 - x^26*y*z0^3 + x^26*z0^4 - 2*x^29 + 2*x^27*y*z0 + 2*x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 + x^26*y*z0 - 2*x^26*z0^2 + 2*x^24*y*z0^3 + x^24*z0^4 - x^27 - x^25*y*z0 - 2*x^23*y*z0^3 - x^23*z0^4 + x^26 + x^24*y*z0 + 2*x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^22*z0^4 - 2*x^25 - x^23*y*z0 - x^23*z0^2 + 2*x^21*y*z0^3 + x^21*z0^4 + x^24 - x^22*y*z0 + 2*x^20*y*z0^3 + x^20*z0^4 - x^23 - x^21*z0^2 + 2*x^19*y*z0^3 + 2*x^19*z0^4 - x^22 - 2*x^20*z0^2 + x^18*y*z0^3 - 2*x^18*z0^4 - x^21 - x^19*y*z0 - 2*x^17*z0^4 - 2*x^20 + x^18*y*z0 + 2*x^18*z0^2 - 2*x^19 - 2*x^17*y*z0 + 2*x^17*z0^2 - 2*x^15*y*z0^3 + x^15*z0^4 + x^18 + x^16*z0^2 - x^14*y*z0^3 - x^14*z0^4 - x^17 - 2*x^15*y*z0 - 2*x^15*z0^2 - x^13*z0^4 - x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 - x^12*z0^4 + 2*x^13*z0^2 - x^12*z0^2 - 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - 2*x^11*y*z0 + 2*x^11*z0^2 + 2*x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^12 + x^10*y*z0 - x^8*y*z0^3 - 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 + x^7*z0^4 - 2*x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 + x^9 - 2*x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 - x^5*z0^4 + x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 + 2*x^7 + x^5*y*z0 + x^5*z0^2 - x^3*z0^4 - 2*x^6 + x^4*z0^2 - 2*x^2*y*z0^3 - x^2*z0^4 - x^5 - x^3*y*z0 + x^3*z0^2 - x^3)/y) * dx, - ((2*x^61*z0^3 + x^60*z0^3 - 2*x^58*y^2*z0^3 - x^57*y^2*z0^3 + 2*x^60*z0 + 2*x^58*z0^3 - x^59*z0 - 2*x^57*y^2*z0 - 2*x^57*z0^3 + x^55*y^2*z0^3 + x^56*y^2*z0 + x^54*y^2*z0^3 - 2*x^57*z0 - 2*x^55*z0^3 + x^56*z0 + 2*x^54*z0^3 + 2*x^54*z0 + 2*x^52*z0^3 - x^53*z0 - 2*x^51*z0^3 - 2*x^51*z0 - 2*x^49*z0^3 + x^50*z0 + 2*x^48*z0^3 + 2*x^48*z0 + 2*x^46*z0^3 - x^47*z0 - 2*x^45*z0^3 - 2*x^45*z0 - 2*x^43*z0^3 + x^44*z0 + 2*x^42*z0^3 + 2*x^41*z0^3 + 2*x^39*y*z0^4 + 2*x^42*z0 + x^40*y*z0^2 + x^40*z0^3 - 2*x^38*y*z0^4 - x^41*z0 - x^37*y*z0^4 - x^38*z0^3 + x^36*y*z0^4 + x^39*z0 - x^37*y*z0^2 + 2*x^37*z0^3 + 2*x^35*y*z0^4 - x^38*y - 2*x^36*y*z0^2 + 2*x^34*y*z0^4 - 2*x^37*z0 + x^35*y*z0^2 + x^35*z0^3 - x^33*y*z0^4 + x^36*y + x^36*z0 + x^34*y^2*z0 - 2*x^34*y*z0^2 - x^34*z0^3 + 2*x^35*z0 + 2*x^33*y*z0^2 + x^33*z0^3 - x^31*y*z0^4 - x^34*y - 2*x^34*z0 - x^32*y*z0^2 + x^32*z0^3 - x^33*y - x^31*y*z0^2 + x^31*z0^3 + 2*x^29*y*z0^4 - x^32*y + x^32*z0 + 2*x^30*y*z0^2 - 2*x^28*y*z0^4 - 2*x^31*y + x^29*y*z0^2 + 2*x^29*z0^3 + x^27*y*z0^4 + 2*x^30*z0 - x^28*y*z0^2 - 2*x^28*z0^3 - x^26*y*z0^4 + 2*x^29*y + 2*x^29*z0 + x^25*y*z0^4 - x^28*y + x^28*z0 + x^26*y*z0^2 - 2*x^26*z0^3 - x^24*y*z0^4 - 2*x^27*z0 + 2*x^25*y*z0^2 + 2*x^25*z0^3 + 2*x^23*y*z0^4 - x^26*y + 2*x^24*y*z0^2 + x^24*z0^3 + 2*x^22*y*z0^4 + 2*x^25*y - 2*x^25*z0 + x^23*y*z0^2 + x^23*z0^3 - x^24*z0 + x^22*y*z0^2 - x^22*z0^3 - 2*x^20*y*z0^4 - 2*x^23*y + 2*x^23*z0 - x^21*y*z0^2 + 2*x^19*y*z0^4 - 2*x^22*y - 2*x^22*z0 - 2*x^20*y*z0^2 - x^18*y*z0^4 - x^21*z0 - x^19*y*z0^2 + 2*x^19*z0^3 + 2*x^17*y*z0^4 + x^20*z0 + 2*x^18*y*z0^2 + 2*x^18*z0^3 + x^16*y*z0^4 - 2*x^19*y - 2*x^19*z0 + x^17*y*z0^2 + 2*x^17*z0^3 + x^15*y*z0^4 + 2*x^18*y - 2*x^18*z0 - x^16*y*z0^2 + 2*x^16*z0^3 - 2*x^14*y*z0^4 - 2*x^17*y - 2*x^17*z0 + 2*x^15*y*z0^2 - x^15*z0^3 + 2*x^13*y*z0^4 - 2*x^16*z0 - 2*x^14*y*z0^2 + x^12*y*z0^4 - x^15*y - x^15*z0 - 2*x^13*y*z0^2 - 2*x^13*z0^3 + 2*x^11*y*z0^4 - x^14*y + x^14*z0 - 2*x^12*y*z0^2 + 2*x^12*z0^3 + 2*x^10*y*z0^4 + 2*x^13*y - 2*x^13*z0 - x^11*y*z0^2 - x^11*z0^3 + x^10*y*z0^2 - 2*x^10*z0^3 - 2*x^8*y*z0^4 - 2*x^11*y + 2*x^11*z0 - 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 + x^10*y + x^10*z0 + x^8*y*z0^2 + x^6*y*z0^4 - 2*x^9*y - 2*x^9*z0 + x^7*y*z0^2 - x^7*z0^3 + x^8*y + 2*x^8*z0 - x^6*z0^3 - 2*x^4*y*z0^4 - 2*x^7*y - 2*x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + 2*x^3*y*z0^4 - 2*x^6*y + x^6*z0 + 2*x^4*y*z0^2 - 2*x^4*z0^3 - 2*x^2*y*z0^4 + 2*x^5*y - 2*x^5*z0 - x^3*y*z0^2 - x^3*z0^3 - x^4*y - x^4*z0 + 2*x^2*y*z0^2 - x^3*y - 2*x^2*y - x^2*z0)/y) * dx, - ((2*x^61*z0^4 + x^60*z0^4 - 2*x^58*y^2*z0^4 - x^59*z0^4 - x^57*y^2*z0^4 - 2*x^60*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 + x^61 + 2*x^57*y^2*z0^2 - x^57*z0^4 - x^60 - x^58*y^2 + x^56*z0^4 + x^57*y^2 + 2*x^57*z0^2 + 2*x^55*z0^4 - x^58 + x^54*z0^4 + x^57 - x^53*z0^4 - 2*x^54*z0^2 - 2*x^52*z0^4 + x^55 - x^51*z0^4 - x^54 + x^50*z0^4 + 2*x^51*z0^2 + 2*x^49*z0^4 - x^52 + x^48*z0^4 + x^51 - x^47*z0^4 - 2*x^48*z0^2 - 2*x^46*z0^4 + x^49 - x^45*z0^4 - x^48 + x^44*z0^4 + 2*x^45*z0^2 + 2*x^43*z0^4 - x^46 + x^42*z0^4 + x^45 - x^41*z0^4 - 2*x^42*z0^2 + x^40*y*z0^3 + x^43 + 2*x^39*z0^4 - x^42 - 2*x^38*y*z0^3 - 2*x^39*y*z0 + 2*x^39*z0^2 - x^37*y*z0^3 + x^37*z0^4 + x^40 - x^38*y*z0 + x^36*z0^4 - x^39 + 2*x^37*y*z0 - 2*x^37*z0^2 + 2*x^35*y*z0^3 - 2*x^35*z0^4 - 2*x^38 - 2*x^36*z0^2 + x^34*y^2*z0^2 - 2*x^34*y*z0^3 - x^37 + 2*x^35*y*z0 - x^35*z0^2 - 2*x^33*y*z0^3 + 2*x^36 - 2*x^34*y*z0 - 2*x^34*z0^2 - x^32*z0^4 - x^35 + x^33*y*z0 + x^33*z0^2 - 2*x^31*y*z0^3 - 2*x^31*z0^4 - x^32*y*z0 - 2*x^32*z0^2 + 2*x^30*y*z0^3 - 2*x^30*z0^4 + 2*x^31*y*z0 - 2*x^29*y*z0^3 + x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 - x^30*z0^2 - x^28*y*z0^3 - x^28*z0^4 - x^31 - x^29*z0^2 - 2*x^27*y*z0^3 + x^30 + x^28*y*z0 + 2*x^28*z0^2 + x^26*z0^4 - x^29 - 2*x^27*y*z0 + x^27*z0^2 + 2*x^25*z0^4 + 2*x^26*y*z0 - x^26*z0^2 + x^24*y*z0^3 - x^24*z0^4 + 2*x^25*y*z0 + 2*x^25*z0^2 + x^23*y*z0^3 - x^26 - x^24*y*z0 + 2*x^24*z0^2 - 2*x^22*y*z0^3 - 2*x^25 - 2*x^23*y*z0 - x^23*z0^2 + x^21*y*z0^3 - x^21*z0^4 - x^24 + 2*x^20*y*z0^3 - x^23 - x^21*y*z0 + 2*x^21*z0^2 - x^22 - 2*x^20*y*z0 + 2*x^20*z0^2 - 2*x^18*z0^4 - x^21 + 2*x^19*y*z0 - x^19*z0^2 + 2*x^17*y*z0^3 - 2*x^17*z0^4 - 2*x^20 - 2*x^18*y*z0 + x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 - 2*x^19 - x^17*y*z0 - x^17*z0^2 - 2*x^15*y*z0^3 - x^15*z0^4 + x^16*y*z0 + 2*x^16*z0^2 + 2*x^14*y*z0^3 + 2*x^14*z0^4 - x^17 - x^15*y*z0 + x^15*z0^2 - 2*x^13*y*z0^3 + x^13*z0^4 - 2*x^16 + 2*x^14*z0^2 - 2*x^12*z0^4 + 2*x^15 + x^13*y*z0 - x^11*y*z0^3 - 2*x^11*z0^4 - x^14 + x^12*y*z0 + 2*x^12*z0^2 + 2*x^10*y*z0^3 - 2*x^10*z0^4 - x^11*y*z0 + x^11*z0^2 - 2*x^9*y*z0^3 + 2*x^10*y*z0 - x^10*z0^2 - x^8*y*z0^3 + 2*x^11 + 2*x^9*y*z0 - x^9*z0^2 - 2*x^7*y*z0^3 - 2*x^10 - x^8*z0^2 + 2*x^6*y*z0^3 - 2*x^7*y*z0 - x^7*z0^2 + 2*x^6*y*z0 + 2*x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 + x^7 - 2*x^5*y*z0 + x^5*z0^2 - x^3*y*z0^3 + x^6 - 2*x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - x^2*z0^4 + x^5 - 2*x^3*z0^2 - x^2)/y) * dx, - ((2*x^61*z0^3 - 2*x^58*y^2*z0^3 + 2*x^61*z0 + x^59*z0^3 - x^60*z0 - 2*x^58*y^2*z0 + x^58*z0^3 - x^56*y^2*z0^3 - x^59*z0 + x^57*y^2*z0 + x^57*z0^3 + 2*x^55*y^2*z0^3 - 2*x^58*z0 + x^56*y^2*z0 - x^56*z0^3 - x^54*y^2*z0^3 + x^57*z0 - x^55*z0^3 + x^56*z0 - x^54*z0^3 + 2*x^55*z0 + x^53*z0^3 - x^54*z0 + x^52*z0^3 - x^53*z0 + x^51*z0^3 - 2*x^52*z0 - x^50*z0^3 + x^51*z0 - x^49*z0^3 + x^50*z0 - x^48*z0^3 + 2*x^49*z0 + x^47*z0^3 - x^48*z0 + x^46*z0^3 - x^47*z0 + x^45*z0^3 - 2*x^46*z0 - x^44*z0^3 + x^45*z0 - x^43*z0^3 + x^44*z0 - x^42*z0^3 + 2*x^43*z0 - 2*x^41*z0^3 + 2*x^39*y*z0^4 - x^42*z0 + x^40*y*z0^2 + x^40*z0^3 + x^41*z0 + 2*x^39*y*z0^2 - x^37*y*z0^4 + x^40*y + 2*x^40*z0 - x^38*y*z0^2 - x^38*z0^3 - 2*x^36*y*z0^4 + 2*x^39*y + 2*x^39*z0 - 2*x^37*y*z0^2 - 2*x^37*z0^3 + 2*x^35*y*z0^4 + 2*x^38*y - x^38*z0 - x^36*y*z0^2 - 2*x^36*z0^3 + x^34*y^2*z0^3 - 2*x^34*y*z0^4 + 2*x^37*y + x^37*z0 + 2*x^35*z0^3 - 2*x^36*y + 2*x^32*y*z0^4 - 2*x^35*z0 + 2*x^33*y*z0^2 - x^33*z0^3 - x^31*y*z0^4 - 2*x^34*y + 2*x^34*z0 - x^32*z0^3 + x^30*y*z0^4 - x^33*y - 2*x^33*z0 - 2*x^31*y*z0^2 + x^31*z0^3 - x^32*y + x^32*z0 - 2*x^30*y*z0^2 - x^30*z0^3 - x^28*y*z0^4 + 2*x^31*y + 2*x^31*z0 + 2*x^29*y*z0^2 - x^29*z0^3 - 2*x^27*y*z0^4 - 2*x^30*y + x^30*z0 - x^28*y*z0^2 - x^28*z0^3 - x^26*y*z0^4 - 2*x^29*y + 2*x^29*z0 + 2*x^27*y*z0^2 + 2*x^27*z0^3 - 2*x^25*y*z0^4 + x^28*z0 - x^27*y - 2*x^25*y*z0^2 - x^25*z0^3 + x^23*y*z0^4 - x^26*y - 2*x^26*z0 + x^24*y*z0^2 + x^24*z0^3 - 2*x^25*z0 + x^23*z0^3 - 2*x^21*y*z0^4 - x^24*y + x^24*z0 + 2*x^22*y*z0^2 + x^22*z0^3 - 2*x^20*y*z0^4 + 2*x^23*z0 - 2*x^21*y*z0^2 - 2*x^19*y*z0^4 + x^22*y + 2*x^22*z0 - 2*x^20*y*z0^2 + x^20*z0^3 + x^18*y*z0^4 - x^21*y - 2*x^19*z0^3 + 2*x^17*y*z0^4 - x^20*z0 + x^18*y*z0^2 - 2*x^16*y*z0^4 + 2*x^19*y - x^17*y*z0^2 + 2*x^18*y + 2*x^18*z0 + 2*x^16*y*z0^2 + x^16*z0^3 + 2*x^14*y*z0^4 - x^17*y + 2*x^15*y*z0^2 - x^15*z0^3 + x^14*y*z0^2 - 2*x^14*z0^3 + 2*x^12*y*z0^4 - 2*x^15*y + x^15*z0 - 2*x^11*y*z0^4 + x^14*y - x^14*z0 - x^12*y*z0^2 - x^12*z0^3 + x^10*y*z0^4 - 2*x^13*y - x^13*z0 - 2*x^11*y*z0^2 + 2*x^11*z0^3 - x^9*y*z0^4 + 2*x^12*y - 2*x^12*z0 + x^10*y*z0^2 + x^8*y*z0^4 + 2*x^11*y + x^11*z0 - x^9*y*z0^2 + x^9*z0^3 + 2*x^7*y*z0^4 - 2*x^10*y - 2*x^10*z0 + 2*x^8*y*z0^2 + x^8*z0^3 - x^9*y + x^7*y*z0^2 + x^7*z0^3 + 2*x^5*y*z0^4 - 2*x^8*y - x^6*y*z0^2 - 2*x^6*z0^3 + x^7*y - 2*x^5*y*z0^2 + x^5*z0^3 - 2*x^3*y*z0^4 + x^6*z0 - x^4*y*z0^2 - x^4*z0^3 - 2*x^2*y*z0^4 - 2*x^5*y - x^5*z0 + 2*x^3*z0^3 - 2*x^4*y + 2*x^2*y*z0^2 + 2*x^2*z0^3 - x^2*y)/y) * dx, - ((2*x^60*z0^4 - x^61*z0^2 - x^59*z0^4 - 2*x^57*y^2*z0^4 + x^60*z0^2 + x^58*y^2*z0^2 + x^56*y^2*z0^4 - x^61 - x^57*y^2*z0^2 - 2*x^57*z0^4 - x^60 + x^58*y^2 + x^58*z0^2 + x^56*z0^4 + x^57*y^2 - x^57*z0^2 + x^58 + 2*x^54*z0^4 + x^57 - x^55*z0^2 - x^53*z0^4 + x^54*z0^2 - x^55 - 2*x^51*z0^4 - x^54 + x^52*z0^2 + x^50*z0^4 - x^51*z0^2 + x^52 + 2*x^48*z0^4 + x^51 - x^49*z0^2 - x^47*z0^4 + x^48*z0^2 - x^49 - 2*x^45*z0^4 - x^48 + x^46*z0^2 + x^44*z0^4 - x^45*z0^2 + x^46 + 2*x^42*z0^4 + x^45 - x^43*z0^2 + x^41*z0^4 + x^42*z0^2 + x^40*z0^4 - x^43 - x^41*z0^2 - x^39*y*z0^3 - x^42 + 2*x^40*y*z0 - 2*x^40*z0^2 - x^38*z0^4 + 2*x^41 - x^40 - 2*x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 - 2*x^36*z0^4 + x^34*y^2*z0^4 + x^37*y*z0 - x^37*z0^2 - x^35*y*z0^3 - x^35*z0^4 + 2*x^38 - x^36*y*z0 + x^34*y*z0^3 + 2*x^34*z0^4 + x^35*y*z0 - x^35*z0^2 - x^33*z0^4 + 2*x^36 + x^34*y*z0 - 2*x^34*z0^2 - 2*x^32*y*z0^3 - x^32*z0^4 - 2*x^33*y*z0 - x^33*z0^2 + 2*x^31*y*z0^3 + x^31*z0^4 - 2*x^34 - 2*x^32*y*z0 + x^32*z0^2 - 2*x^30*y*z0^3 + x^30*z0^4 - x^33 + x^31*y*z0 + 2*x^31*z0^2 + x^29*y*z0^3 - x^29*z0^4 - x^30*y*z0 + x^30*z0^2 + x^28*y*z0^3 - x^28*z0^4 + 2*x^31 - 2*x^29*y*z0 + x^29*z0^2 + x^27*y*z0^3 - 2*x^30 - x^28*y*z0 - x^26*y*z0^3 + 2*x^27*y*z0 - 2*x^27*z0^2 - 2*x^25*z0^4 - x^26*y*z0 + x^26*z0^2 + 2*x^24*y*z0^3 + x^24*z0^4 - x^27 + x^25*y*z0 - x^25*z0^2 + x^23*y*z0^3 + x^23*z0^4 + x^24*y*z0 - x^24*z0^2 + 2*x^22*y*z0^3 + 2*x^22*z0^4 + 2*x^23*y*z0 - x^23*z0^2 + x^21*z0^4 + 2*x^24 - x^22*y*z0 + x^20*y*z0^3 + x^20*z0^4 + x^23 - x^21*y*z0 + x^21*z0^2 + 2*x^19*y*z0^3 - x^19*z0^4 + 2*x^22 + x^20*z0^2 - x^18*y*z0^3 - x^19*y*z0 - 2*x^17*y*z0^3 + 2*x^17*z0^4 - x^20 - 2*x^18*y*z0 - 2*x^16*y*z0^3 - x^16*z0^4 + x^19 + x^17*z0^2 - x^15*z0^4 - 2*x^18 + 2*x^16*y*z0 - x^14*y*z0^3 - x^14*z0^4 - x^17 + x^15*y*z0 - 2*x^15*z0^2 - x^13*y*z0^3 + 2*x^13*z0^4 + x^14*y*z0 - 2*x^12*y*z0^3 - x^12*z0^4 + x^15 - x^13*y*z0 - x^13*z0^2 - x^11*y*z0^3 + x^11*z0^4 + x^14 - x^12*z0^2 - 2*x^10*z0^4 + 2*x^13 + x^11*y*z0 + 2*x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 + x^10*y*z0 - 2*x^10*z0^2 - 2*x^8*y*z0^3 - x^8*z0^4 - x^11 + x^9*y*z0 - x^7*y*z0^3 + 2*x^10 - x^8*z0^2 - 2*x^6*y*z0^3 + 2*x^6*z0^4 + 2*x^9 + x^7*y*z0 - x^7*z0^2 + 2*x^5*y*z0^3 - 2*x^5*z0^4 - x^8 - x^6*y*z0 - 2*x^4*y*z0^3 + x^4*z0^4 + x^7 - 2*x^5*y*z0 + x^5*z0^2 - x^3*z0^4 + 2*x^6 + 2*x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 - 2*x^2*z0^4 - x^5 - 2*x^3*y*z0 - x^3*z0^2 - x^2*y*z0 + 2*x^2*z0^2 + 2*x^3)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 - x^60*z0^4 + x^58*y^2*z0^4 + 2*x^61*z0^2 + x^57*y^2*z0^4 - 2*x^60*z0^2 - 2*x^58*y^2*z0^2 + x^58*z0^4 - x^61 + 2*x^57*y^2*z0^2 + x^57*z0^4 + 2*x^60 + x^58*y^2 - 2*x^58*z0^2 - 2*x^57*y^2 + 2*x^57*z0^2 - x^55*z0^4 + x^58 - x^54*z0^4 - 2*x^57 + 2*x^55*z0^2 - 2*x^54*z0^2 + x^52*z0^4 - x^55 + x^51*z0^4 + 2*x^54 - 2*x^52*z0^2 + 2*x^51*z0^2 - x^49*z0^4 + x^52 - x^48*z0^4 - 2*x^51 + 2*x^49*z0^2 - 2*x^48*z0^2 + x^46*z0^4 - x^49 + x^45*z0^4 + 2*x^48 - 2*x^46*z0^2 + 2*x^45*z0^2 - x^43*z0^4 + x^46 - x^42*z0^4 - 2*x^45 + 2*x^43*z0^2 + x^41*z0^4 - 2*x^42*z0^2 + 2*x^40*y*z0^3 + 2*x^40*z0^4 - x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^39*z0^4 + 2*x^42 + x^40*y*z0 - x^40*z0^2 + 2*x^38*z0^4 + x^41 - x^39*y*z0 + x^37*y*z0^3 - x^37*z0^4 + 2*x^40 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + x^36*z0^4 - x^39 - 2*x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 - 2*x^35*z0^4 + x^38 - x^36*y*z0 - 2*x^34*y*z0^3 - 2*x^37 + x^35*y^2 - 2*x^35*y*z0 + 2*x^35*z0^2 - x^33*y*z0^3 - 2*x^33*z0^4 + 2*x^36 - x^34*y*z0 + 2*x^34*z0^2 + x^32*y*z0^3 - 2*x^32*z0^4 - 2*x^33*y*z0 + 2*x^31*z0^4 + x^34 - x^32*y*z0 - x^32*z0^2 - 2*x^30*y*z0^3 - x^30*z0^4 + x^33 + x^31*y*z0 + 2*x^31*z0^2 + 2*x^29*y*z0^3 - x^29*z0^4 + 2*x^32 + x^30*y*z0 - x^28*y*z0^3 - 2*x^28*z0^4 - x^31 - x^29*y*z0 + x^27*y*z0^3 + x^27*z0^4 - 2*x^28*z0^2 + 2*x^26*y*z0^3 + x^26*z0^4 + 2*x^27*y*z0 - x^25*y*z0^3 + 2*x^28 - 2*x^26*y*z0 + 2*x^26*z0^2 + x^24*y*z0^3 + 2*x^24*z0^4 - 2*x^27 + x^25*y*z0 - x^25*z0^2 - 2*x^23*z0^4 + 2*x^26 + 2*x^24*y*z0 + x^24*z0^2 - x^22*y*z0^3 - x^25 + 2*x^23*y*z0 - x^23*z0^2 + 2*x^21*y*z0^3 - x^24 + 2*x^22*y*z0 + x^22*z0^2 + x^20*y*z0^3 - x^23 + 2*x^21*y*z0 + x^21*z0^2 - x^19*y*z0^3 - 2*x^22 - 2*x^20*y*z0 + 2*x^18*y*z0^3 - x^21 - 2*x^19*y*z0 - 2*x^19*z0^2 - x^17*y*z0^3 + x^17*z0^4 + 2*x^20 + x^18*y*z0 + 2*x^18*z0^2 + 2*x^16*y*z0^3 - 2*x^16*z0^4 + x^19 + x^17*y*z0 - x^17*z0^2 - 2*x^15*y*z0^3 + 2*x^15*z0^4 + 2*x^18 + 2*x^16*y*z0 - 2*x^16*z0^2 - x^17 + 2*x^15*y*z0 + x^15*z0^2 - 2*x^13*y*z0^3 + 2*x^16 - x^14*y*z0 - x^14*z0^2 - 2*x^12*y*z0^3 + 2*x^12*z0^4 + 2*x^15 + x^13*y*z0 - 2*x^13*z0^2 - 2*x^11*y*z0^3 - 2*x^11*z0^4 - x^12*y*z0 - 2*x^12*z0^2 - x^10*y*z0^3 - 2*x^10*z0^4 + x^13 + x^11*y*z0 + 2*x^11*z0^2 + x^9*y*z0^3 - x^9*z0^4 + x^10*y*z0 + 2*x^10*z0^2 + 2*x^8*z0^4 - 2*x^11 + x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 + x^7*z0^4 + 2*x^10 + x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 + 2*x^7*y*z0 + 2*x^5*y*z0^3 - 2*x^8 - 2*x^6*y*z0 + 2*x^6*z0^2 + 2*x^4*y*z0^3 + 2*x^4*z0^4 - x^7 - x^5*y*z0 - x^5*z0^2 + 2*x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^6 + x^4*y*z0 + x^4*z0^2 + 2*x^2*z0^4 - x^3*y*z0 + x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 - 2*x^3)/y) * dx, - ((-x^61*z0^3 - 2*x^60*z0^3 + x^58*y^2*z0^3 + 2*x^61*z0 + x^59*z0^3 + 2*x^57*y^2*z0^3 + 2*x^60*z0 - 2*x^58*y^2*z0 + 2*x^58*z0^3 - x^56*y^2*z0^3 - x^59*z0 - 2*x^57*y^2*z0 + 2*x^57*z0^3 - x^55*y^2*z0^3 - 2*x^58*z0 + x^56*y^2*z0 - x^56*z0^3 - 2*x^57*z0 - 2*x^55*z0^3 + x^56*z0 - 2*x^54*z0^3 + 2*x^55*z0 + x^53*z0^3 + 2*x^54*z0 + 2*x^52*z0^3 - x^53*z0 + 2*x^51*z0^3 - 2*x^52*z0 - x^50*z0^3 - 2*x^51*z0 - 2*x^49*z0^3 + x^50*z0 - 2*x^48*z0^3 + 2*x^49*z0 + x^47*z0^3 + 2*x^48*z0 + 2*x^46*z0^3 - x^47*z0 + 2*x^45*z0^3 - 2*x^46*z0 - x^44*z0^3 - 2*x^45*z0 - 2*x^43*z0^3 + x^44*z0 - 2*x^42*z0^3 + 2*x^43*z0 - x^39*y*z0^4 + 2*x^42*z0 + 2*x^40*y*z0^2 - 2*x^40*z0^3 + x^41*z0 + 2*x^39*y*z0^2 - x^39*z0^3 + x^37*y*z0^4 + x^40*y + x^40*z0 + x^38*y*z0^2 - 2*x^38*z0^3 - x^36*y*z0^4 - 2*x^39*y - x^39*z0 + x^37*y*z0^2 - 2*x^37*z0^3 - 2*x^38*y - 2*x^38*z0 - x^36*y*z0^2 - x^36*z0^3 + 2*x^34*y*z0^4 + 2*x^37*y + x^37*z0 + x^35*y^2*z0 - 2*x^36*y - 2*x^36*z0 - 2*x^34*y*z0^2 + 2*x^34*z0^3 - 2*x^32*y*z0^4 + x^35*y + x^33*z0^3 + x^31*y*z0^4 + x^34*y - 2*x^34*z0 - x^32*y*z0^2 + x^32*z0^3 - 2*x^33*y - x^33*z0 - x^31*y*z0^2 + 2*x^31*z0^3 - x^29*y*z0^4 + 2*x^32*z0 - 2*x^30*y*z0^2 + 2*x^30*z0^3 - 2*x^31*y - x^31*z0 - 2*x^29*y*z0^2 - x^29*z0^3 + 2*x^27*y*z0^4 - x^30*z0 + 2*x^28*y*z0^2 + 2*x^28*z0^3 + x^26*y*z0^4 + 2*x^29*y - 2*x^29*z0 + 2*x^27*y*z0^2 + x^25*y*z0^4 - x^28*y - 2*x^28*z0 - x^26*y*z0^2 - 2*x^24*y*z0^4 + x^27*y - 2*x^27*z0 + x^25*y*z0^2 - x^23*y*z0^4 + x^26*y + 2*x^26*z0 + 2*x^24*y*z0^2 + x^22*y*z0^4 - x^21*y*z0^4 - x^24*y - 2*x^24*z0 + 2*x^22*z0^3 + 2*x^20*y*z0^4 - x^23*y - x^21*y*z0^2 - 2*x^21*z0^3 - x^19*y*z0^4 + x^22*y + 2*x^22*z0 + 2*x^20*y*z0^2 + x^20*z0^3 - 2*x^18*y*z0^4 - x^21*y + 2*x^21*z0 - x^19*y*z0^2 + x^19*z0^3 + x^17*y*z0^4 - x^20*y - 2*x^20*z0 - x^18*y*z0^2 - 2*x^16*y*z0^4 + x^19*y - 2*x^19*z0 + 2*x^17*y*z0^2 + x^17*z0^3 + x^15*y*z0^4 + x^18*y + x^18*z0 - 2*x^16*y*z0^2 - x^16*z0^3 - x^14*y*z0^4 + x^17*y - 2*x^17*z0 - 2*x^15*y*z0^2 - 2*x^15*z0^3 - 2*x^16*y + x^16*z0 + 2*x^14*y*z0^2 + x^14*z0^3 + x^12*y*z0^4 - 2*x^15*z0 - x^13*y*z0^2 + 2*x^13*z0^3 + 2*x^11*y*z0^4 - 2*x^14*y + 2*x^14*z0 - x^12*z0^3 - x^10*y*z0^4 - 2*x^11*y*z0^2 - x^12*y - 2*x^12*z0 + x^10*y*z0^2 - x^10*z0^3 - 2*x^8*y*z0^4 + 2*x^11*y + x^9*y*z0^2 + x^9*z0^3 + 2*x^7*y*z0^4 - 2*x^10*z0 + x^8*y*z0^2 + x^8*z0^3 - 2*x^6*y*z0^4 - 2*x^9*y + x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y + x^8*z0 - 2*x^6*y*z0^2 - x^6*z0^3 + 2*x^7*y + 2*x^7*z0 - 2*x^5*z0^3 + 2*x^3*y*z0^4 - x^6*y + x^6*z0 - 2*x^4*y*z0^2 - x^2*y*z0^4 - x^5*y + x^5*z0 + x^3*y*z0^2 - 2*x^3*z0^3 + x^4*y - 2*x^4*z0 - x^2*y*z0^2 - x^2*z0^3 - 2*x^3*y + x^3*z0 + x^2*y + 2*x^2*z0)/y) * dx, - ((x^61*z0^2 - 2*x^59*z0^4 - x^58*y^2*z0^2 + 2*x^56*y^2*z0^4 + 2*x^60 - x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 - 2*x^57 + x^55*z0^2 - 2*x^53*z0^4 + 2*x^54 - x^52*z0^2 + 2*x^50*z0^4 - 2*x^51 + x^49*z0^2 - 2*x^47*z0^4 + 2*x^48 - x^46*z0^2 + 2*x^44*z0^4 - 2*x^45 + x^43*z0^2 - 2*x^41*z0^4 + x^40*z0^4 + x^41*z0^2 + x^39*y*z0^3 + 2*x^42 - 2*x^40*y*z0 - 2*x^40*z0^2 + x^38*y*z0^3 - x^39*z0^2 - 2*x^37*z0^4 - 2*x^40 + x^38*z0^2 - 2*x^36*y*z0^3 + 2*x^36*z0^4 + x^37*y*z0 + x^37*z0^2 + x^35*y^2*z0^2 - 2*x^35*y*z0^3 + x^35*z0^4 + x^38 + x^36*y*z0 + x^36*z0^2 - x^37 + x^35*z0^2 - x^33*y*z0^3 + 2*x^33*z0^4 - x^36 - x^34*y*z0 - 2*x^34*z0^2 - 2*x^32*y*z0^3 - 2*x^32*z0^4 - x^35 + x^33*y*z0 - x^33*z0^2 - 2*x^31*y*z0^3 - x^31*z0^4 - 2*x^32*y*z0 + 2*x^32*z0^2 - 2*x^30*y*z0^3 - x^31*y*z0 + x^31*z0^2 + 2*x^29*y*z0^3 - 2*x^29*z0^4 + 2*x^32 + x^30*z0^2 + 2*x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^31 + 2*x^27*y*z0^3 - x^27*z0^4 - x^28*z0^2 + 2*x^26*y*z0^3 + 2*x^26*z0^4 + 2*x^29 + x^27*y*z0 + 2*x^27*z0^2 + 2*x^25*z0^4 + x^28 + 2*x^26*y*z0 + x^26*z0^2 + x^24*z0^4 - 2*x^27 - x^25*y*z0 - 2*x^25*z0^2 + 2*x^23*y*z0^3 - x^23*z0^4 - 2*x^26 + 2*x^24*y*z0 + x^24*z0^2 + x^22*y*z0^3 - 2*x^25 + 2*x^23*z0^2 + x^21*y*z0^3 + x^24 + 2*x^22*y*z0 + 2*x^20*y*z0^3 + 2*x^23 + 2*x^21*y*z0 - x^21*z0^2 - 2*x^19*z0^4 - 2*x^22 - x^20*y*z0 + x^20*z0^2 + 2*x^18*y*z0^3 - 2*x^18*z0^4 - 2*x^21 - 2*x^19*y*z0 + 2*x^19*z0^2 - 2*x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^20 - x^18*y*z0 + 2*x^18*z0^2 + 2*x^16*y*z0^3 - 2*x^16*z0^4 - 2*x^19 + 2*x^17*y*z0 + 2*x^17*z0^2 - x^15*y*z0^3 + x^15*z0^4 - 2*x^18 - x^16*y*z0 + 2*x^16*z0^2 + x^14*z0^4 + x^17 + 2*x^15*y*z0 - 2*x^13*z0^4 + 2*x^16 + 2*x^14*y*z0 + 2*x^14*z0^2 + 2*x^12*y*z0^3 - x^13*y*z0 + x^13*z0^2 - 2*x^11*y*z0^3 - 2*x^11*z0^4 + 2*x^12*y*z0 - x^12*z0^2 + 2*x^10*y*z0^3 + x^10*z0^4 + 2*x^13 + 2*x^11*y*z0 - x^11*z0^2 - 2*x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^10*z0^2 - 2*x^8*y*z0^3 - x^8*z0^4 + x^11 + x^9*y*z0 - x^7*y*z0^3 + x^7*z0^4 - 2*x^10 + 2*x^8*z0^2 + 2*x^7*y*z0 + x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 + x^4*y*z0^3 - 2*x^4*z0^4 + 2*x^7 + 2*x^5*y*z0 - 2*x^5*z0^2 + 2*x^3*y*z0^3 + x^4*y*z0 - x^2*y*z0^3 + 2*x^2*z0^4 - x^5 + 2*x^3*y*z0 - x^3*z0^2 - x^2*y*z0 - 2*x^2)/y) * dx, - ((-2*x^61*z0^3 + 2*x^58*y^2*z0^3 - x^60*z0 - 2*x^58*z0^3 - 2*x^59*z0 + x^57*y^2*z0 + 2*x^57*z0^3 - x^55*y^2*z0^3 + 2*x^56*y^2*z0 - 2*x^54*y^2*z0^3 + x^57*z0 + 2*x^55*z0^3 + 2*x^56*z0 - 2*x^54*z0^3 - x^54*z0 - 2*x^52*z0^3 - 2*x^53*z0 + 2*x^51*z0^3 + x^51*z0 + 2*x^49*z0^3 + 2*x^50*z0 - 2*x^48*z0^3 - x^48*z0 - 2*x^46*z0^3 - 2*x^47*z0 + 2*x^45*z0^3 + x^45*z0 + 2*x^43*z0^3 + 2*x^44*z0 - 2*x^42*z0^3 - 2*x^41*z0^3 - 2*x^39*y*z0^4 - x^42*z0 - x^40*y*z0^2 - x^40*z0^3 + 2*x^38*y*z0^4 - 2*x^41*z0 + 2*x^39*z0^3 + x^37*y*z0^4 - 2*x^40*z0 + 2*x^38*y*z0^2 - x^36*y*z0^4 - 2*x^39*y + 2*x^39*z0 + 2*x^37*y*z0^2 + x^37*z0^3 + x^35*y^2*z0^3 + 2*x^35*y*z0^4 - 2*x^38*y + x^36*y*z0^2 - 2*x^36*z0^3 - 2*x^34*y*z0^4 + 2*x^35*y*z0^2 + 2*x^35*z0^3 - x^33*y*z0^4 - 2*x^36*y + 2*x^36*z0 + x^34*y*z0^2 - x^34*z0^3 - 2*x^32*y*z0^4 - x^35*z0 + 2*x^33*y*z0^2 - 2*x^33*z0^3 + x^31*y*z0^4 + x^34*y + 2*x^32*y*z0^2 + x^32*z0^3 + 2*x^30*y*z0^4 - 2*x^33*y + 2*x^33*z0 - 2*x^31*y*z0^2 - x^29*y*z0^4 + x^32*z0 + 2*x^30*z0^3 + x^31*y - 2*x^29*z0^3 + 2*x^27*y*z0^4 - 2*x^28*z0^3 + 2*x^26*y*z0^4 - x^29*z0 - x^27*y*z0^2 - x^27*z0^3 + 2*x^25*y*z0^4 + 2*x^28*z0 - x^26*y*z0^2 - x^26*z0^3 + x^24*y*z0^4 + x^27*y + 2*x^27*z0 - 2*x^25*y*z0^2 + x^25*z0^3 + 2*x^23*y*z0^4 + 2*x^26*y - x^26*z0 - x^24*y*z0^2 - x^24*z0^3 + x^25*y - 2*x^25*z0 - 2*x^23*y*z0^2 - 2*x^23*z0^3 + 2*x^21*y*z0^4 + 2*x^24*z0 - x^22*y*z0^2 - x^22*z0^3 + x^20*y*z0^4 - 2*x^23*y + x^23*z0 - 2*x^21*y*z0^2 - 2*x^21*z0^3 - x^19*y*z0^4 + 2*x^22*y - 2*x^22*z0 - 2*x^20*y*z0^2 + x^20*z0^3 - 2*x^18*y*z0^4 - 2*x^21*y - x^21*z0 + 2*x^19*y*z0^2 + x^19*z0^3 + 2*x^17*y*z0^4 - 2*x^20*y + x^20*z0 + x^19*y + x^19*z0 + x^17*y*z0^2 + 2*x^17*z0^3 + 2*x^15*y*z0^4 - x^18*y - x^16*z0^3 - x^14*y*z0^4 - 2*x^17*y + x^15*y*z0^2 + 2*x^15*z0^3 + 2*x^13*y*z0^4 + x^16*y + x^14*y*z0^2 - x^14*z0^3 + 2*x^15*y - 2*x^15*z0 - 2*x^13*y*z0^2 + x^11*y*z0^4 + 2*x^14*z0 + 2*x^12*y*z0^2 - x^12*z0^3 + 2*x^10*y*z0^4 + 2*x^13*y + x^11*y*z0^2 + 2*x^11*z0^3 - 2*x^9*y*z0^4 - x^12*y + 2*x^12*z0 - x^10*y*z0^2 - 2*x^8*y*z0^4 + x^11*y - 2*x^9*y*z0^2 + x^7*y*z0^4 + x^8*y*z0^2 + 2*x^8*z0^3 - x^6*y*z0^4 - 2*x^9*z0 - x^8*y + x^8*z0 + 2*x^6*y*z0^2 + 2*x^4*y*z0^4 + x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 + x^6*y + x^6*z0 + 2*x^4*y*z0^2 - 2*x^2*y*z0^4 - 2*x^5*y - x^3*y*z0^2 + 2*x^3*z0^3 + 2*x^4*y + 2*x^4*z0 + x^2*y*z0^2 + 2*x^3*y - x^3*z0 + x^2*y + 2*x^2*z0)/y) * dx, - ((-x^61*z0^4 - 2*x^60*z0^4 + x^58*y^2*z0^4 + x^61*z0^2 - x^59*z0^4 + 2*x^57*y^2*z0^4 + 2*x^60*z0^2 - x^58*y^2*z0^2 + x^58*z0^4 + x^56*y^2*z0^4 + 2*x^61 - 2*x^57*y^2*z0^2 + 2*x^57*z0^4 - 2*x^58*y^2 - x^58*z0^2 + x^56*z0^4 - 2*x^57*z0^2 - x^55*z0^4 - 2*x^58 - 2*x^54*z0^4 + x^55*z0^2 - x^53*z0^4 + 2*x^54*z0^2 + x^52*z0^4 + 2*x^55 + 2*x^51*z0^4 - x^52*z0^2 + x^50*z0^4 - 2*x^51*z0^2 - x^49*z0^4 - 2*x^52 - 2*x^48*z0^4 + x^49*z0^2 - x^47*z0^4 + 2*x^48*z0^2 + x^46*z0^4 + 2*x^49 + 2*x^45*z0^4 - x^46*z0^2 + x^44*z0^4 - 2*x^45*z0^2 - x^43*z0^4 - 2*x^46 - 2*x^42*z0^4 + x^43*z0^2 - x^41*z0^4 + 2*x^42*z0^2 + 2*x^40*y*z0^3 + x^40*z0^4 + 2*x^43 + x^41*z0^2 + x^39*y*z0^3 - x^39*z0^4 - 2*x^40*y*z0 + x^40*z0^2 - x^38*y*z0^3 - x^38*z0^4 - x^39*y*z0 + 2*x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 + x^35*y^2*z0^4 - 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - 2*x^36*z0^4 + x^39 - 2*x^37*y*z0 - 2*x^35*z0^4 - 2*x^38 - x^36*y*z0 - 2*x^36*z0^2 + 2*x^34*y*z0^3 + x^37 + 2*x^35*y*z0 - x^33*z0^4 - 2*x^36 - x^34*z0^2 - 2*x^32*y*z0^3 - 2*x^32*z0^4 + x^33*z0^2 - 2*x^31*y*z0^3 - 2*x^31*z0^4 - 2*x^34 - 2*x^32*y*z0 - x^32*z0^2 - 2*x^30*y*z0^3 - x^33 + 2*x^31*y*z0 + x^31*z0^2 - x^29*y*z0^3 - x^29*z0^4 - 2*x^32 - x^30*y*z0 - x^30*z0^2 - x^28*y*z0^3 + x^28*z0^4 - x^31 + x^29*z0^2 - 2*x^30 + x^28*y*z0 + 2*x^28*z0^2 + x^26*y*z0^3 - 2*x^26*z0^4 - 2*x^29 + 2*x^27*z0^2 + x^25*y*z0^3 + 2*x^25*z0^4 - 2*x^26*y*z0 - x^26*z0^2 - x^24*y*z0^3 - x^24*z0^4 - 2*x^27 + x^25*y*z0 - 2*x^23*y*z0^3 - x^23*z0^4 + x^26 - x^24*z0^2 - x^22*y*z0^3 + 2*x^22*z0^4 - x^25 + x^23*y*z0 - x^23*z0^2 - 2*x^21*y*z0^3 - x^21*z0^4 + x^24 - 2*x^22*y*z0 + 2*x^20*y*z0^3 + 2*x^20*z0^4 - x^23 - 2*x^21*y*z0 - x^22 - 2*x^20*y*z0 + x^20*z0^2 + x^18*z0^4 - 2*x^21 + 2*x^19*y*z0 + 2*x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 - x^20 - 2*x^18*y*z0 - x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 - 2*x^17*y*z0 - 2*x^17*z0^2 + 2*x^15*y*z0^3 - 2*x^15*z0^4 - x^18 - x^16*z0^2 + x^14*z0^4 + x^15*y*z0 + 2*x^15*z0^2 + x^13*y*z0^3 + x^13*z0^4 + 2*x^16 - 2*x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 + x^11*z0^4 + 2*x^14 - 2*x^12*y*z0 - 2*x^12*z0^2 - 2*x^10*z0^4 + x^13 - x^11*y*z0 + 2*x^11*z0^2 + x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 + 2*x^9*z0^2 + x^7*y*z0^3 + x^10 + 2*x^8*z0^2 + x^6*y*z0^3 + 2*x^6*z0^4 - x^9 - x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 + 2*x^8 + 2*x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 + 2*x^7 + x^5*z0^2 + x^3*y*z0^3 - x^3*z0^4 - 2*x^6 + 2*x^4*y*z0 - 2*x^2*y*z0^3 + 2*x^2*z0^4 - x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 + x^2*z0^2 + x^3 + 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^60*z0^4 + 2*x^61*z0^2 + 2*x^59*z0^4 + x^57*y^2*z0^4 - 2*x^58*y^2*z0^2 - 2*x^56*y^2*z0^4 + 2*x^61 + x^57*z0^4 + 2*x^60 - 2*x^58*y^2 - 2*x^58*z0^2 - 2*x^56*z0^4 - 2*x^57*y^2 - 2*x^58 - x^54*z0^4 - 2*x^57 + 2*x^55*z0^2 + 2*x^53*z0^4 + 2*x^55 + x^51*z0^4 + 2*x^54 - 2*x^52*z0^2 - 2*x^50*z0^4 - 2*x^52 - x^48*z0^4 - 2*x^51 + 2*x^49*z0^2 + 2*x^47*z0^4 + 2*x^49 + x^45*z0^4 + 2*x^48 - 2*x^46*z0^2 - 2*x^44*z0^4 - 2*x^46 - x^42*z0^4 - 2*x^45 + 2*x^43*z0^2 - 2*x^41*z0^4 + 2*x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^39*z0^4 + 2*x^42 + x^40*y*z0 + x^40*z0^2 - x^38*y*z0^3 + 2*x^38*z0^4 + x^41 - x^39*y*z0 - 2*x^39*z0^2 - x^37*y*z0^3 - x^40 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 - x^37*y*z0 - x^37*z0^2 + 2*x^35*y*z0^3 + 2*x^35*z0^4 + x^38 + x^36*y^2 - 2*x^36*y*z0 + 2*x^36*z0^2 - x^37 - 2*x^35*y*z0 + x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 - x^36 + 2*x^34*y*z0 + 2*x^34*z0^2 + 2*x^32*y*z0^3 + x^35 + 2*x^33*z0^2 - 2*x^31*z0^4 + x^34 + 2*x^32*z0^2 + 2*x^30*y*z0^3 + 2*x^30*z0^4 - 2*x^33 + 2*x^31*y*z0 + 2*x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 + 2*x^30*y*z0 + x^30*z0^2 - 2*x^28*y*z0^3 - 2*x^28*z0^4 - x^31 - 2*x^29*y*z0 - x^29*z0^2 + x^27*z0^4 + x^30 + 2*x^28*z0^2 - x^26*y*z0^3 + 2*x^26*z0^4 + 2*x^27*y*z0 + 2*x^27*z0^2 - x^25*z0^4 + x^28 + 2*x^26*y*z0 + x^26*z0^2 - 2*x^24*z0^4 - 2*x^25*y*z0 + x^23*y*z0^3 + 2*x^23*z0^4 + x^26 - x^24*y*z0 - x^24*z0^2 + 2*x^22*z0^4 + 2*x^23*y*z0 + x^23*z0^2 - x^21*y*z0^3 + x^21*z0^4 + 2*x^24 + 2*x^22*y*z0 - x^22*z0^2 - x^20*y*z0^3 + 2*x^20*z0^4 - x^23 - 2*x^21*y*z0 + 2*x^21*z0^2 + 2*x^19*y*z0^3 + 2*x^19*z0^4 + 2*x^22 - 2*x^20*y*z0 + 2*x^20*z0^2 - x^18*y*z0^3 - 2*x^18*z0^4 + 2*x^21 - x^19*y*z0 + 2*x^19*z0^2 - x^17*z0^4 + x^20 + 2*x^18*y*z0 + 2*x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^16*z0^4 + 2*x^19 + 2*x^17*y*z0 + 2*x^15*z0^4 + 2*x^18 - x^16*z0^2 - 2*x^17 + 2*x^15*y*z0 - x^13*z0^4 + 2*x^16 - 2*x^14*y*z0 + 2*x^14*z0^2 - 2*x^12*y*z0^3 + x^12*z0^4 + 2*x^15 + 2*x^13*y*z0 - x^13*z0^2 - 2*x^11*z0^4 + 2*x^14 - 2*x^12*y*z0 + 2*x^12*z0^2 - x^10*y*z0^3 + x^10*z0^4 + x^13 + x^11*y*z0 + 2*x^11*z0^2 - x^9*z0^4 - x^12 + 2*x^8*y*z0^3 - 2*x^9*y*z0 + 2*x^9*z0^2 + 2*x^7*y*z0^3 + x^10 + x^8*y*z0 - 2*x^8*z0^2 - 2*x^6*z0^4 - x^9 + x^7*y*z0 + x^7*z0^2 - x^5*z0^4 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + 2*x^4*y*z0^3 + 2*x^4*z0^4 - x^7 + 2*x^5*y*z0 + 2*x^5*z0^2 + x^3*z0^4 + x^6 + 2*x^2*y*z0^3 - 2*x^5 + 2*x^3*z0^2 - x^2*y*z0 + x^2*z0^2 + 2*x^3)/y) * dx, - ((x^61*z0^3 - 2*x^60*z0^3 - x^58*y^2*z0^3 + x^61*z0 + 2*x^59*z0^3 + 2*x^57*y^2*z0^3 + 2*x^60*z0 - x^58*y^2*z0 + x^58*z0^3 - 2*x^56*y^2*z0^3 - 2*x^59*z0 - 2*x^57*y^2*z0 - 2*x^57*z0^3 - 2*x^55*y^2*z0^3 - x^58*z0 + 2*x^56*y^2*z0 - 2*x^56*z0^3 - x^54*y^2*z0^3 - 2*x^57*z0 - x^55*z0^3 + 2*x^56*z0 + 2*x^54*z0^3 + x^55*z0 + 2*x^53*z0^3 + 2*x^54*z0 + x^52*z0^3 - 2*x^53*z0 - 2*x^51*z0^3 - x^52*z0 - 2*x^50*z0^3 - 2*x^51*z0 - x^49*z0^3 + 2*x^50*z0 + 2*x^48*z0^3 + x^49*z0 + 2*x^47*z0^3 + 2*x^48*z0 + x^46*z0^3 - 2*x^47*z0 - 2*x^45*z0^3 - x^46*z0 - 2*x^44*z0^3 - 2*x^45*z0 - x^43*z0^3 + 2*x^44*z0 + 2*x^42*z0^3 + x^43*z0 - 2*x^41*z0^3 + x^39*y*z0^4 + 2*x^42*z0 - 2*x^40*y*z0^2 + 2*x^40*z0^3 + x^38*y*z0^4 - x^41*z0 + x^39*y*z0^2 - x^39*z0^3 - 2*x^40*y - x^40*z0 + 2*x^38*y*z0^2 + 2*x^38*z0^3 + 2*x^36*y*z0^4 + 2*x^39*z0 + 2*x^37*y*z0^2 + x^37*z0^3 - 2*x^35*y*z0^4 + 2*x^38*z0 + x^36*y^2*z0 - x^36*y*z0^2 + 2*x^36*z0^3 + x^37*y + 2*x^37*z0 + x^35*y*z0^2 + x^35*z0^3 - x^33*y*z0^4 + x^36*y + 2*x^36*z0 - x^34*y*z0^2 + x^34*z0^3 - x^32*y*z0^4 + x^35*z0 + 2*x^33*y*z0^2 + x^33*z0^3 + 2*x^31*y*z0^4 - x^34*y + 2*x^34*z0 - 2*x^32*z0^3 + 2*x^30*y*z0^4 + 2*x^33*z0 + x^31*y*z0^2 - x^31*z0^3 - 2*x^29*y*z0^4 + 2*x^32*y - x^30*y*z0^2 - 2*x^30*z0^3 + 2*x^28*y*z0^4 + x^31*y - 2*x^31*z0 - x^30*y - 2*x^30*z0 + x^28*z0^3 - 2*x^26*y*z0^4 + x^29*z0 + x^27*y*z0^2 + x^27*z0^3 - x^25*y*z0^4 + x^28*y - x^28*z0 - x^26*y*z0^2 + 2*x^26*z0^3 - 2*x^24*y*z0^4 - 2*x^27*y + 2*x^27*z0 + x^25*y*z0^2 + 2*x^25*z0^3 - x^23*y*z0^4 - 2*x^26*y + 2*x^26*z0 - x^24*z0^3 - x^25*y - x^25*z0 - 2*x^23*y*z0^2 - x^23*z0^3 - x^21*y*z0^4 - 2*x^24*y + x^24*z0 + 2*x^22*z0^3 - x^20*y*z0^4 - x^23*y - x^23*z0 + x^21*y*z0^2 - x^21*z0^3 + 2*x^19*y*z0^4 - 2*x^22*y + x^22*z0 + 2*x^20*y*z0^2 + x^20*z0^3 + x^21*y - 2*x^21*z0 + x^19*y*z0^2 - x^19*z0^3 - 2*x^17*y*z0^4 + x^20*y + x^20*z0 + 2*x^16*y*z0^4 - 2*x^19*z0 + 2*x^17*y*z0^2 - x^17*z0^3 - x^18*y - x^18*z0 - 2*x^16*y*z0^2 + x^16*z0^3 - x^17*y + 2*x^17*z0 - x^15*y*z0^2 - 2*x^15*z0^3 - 2*x^13*y*z0^4 + x^16*z0 + x^14*y*z0^2 - x^14*z0^3 + 2*x^12*y*z0^4 + x^15*z0 - 2*x^13*y*z0^2 + 2*x^13*z0^3 + x^14*y - x^14*z0 + 2*x^12*z0^3 + 2*x^10*y*z0^4 - 2*x^13*y - x^13*z0 - 2*x^11*y*z0^2 - x^11*z0^3 + x^9*y*z0^4 + 2*x^12*y + x^12*z0 + x^10*y*z0^2 + x^8*y*z0^4 - x^11*z0 - x^9*y*z0^2 - 2*x^9*z0^3 + x^7*y*z0^4 + x^10*y - 2*x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 + 2*x^6*y*z0^4 - 2*x^9*y + 2*x^9*z0 - 2*x^7*y*z0^2 + 2*x^5*y*z0^4 + x^8*y + 2*x^8*z0 + 2*x^6*z0^3 + x^4*y*z0^4 + x^7*y + x^7*z0 + x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 - x^6*y - 2*x^4*y*z0^2 + 2*x^4*z0^3 + x^2*y*z0^4 - 2*x^5*y - x^3*z0^3 + 2*x^4*y + 2*x^4*z0 - x^2*y*z0^2 + 2*x^2*z0^3 + 2*x^3*y - 2*x^3*z0 + 2*x^2*y + x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + x^60*z0^4 + 2*x^58*y^2*z0^4 - x^61*z0^2 + x^59*z0^4 - x^57*y^2*z0^4 + 2*x^60*z0^2 + x^58*y^2*z0^2 + 2*x^58*z0^4 - x^56*y^2*z0^4 - x^61 - 2*x^57*y^2*z0^2 - x^57*z0^4 - 2*x^60 + x^58*y^2 + x^58*z0^2 - x^56*z0^4 + 2*x^57*y^2 - 2*x^57*z0^2 - 2*x^55*z0^4 + x^58 + x^54*z0^4 + 2*x^57 - x^55*z0^2 + x^53*z0^4 + 2*x^54*z0^2 + 2*x^52*z0^4 - x^55 - x^51*z0^4 - 2*x^54 + x^52*z0^2 - x^50*z0^4 - 2*x^51*z0^2 - 2*x^49*z0^4 + x^52 + x^48*z0^4 + 2*x^51 - x^49*z0^2 + x^47*z0^4 + 2*x^48*z0^2 + 2*x^46*z0^4 - x^49 - x^45*z0^4 - 2*x^48 + x^46*z0^2 - x^44*z0^4 - 2*x^45*z0^2 - 2*x^43*z0^4 + x^46 + x^42*z0^4 + 2*x^45 - x^43*z0^2 + x^41*z0^4 + 2*x^42*z0^2 - x^40*y*z0^3 - 2*x^40*z0^4 - x^43 - x^41*z0^2 - x^39*y*z0^3 - 2*x^42 + 2*x^40*y*z0 + x^40*z0^2 - 2*x^38*y*z0^3 - 2*x^39*y*z0 - 2*x^39*z0^2 - 2*x^37*y*z0^3 - 2*x^37*z0^4 - 2*x^40 + x^38*y*z0 - 2*x^38*z0^2 + x^36*y^2*z0^2 + 2*x^36*y*z0^3 - x^39 - 2*x^37*z0^2 + 2*x^35*y*z0^3 + x^35*z0^4 + 2*x^38 - x^36*y*z0 + 2*x^36*z0^2 + 2*x^34*y*z0^3 - 2*x^37 - 2*x^35*y*z0 - x^35*z0^2 + 2*x^33*y*z0^3 + 2*x^33*z0^4 - x^36 - x^34*z0^2 + x^32*z0^4 + 2*x^33*y*z0 + x^33*z0^2 + x^31*y*z0^3 + 2*x^31*z0^4 - 2*x^34 + 2*x^32*y*z0 + x^32*z0^2 - 2*x^30*z0^4 - 2*x^33 - 2*x^31*y*z0 + 2*x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - x^32 + x^30*y*z0 - 2*x^30*z0^2 - x^28*y*z0^3 - x^28*z0^4 + 2*x^31 + 2*x^29*y*z0 + 2*x^29*z0^2 + 2*x^27*y*z0^3 + 2*x^27*z0^4 + x^30 - x^28*y*z0 - x^28*z0^2 - 2*x^26*y*z0^3 + x^26*z0^4 - x^29 + 2*x^27*y*z0 + x^27*z0^2 - x^25*y*z0^3 + x^25*z0^4 + 2*x^26*y*z0 - x^26*z0^2 - x^24*y*z0^3 + 2*x^24*z0^4 + x^27 + x^25*z0^2 + 2*x^23*z0^4 + x^26 - x^24*y*z0 - 2*x^24*z0^2 - x^22*y*z0^3 - 2*x^22*z0^4 - x^21*z0^4 + 2*x^24 - x^22*y*z0 + x^22*z0^2 - 2*x^20*y*z0^3 - x^20*z0^4 - x^21*y*z0 - x^19*y*z0^3 + 2*x^22 - x^20*y*z0 - x^20*z0^2 + 2*x^18*y*z0^3 + 2*x^18*z0^4 + x^21 + 2*x^19*z0^2 + 2*x^17*y*z0^3 - 2*x^20 - x^18*y*z0 + 2*x^18*z0^2 - 2*x^16*y*z0^3 + x^19 - 2*x^17*y*z0 + x^17*z0^2 + 2*x^15*y*z0^3 - x^15*z0^4 - 2*x^18 - x^16*y*z0 + x^16*z0^2 - 2*x^14*z0^4 - 2*x^15*y*z0 + 2*x^15*z0^2 + x^13*y*z0^3 + x^13*z0^4 + 2*x^14*y*z0 - 2*x^14*z0^2 + 2*x^12*y*z0^3 - 2*x^12*z0^4 - x^15 + x^13*y*z0 - x^13*z0^2 + 2*x^11*y*z0^3 - 2*x^14 + x^12*y*z0 - x^12*z0^2 - 2*x^10*y*z0^3 - 2*x^10*z0^4 - 2*x^13 + 2*x^11*z0^2 - 2*x^9*y*z0^3 - x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 + x^8*y*z0^3 + x^8*z0^4 + 2*x^11 - 2*x^9*z0^2 + x^7*y*z0^3 + 2*x^7*z0^4 + x^10 + 2*x^8*y*z0 - x^8*z0^2 + 2*x^6*y*z0^3 - x^9 + 2*x^7*y*z0 + x^7*z0^2 - 2*x^5*y*z0^3 + 2*x^5*z0^4 - x^8 + x^6*y*z0 + x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 - 2*x^5*y*z0 + x^5*z0^2 + x^3*y*z0^3 + x^3*z0^4 + x^6 + x^4*z0^2 + x^2*y*z0^3 - x^2*z0^4 + x^5 - x^3*y*z0 + 2*x^3*z0^2 - x^2*y*z0 - x^2*z0^2 - x^3 + 2*x^2)/y) * dx, - ((2*x^61*z0^3 + 2*x^60*z0^3 - 2*x^58*y^2*z0^3 + 2*x^59*z0^3 - 2*x^57*y^2*z0^3 + x^60*z0 - 2*x^56*y^2*z0^3 + 2*x^59*z0 - x^57*y^2*z0 - 2*x^57*z0^3 - 2*x^55*y^2*z0^3 - 2*x^56*y^2*z0 - 2*x^56*z0^3 - x^57*z0 - 2*x^56*z0 + 2*x^54*z0^3 + 2*x^53*z0^3 + x^54*z0 + 2*x^53*z0 - 2*x^51*z0^3 - 2*x^50*z0^3 - x^51*z0 - 2*x^50*z0 + 2*x^48*z0^3 + 2*x^47*z0^3 + x^48*z0 + 2*x^47*z0 - 2*x^45*z0^3 - 2*x^44*z0^3 - x^45*z0 - 2*x^44*z0 + 2*x^42*z0^3 - x^41*z0^3 + 2*x^39*y*z0^4 + x^42*z0 + x^40*y*z0^2 - 2*x^40*z0^3 + 2*x^38*y*z0^4 + 2*x^41*z0 + x^39*z0^3 + 2*x^37*y*z0^4 - x^40*z0 - 2*x^38*y*z0^2 - x^38*z0^3 + x^36*y^2*z0^3 - 2*x^39*y - 2*x^39*z0 + x^37*y*z0^2 + 2*x^37*z0^3 + 2*x^35*y*z0^4 - x^38*y - x^36*y*z0^2 + x^37*z0 + x^35*y*z0^2 + x^33*y*z0^4 - 2*x^36*z0 - x^34*y*z0^2 - x^34*z0^3 - x^32*y*z0^4 - 2*x^35*y + x^35*z0 - 2*x^33*z0^3 + x^31*y*z0^4 - x^34*y - 2*x^34*z0 - x^32*y*z0^2 - 2*x^32*z0^3 - x^30*y*z0^4 - 2*x^33*y - x^33*z0 + 2*x^31*y*z0^2 + 2*x^31*z0^3 - x^29*y*z0^4 + x^32*y - x^32*z0 - 2*x^30*y*z0^2 + x^30*z0^3 + x^28*y*z0^4 - 2*x^31*y + x^31*z0 + 2*x^29*y*z0^2 - x^27*y*z0^4 - 2*x^30*y - 2*x^26*y*z0^4 - x^29*y - x^29*z0 + x^27*y*z0^2 + 2*x^27*z0^3 + 2*x^25*y*z0^4 - x^28*y + 2*x^28*z0 + 2*x^26*y*z0^2 - x^26*z0^3 - 2*x^24*y*z0^4 - x^27*y - x^27*z0 + 2*x^25*y*z0^2 - x^25*z0^3 - 2*x^23*y*z0^4 + x^26*y + x^26*z0 + x^24*y*z0^2 + 2*x^22*y*z0^4 - 2*x^25*y + x^23*y*z0^2 - x^23*z0^3 + x^21*y*z0^4 - 2*x^24*y - x^24*z0 - x^22*y*z0^2 - 2*x^22*z0^3 + 2*x^20*y*z0^4 + 2*x^19*y*z0^4 + x^22*z0 - 2*x^20*y*z0^2 + 2*x^20*z0^3 - 2*x^18*y*z0^4 + x^19*y*z0^2 + 2*x^19*z0^3 + 2*x^17*y*z0^4 + x^20*y - 2*x^20*z0 - x^18*y*z0^2 - 2*x^16*y*z0^4 + x^19*y - 2*x^19*z0 + 2*x^17*y*z0^2 - x^17*z0^3 - 2*x^15*y*z0^4 + 2*x^18*y + 2*x^18*z0 - 2*x^16*y*z0^2 - x^16*z0^3 + x^14*y*z0^4 - 2*x^17*z0 - x^15*y*z0^2 + 2*x^15*z0^3 + x^13*y*z0^4 - x^16*y + 2*x^16*z0 - x^14*y*z0^2 - 2*x^14*z0^3 - x^12*y*z0^4 + x^15*y - 2*x^15*z0 + x^13*y*z0^2 + x^13*z0^3 - 2*x^11*y*z0^4 + x^14*y - x^14*z0 - 2*x^12*y*z0^2 + x^10*y*z0^4 + x^13*y - x^13*z0 + 2*x^11*y*z0^2 + 2*x^11*z0^3 - x^9*y*z0^4 + 2*x^12*z0 - 2*x^10*y*z0^2 - x^10*z0^3 - x^8*y*z0^4 - x^11*y - 2*x^11*z0 + x^9*z0^3 + x^7*y*z0^4 + 2*x^10*y - x^10*z0 - x^8*y*z0^2 - 2*x^8*z0^3 - x^6*y*z0^4 - x^9*y + 2*x^9*z0 - x^7*y*z0^2 + 2*x^5*y*z0^4 + x^8*z0 + 2*x^6*y*z0^2 + 2*x^6*z0^3 + x^4*y*z0^4 - x^7*z0 + 2*x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 - x^6*y + x^6*z0 - x^4*y*z0^2 - x^2*y*z0^4 - 2*x^5*y + x^5*z0 - 2*x^3*y*z0^2 + 2*x^3*z0^3 + x^4*y - x^2*y*z0^2 - x^2*z0^3 + x^3*z0 + x^2*y + 2*x^2*z0)/y) * dx, - ((-x^60*z0^4 - 2*x^61*z0^2 - 2*x^59*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 + 2*x^56*y^2*z0^4 - 2*x^61 - x^57*y^2*z0^2 + x^57*z0^4 + 2*x^60 + 2*x^58*y^2 + 2*x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 - x^57*z0^2 + 2*x^58 - x^54*z0^4 - 2*x^57 - 2*x^55*z0^2 - 2*x^53*z0^4 + x^54*z0^2 - 2*x^55 + x^51*z0^4 + 2*x^54 + 2*x^52*z0^2 + 2*x^50*z0^4 - x^51*z0^2 + 2*x^52 - x^48*z0^4 - 2*x^51 - 2*x^49*z0^2 - 2*x^47*z0^4 + x^48*z0^2 - 2*x^49 + x^45*z0^4 + 2*x^48 + 2*x^46*z0^2 + 2*x^44*z0^4 - x^45*z0^2 + 2*x^46 - x^42*z0^4 - 2*x^45 - 2*x^43*z0^2 + 2*x^41*z0^4 + x^42*z0^2 - x^40*z0^4 - 2*x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + 2*x^39*z0^4 + 2*x^42 - x^40*y*z0 + x^40*z0^2 - 2*x^38*z0^4 + x^36*y^2*z0^4 - x^41 + x^39*z0^2 - 2*x^37*y*z0^3 - 2*x^40 - x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 - 2*x^39 - x^35*y*z0^3 + x^35*z0^4 - x^38 - 2*x^36*y*z0 - x^36*z0^2 + x^34*y*z0^3 - x^34*z0^4 + x^37 + x^35*y*z0 - x^35*z0^2 + 2*x^33*y*z0^3 + x^33*z0^4 + x^34*y*z0 - x^34*z0^2 - 2*x^32*y*z0^3 + x^32*z0^4 - x^33*y*z0 + 2*x^33*z0^2 + x^31*y*z0^3 + 2*x^34 - x^32*z0^2 - 2*x^30*z0^4 - 2*x^33 - 2*x^31*y*z0 - 2*x^31*z0^2 + x^29*z0^4 - x^30*y*z0 + x^30*z0^2 - 2*x^28*y*z0^3 + x^28*z0^4 + x^31 - 2*x^29*y*z0 + 2*x^29*z0^2 - x^27*y*z0^3 - 2*x^27*z0^4 + x^30 - 2*x^28*y*z0 - x^26*y*z0^3 + 2*x^29 + 2*x^27*y*z0 + x^27*z0^2 + x^25*y*z0^3 - 2*x^25*z0^4 - 2*x^28 + 2*x^26*y*z0 - 2*x^26*z0^2 + 2*x^24*y*z0^3 + 2*x^24*z0^4 + x^27 - 2*x^25*y*z0 - x^25*z0^2 + x^23*y*z0^3 - 2*x^23*z0^4 + x^26 + 2*x^24*z0^2 + 2*x^22*y*z0^3 + x^25 - x^23*z0^2 - x^21*y*z0^3 - x^21*z0^4 + 2*x^22*z0^2 - 2*x^20*y*z0^3 + x^23 + 2*x^19*y*z0^3 - x^19*z0^4 + 2*x^22 + 2*x^20*y*z0 - 2*x^20*z0^2 - x^18*y*z0^3 + x^18*z0^4 + x^21 - x^19*y*z0 - 2*x^19*z0^2 - x^17*y*z0^3 - x^20 - 2*x^18*z0^2 - x^16*y*z0^3 + x^16*z0^4 - x^19 + x^17*y*z0 - 2*x^17*z0^2 + 2*x^15*y*z0^3 - x^15*z0^4 - 2*x^16*y*z0 + 2*x^14*y*z0^3 + x^14*z0^4 - x^15*y*z0 - x^15*z0^2 - 2*x^13*y*z0^3 - 2*x^16 + 2*x^14*y*z0 + 2*x^12*y*z0^3 - 2*x^15 + 2*x^13*y*z0 - 2*x^13*z0^2 + 2*x^11*y*z0^3 + x^14 - 2*x^12*y*z0 + 2*x^12*z0^2 - 2*x^10*y*z0^3 + x^10*z0^4 - x^13 - x^11*z0^2 - 2*x^9*y*z0^3 + 2*x^10*y*z0 + x^10*z0^2 + x^8*y*z0^3 + x^8*z0^4 + 2*x^9*y*z0 + x^9*z0^2 + x^10 - x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 - x^9 - x^7*z0^2 + 2*x^5*y*z0^3 + 2*x^5*z0^4 - x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 - x^5*y*z0 - 2*x^5*z0^2 + 2*x^3*y*z0^3 + x^6 + x^4*y*z0 + 2*x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 - x^3*y*z0 - 2*x^3*z0^2 + x^2*y*z0 + 2*x^3 - 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 + x^60*z0^4 + x^58*y^2*z0^4 + 2*x^61*z0^2 + x^59*z0^4 - x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 + x^58*z0^4 - x^56*y^2*z0^4 + x^61 + x^57*y^2*z0^2 - x^57*z0^4 - x^60 - x^58*y^2 - 2*x^58*z0^2 - x^56*z0^4 + x^57*y^2 + x^57*z0^2 - x^55*z0^4 - x^58 + x^54*z0^4 + x^57 + 2*x^55*z0^2 + x^53*z0^4 - x^54*z0^2 + x^52*z0^4 + x^55 - x^51*z0^4 - x^54 - 2*x^52*z0^2 - x^50*z0^4 + x^51*z0^2 - x^49*z0^4 - x^52 + x^48*z0^4 + x^51 + 2*x^49*z0^2 + x^47*z0^4 - x^48*z0^2 + x^46*z0^4 + x^49 - x^45*z0^4 - x^48 - 2*x^46*z0^2 - x^44*z0^4 + x^45*z0^2 - x^43*z0^4 - x^46 + x^42*z0^4 + x^45 + 2*x^43*z0^2 - 2*x^41*z0^4 - x^42*z0^2 + 2*x^40*y*z0^3 - x^40*z0^4 + x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 - x^42 + x^40*y*z0 + x^40*z0^2 + x^38*y*z0^3 - x^38*z0^4 + 2*x^41 + 2*x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 + x^40 + 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 - x^39 + x^37*y^2 - x^37*y*z0 - x^37*z0^2 + x^35*z0^4 + x^38 + x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 - x^34*z0^4 - 2*x^35*z0^2 + x^34*y*z0 - x^34*z0^2 + 2*x^32*y*z0^3 - 2*x^32*z0^4 - 2*x^35 - 2*x^33*z0^2 - x^34 - 2*x^32*y*z0 + x^32*z0^2 + x^30*y*z0^3 + 2*x^33 + 2*x^31*z0^2 + x^29*z0^4 - x^32 - x^30*y*z0 + x^30*z0^2 - x^28*y*z0^3 + x^28*z0^4 - 2*x^29*y*z0 + 2*x^29*z0^2 + x^27*y*z0^3 - x^27*z0^4 + x^30 - 2*x^28*y*z0 - x^28*z0^2 + x^26*z0^4 + 2*x^29 + x^27*y*z0 + x^27*z0^2 + 2*x^25*z0^4 - x^28 - 2*x^26*z0^2 - 2*x^24*y*z0^3 + 2*x^24*z0^4 + 2*x^25*y*z0 + 2*x^25*z0^2 - x^23*y*z0^3 + 2*x^23*z0^4 + x^24*y*z0 - x^24*z0^2 - x^22*y*z0^3 - x^22*z0^4 + x^23*y*z0 - 2*x^23*z0^2 + 2*x^21*y*z0^3 + 2*x^21*z0^4 - x^24 + 2*x^22*y*z0 + x^22*z0^2 - 2*x^20*y*z0^3 - x^20*z0^4 - 2*x^23 - x^21*y*z0 + 2*x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 - 2*x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 - x^18*z0^4 - x^19*y*z0 + 2*x^19*z0^2 + 2*x^17*z0^4 - x^18*y*z0 + 2*x^18*z0^2 + 2*x^16*y*z0^3 + x^16*z0^4 - 2*x^19 + 2*x^17*y*z0 - 2*x^17*z0^2 - x^18 - 2*x^14*y*z0^3 + x^14*z0^4 + 2*x^17 + x^15*y*z0 + 2*x^15*z0^2 + 2*x^13*y*z0^3 + x^13*z0^4 + x^16 + x^14*y*z0 - 2*x^14*z0^2 - x^12*y*z0^3 - 2*x^12*z0^4 + x^15 - 2*x^13*y*z0 - x^11*y*z0^3 - x^11*z0^4 + x^12*y*z0 - x^12*z0^2 + 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - x^11*y*z0 - 2*x^11*z0^2 + 2*x^9*y*z0^3 - 2*x^9*z0^4 + x^12 + 2*x^10*y*z0 + 2*x^10*z0^2 + x^8*y*z0^3 + x^8*z0^4 + x^9*y*z0 + x^9*z0^2 - 2*x^7*y*z0^3 + 2*x^7*z0^4 + 2*x^10 + x^8*z0^2 + 2*x^6*y*z0^3 - x^6*z0^4 + 2*x^9 + 2*x^7*y*z0 + x^7*z0^2 + 2*x^5*y*z0^3 + 2*x^5*z0^4 + x^8 + 2*x^6*z0^2 + x^4*y*z0^3 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*z0^2 + 2*x^3*y*z0^3 + x^3*z0^4 - 2*x^2*z0^4 + x^3*y*z0 - x^3*z0^2 + 2*x^2*y*z0 - 2*x^2*z0^2 - x^3)/y) * dx, - ((-2*x^61*z0^3 - x^60*z0^3 + 2*x^58*y^2*z0^3 + x^61*z0 + x^59*z0^3 + x^57*y^2*z0^3 + 2*x^60*z0 - x^58*y^2*z0 + 2*x^58*z0^3 - x^56*y^2*z0^3 + 2*x^59*z0 - 2*x^57*y^2*z0 - x^57*z0^3 - x^58*z0 - 2*x^56*y^2*z0 - x^56*z0^3 + 2*x^54*y^2*z0^3 - 2*x^57*z0 - 2*x^55*z0^3 - 2*x^56*z0 + x^54*z0^3 + x^55*z0 + x^53*z0^3 + 2*x^54*z0 + 2*x^52*z0^3 + 2*x^53*z0 - x^51*z0^3 - x^52*z0 - x^50*z0^3 - 2*x^51*z0 - 2*x^49*z0^3 - 2*x^50*z0 + x^48*z0^3 + x^49*z0 + x^47*z0^3 + 2*x^48*z0 + 2*x^46*z0^3 + 2*x^47*z0 - x^45*z0^3 - x^46*z0 - x^44*z0^3 - 2*x^45*z0 - 2*x^43*z0^3 - 2*x^44*z0 + x^42*z0^3 + x^43*z0 - x^41*z0^3 - 2*x^39*y*z0^4 + 2*x^42*z0 - x^40*y*z0^2 + x^40*z0^3 - 2*x^38*y*z0^4 - 2*x^41*z0 + x^39*y*z0^2 + 2*x^37*y*z0^4 - 2*x^40*y - x^40*z0 - 2*x^38*y*z0^2 + x^38*z0^3 + x^36*y*z0^4 + x^39*z0 + x^37*y^2*z0 - 2*x^37*y*z0^2 + 2*x^37*z0^3 + 2*x^35*y*z0^4 - x^38*y + 2*x^38*z0 + 2*x^36*y*z0^2 - 2*x^36*z0^3 + x^37*y - x^37*z0 - 2*x^35*y*z0^2 + x^35*z0^3 - 2*x^33*y*z0^4 - 2*x^36*y - 2*x^34*z0^3 - 2*x^32*y*z0^4 + 2*x^35*y - x^35*z0 + 2*x^33*y*z0^2 - x^33*z0^3 + 2*x^34*y - 2*x^34*z0 - 2*x^32*y*z0^2 + x^32*z0^3 + x^30*y*z0^4 - x^33*y + x^31*y*z0^2 - 2*x^31*z0^3 - x^29*y*z0^4 - 2*x^32*y - x^30*y*z0^2 - 2*x^28*y*z0^4 - x^31*y - x^31*z0 + 2*x^29*y*z0^2 + 2*x^29*z0^3 + x^27*y*z0^4 - 2*x^30*y + 2*x^30*z0 - 2*x^28*y*z0^2 + x^26*y*z0^4 + x^29*y - x^27*y*z0^2 - 2*x^27*z0^3 - x^25*y*z0^4 - x^28*y + x^26*z0^3 - x^24*y*z0^4 + 2*x^27*y + x^27*z0 - x^25*z0^3 - x^26*y + x^26*z0 - 2*x^24*y*z0^2 + 2*x^24*z0^3 + x^22*y*z0^4 + 2*x^25*y + 2*x^25*z0 - x^23*y*z0^2 - x^23*z0^3 + 2*x^21*y*z0^4 - x^24*y - 2*x^24*z0 + 2*x^22*z0^3 + 2*x^20*y*z0^4 - x^23*y - x^23*z0 + 2*x^21*y*z0^2 - 2*x^21*z0^3 + x^19*y*z0^4 - x^20*y*z0^2 - 2*x^18*y*z0^4 - 2*x^21*y - 2*x^21*z0 + x^19*y*z0^2 + x^19*z0^3 - 2*x^17*y*z0^4 + x^20*y + x^20*z0 + x^18*y*z0^2 + x^18*z0^3 - 2*x^16*y*z0^4 - x^19*y - x^19*z0 - 2*x^17*y*z0^2 + 2*x^15*y*z0^4 - 2*x^18*z0 + x^16*z0^3 - x^14*y*z0^4 + x^17*y + x^17*z0 - x^15*y*z0^2 + x^15*z0^3 - 2*x^13*y*z0^4 - x^16*z0 - 2*x^14*z0^3 - 2*x^12*y*z0^4 + x^15*y - x^15*z0 - x^13*y*z0^2 - x^11*y*z0^4 + x^14*y + 2*x^12*y*z0^2 + x^12*z0^3 + x^10*y*z0^4 - x^13*z0 - x^11*y*z0^2 + x^9*y*z0^4 + 2*x^12*y + 2*x^12*z0 - 2*x^10*y*z0^2 - 2*x^10*z0^3 - 2*x^8*y*z0^4 + x^11*y - x^11*z0 - x^9*y*z0^2 - x^9*z0^3 + 2*x^10*y + 2*x^10*z0 + x^8*z0^3 + 2*x^9*y + 2*x^9*z0 + x^7*z0^3 + x^5*y*z0^4 + x^8*y - 2*x^8*z0 - x^6*y*z0^2 + x^6*z0^3 + 2*x^7*y - x^7*z0 + x^5*y*z0^2 - x^3*y*z0^4 + x^6*y + x^6*z0 + x^5*y + 2*x^5*z0 - x^3*z0^3 - x^4*y + x^2*y*z0^2 + 2*x^3*z0 - 2*x^2*y - 2*x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + 2*x^60*z0^4 + 2*x^58*y^2*z0^4 + x^61*z0^2 - 2*x^59*z0^4 - 2*x^57*y^2*z0^4 + 2*x^60*z0^2 - x^58*y^2*z0^2 + 2*x^58*z0^4 + 2*x^56*y^2*z0^4 - 2*x^61 - 2*x^57*y^2*z0^2 - 2*x^57*z0^4 - x^60 + 2*x^58*y^2 - x^58*z0^2 + 2*x^56*z0^4 + x^57*y^2 - 2*x^57*z0^2 - 2*x^55*z0^4 + 2*x^58 + 2*x^54*z0^4 + x^57 + x^55*z0^2 - 2*x^53*z0^4 + 2*x^54*z0^2 + 2*x^52*z0^4 - 2*x^55 - 2*x^51*z0^4 - x^54 - x^52*z0^2 + 2*x^50*z0^4 - 2*x^51*z0^2 - 2*x^49*z0^4 + 2*x^52 + 2*x^48*z0^4 + x^51 + x^49*z0^2 - 2*x^47*z0^4 + 2*x^48*z0^2 + 2*x^46*z0^4 - 2*x^49 - 2*x^45*z0^4 - x^48 - x^46*z0^2 + 2*x^44*z0^4 - 2*x^45*z0^2 - 2*x^43*z0^4 + 2*x^46 + 2*x^42*z0^4 + x^45 + x^43*z0^2 + 2*x^42*z0^2 - x^40*y*z0^3 + 2*x^40*z0^4 - 2*x^43 + x^41*z0^2 + x^39*y*z0^3 + x^39*z0^4 - x^42 - 2*x^40*y*z0 + 2*x^40*z0^2 + 2*x^38*y*z0^3 - x^38*z0^4 + 2*x^41 + 2*x^39*z0^2 + x^37*y^2*z0^2 + 2*x^37*y*z0^3 - 2*x^40 - 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - x^36*z0^4 + 2*x^39 + 2*x^37*y*z0 + 2*x^37*z0^2 + x^35*y*z0^3 + 2*x^35*z0^4 + 2*x^36*y*z0 - 2*x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^34*z0^4 + 2*x^37 + 2*x^35*y*z0 - 2*x^35*z0^2 - x^33*y*z0^3 + 2*x^33*z0^4 + x^36 + 2*x^34*y*z0 + 2*x^34*z0^2 + x^32*y*z0^3 + 2*x^32*z0^4 + x^35 + 2*x^33*z0^2 - 2*x^31*y*z0^3 - x^31*z0^4 - 2*x^34 - x^32*y*z0 - x^32*z0^2 + x^30*y*z0^3 - 2*x^30*z0^4 - 2*x^33 + x^31*y*z0 - x^29*z0^4 - x^32 - 2*x^30*y*z0 + 2*x^28*y*z0^3 + 2*x^31 - 2*x^29*y*z0 - 2*x^29*z0^2 + x^27*y*z0^3 - x^27*z0^4 - 2*x^30 + x^28*y*z0 + x^28*z0^2 - x^26*y*z0^3 + x^26*z0^4 + 2*x^29 - 2*x^27*y*z0 + 2*x^27*z0^2 - 2*x^25*y*z0^3 - 2*x^25*z0^4 + x^28 - x^26*y*z0 + 2*x^26*z0^2 - x^24*y*z0^3 + 2*x^27 - 2*x^25*y*z0 + 2*x^25*z0^2 + 2*x^23*z0^4 + x^26 - x^24*z0^2 - 2*x^25 - 2*x^23*y*z0 + 2*x^21*y*z0^3 - x^21*z0^4 + x^24 - 2*x^22*y*z0 + 2*x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^23 + x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 - x^19*z0^4 + 2*x^22 - x^20*y*z0 + 2*x^20*z0^2 + 2*x^18*y*z0^3 + x^18*z0^4 + x^19*y*z0 - 2*x^19*z0^2 - 2*x^17*y*z0^3 + 2*x^17*z0^4 - x^20 - 2*x^18*y*z0 + 2*x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 + 2*x^19 - 2*x^17*y*z0 + x^17*z0^2 + x^15*y*z0^3 + x^15*z0^4 + 2*x^18 + x^16*y*z0 - 2*x^16*z0^2 - x^14*y*z0^3 - x^14*z0^4 + x^17 + x^15*y*z0 - x^15*z0^2 - x^13*z0^4 - 2*x^16 - x^14*y*z0 - x^14*z0^2 + 2*x^12*y*z0^3 - x^12*z0^4 - 2*x^15 + 2*x^13*y*z0 + x^13*z0^2 + 2*x^11*z0^4 + 2*x^14 - x^12*y*z0 - 2*x^12*z0^2 - x^10*y*z0^3 + 2*x^10*z0^4 + x^13 - x^11*y*z0 - 2*x^11*z0^2 - 2*x^9*y*z0^3 + x^9*z0^4 - x^12 - x^10*y*z0 + 2*x^10*z0^2 - x^8*y*z0^3 - x^8*z0^4 + 2*x^11 + 2*x^9*z0^2 + 2*x^7*y*z0^3 - x^7*z0^4 - x^10 + x^8*y*z0 - x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^9 - x^7*z0^2 + 2*x^5*y*z0^3 - x^5*z0^4 - 2*x^8 + x^6*y*z0 - 2*x^4*y*z0^3 - 2*x^4*z0^4 - x^7 - 2*x^5*y*z0 + x^3*y*z0^3 - 2*x^6 - 2*x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + 2*x^3*z0^2 - 2*x^2*y*z0 - 2*x^2*z0^2 - 2*x^3)/y) * dx, - ((-2*x^61*z0^3 + 2*x^58*y^2*z0^3 - 2*x^61*z0 - 2*x^60*z0 + 2*x^58*y^2*z0 + 2*x^58*z0^3 + 2*x^59*z0 + 2*x^57*y^2*z0 - x^57*z0^3 + 2*x^58*z0 - 2*x^56*y^2*z0 + x^54*y^2*z0^3 + 2*x^57*z0 - 2*x^55*z0^3 - 2*x^56*z0 + x^54*z0^3 - 2*x^55*z0 - 2*x^54*z0 + 2*x^52*z0^3 + 2*x^53*z0 - x^51*z0^3 + 2*x^52*z0 + 2*x^51*z0 - 2*x^49*z0^3 - 2*x^50*z0 + x^48*z0^3 - 2*x^49*z0 - 2*x^48*z0 + 2*x^46*z0^3 + 2*x^47*z0 - x^45*z0^3 + 2*x^46*z0 + 2*x^45*z0 - 2*x^43*z0^3 - 2*x^44*z0 + x^42*z0^3 - 2*x^43*z0 - 2*x^41*z0^3 - 2*x^39*y*z0^4 - 2*x^42*z0 - x^40*y*z0^2 + 2*x^40*z0^3 + x^38*y*z0^4 - 2*x^39*y*z0^2 - 2*x^39*z0^3 + x^37*y^2*z0^3 + 2*x^37*y*z0^4 - x^40*y + 2*x^40*z0 + x^38*z0^3 - x^36*y*z0^4 - 2*x^39*y - 2*x^39*z0 + 2*x^37*y*z0^2 + 2*x^37*z0^3 - 2*x^35*y*z0^4 - 2*x^38*y + x^38*z0 - 2*x^36*y*z0^2 + 2*x^36*z0^3 + x^34*y*z0^4 - 2*x^37*y + x^37*z0 + x^35*z0^3 - x^33*y*z0^4 + 2*x^36*y - 2*x^36*z0 + x^34*y*z0^2 + 2*x^34*z0^3 - 2*x^32*y*z0^4 + 2*x^35*y - 2*x^35*z0 + x^33*y*z0^2 + x^31*y*z0^4 + 2*x^34*y - x^34*z0 + x^32*y*z0^2 - x^32*z0^3 - x^33*y - 2*x^33*z0 - x^31*z0^3 - 2*x^32*y + 2*x^32*z0 - 2*x^30*y*z0^2 - x^30*z0^3 + 2*x^31*y + x^29*y*z0^2 - 2*x^29*z0^3 - 2*x^27*y*z0^4 - 2*x^30*z0 - x^28*z0^3 - 2*x^26*y*z0^4 + 2*x^29*z0 + x^27*y*z0^2 + x^27*z0^3 - x^25*y*z0^4 + x^28*y + 2*x^28*z0 - x^26*y*z0^2 + x^26*z0^3 + 2*x^24*y*z0^4 + x^25*y*z0^2 + x^25*z0^3 - 2*x^23*y*z0^4 - x^26*y + x^24*z0^3 + x^22*y*z0^4 - x^25*y - 2*x^25*z0 + 2*x^23*y*z0^2 + x^23*z0^3 - x^21*y*z0^4 + 2*x^24*z0 - 2*x^22*y*z0^2 + 2*x^22*z0^3 - 2*x^20*y*z0^4 - 2*x^23*y + 2*x^23*z0 + 2*x^21*y*z0^2 + 2*x^21*z0^3 - x^19*y*z0^4 - 2*x^22*z0 + 2*x^20*y*z0^2 - x^20*z0^3 + x^18*y*z0^4 + 2*x^21*y + 2*x^21*z0 + 2*x^19*y*z0^2 - x^17*y*z0^4 - 2*x^20*y + 2*x^20*z0 - 2*x^18*z0^3 - x^16*y*z0^4 + x^19*y - 2*x^17*z0^3 + 2*x^15*y*z0^4 + x^18*z0 + x^16*y*z0^2 - x^14*y*z0^4 - x^17*y + x^17*z0 - x^15*y*z0^2 + x^15*z0^3 + 2*x^13*y*z0^4 - x^16*y + 2*x^16*z0 + 2*x^12*y*z0^4 - x^15*y - x^15*z0 - x^13*z0^3 - x^11*y*z0^4 + x^14*z0 + x^12*y*z0^2 + x^12*z0^3 + 2*x^10*y*z0^4 - x^13*y + 2*x^13*z0 - 2*x^11*y*z0^2 + x^11*z0^3 - x^9*y*z0^4 - 2*x^12*z0 - 2*x^10*y*z0^2 - x^10*z0^3 + x^8*y*z0^4 + 2*x^11*z0 - x^9*y*z0^2 + x^9*z0^3 + 2*x^7*y*z0^4 - x^10*y - x^10*z0 - x^8*y*z0^2 - 2*x^6*y*z0^4 - 2*x^9*y + 2*x^9*z0 + x^7*y*z0^2 + x^7*z0^3 + 2*x^8*y - x^8*z0 + x^6*y*z0^2 + x^6*z0^3 - x^4*y*z0^4 - 2*x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - x^6*y - 2*x^4*y*z0^2 + 2*x^2*y*z0^4 + 2*x^5*y - 2*x^5*z0 + x^3*y*z0^2 - 2*x^3*z0^3 - 2*x^4*y - x^4*z0 + x^2*y*z0^2 - 2*x^2*z0^3 - x^3*y + x^2*y + 2*x^2*z0)/y) * dx, - ((-x^61*z0^4 + x^60*z0^4 + x^58*y^2*z0^4 - x^57*y^2*z0^4 + x^58*z0^4 + x^61 - x^57*z0^4 + 2*x^60 - x^58*y^2 - 2*x^57*y^2 - x^55*z0^4 - x^58 + x^54*z0^4 - 2*x^57 + x^52*z0^4 + x^55 - x^51*z0^4 + 2*x^54 - x^49*z0^4 - x^52 + x^48*z0^4 - 2*x^51 + x^46*z0^4 + x^49 - x^45*z0^4 + 2*x^48 - x^43*z0^4 - x^46 + x^42*z0^4 - 2*x^45 + 2*x^41*z0^4 + 2*x^40*y*z0^3 - x^40*z0^4 + x^43 - 2*x^39*z0^4 + x^37*y^2*z0^4 + 2*x^42 - 2*x^40*z0^2 + 2*x^38*y*z0^3 - x^38*z0^4 + 2*x^41 + 2*x^39*y*z0 - x^37*y*z0^3 - 2*x^40 + x^38*y*z0 - 2*x^39 + x^37*y*z0 + 2*x^37*z0^2 - x^35*y*z0^3 + x^35*z0^4 - x^38 - x^36*y*z0 + x^37 - x^35*y*z0 - x^35*z0^2 - 2*x^33*y*z0^3 - x^34*z0^2 + 2*x^32*y*z0^3 + 2*x^35 - x^33*z0^2 + 2*x^31*y*z0^3 - 2*x^34 - 2*x^32*y*z0 - x^32*z0^2 - 2*x^30*y*z0^3 + x^30*z0^4 + 2*x^33 - x^31*y*z0 + 2*x^31*z0^2 - x^29*y*z0^3 - 2*x^29*z0^4 + x^32 + 2*x^30*y*z0 - x^30*z0^2 - 2*x^28*y*z0^3 + 2*x^29*y*z0 - x^27*y*z0^3 - x^27*z0^4 + 2*x^30 - 2*x^28*y*z0 + 2*x^28*z0^2 - 2*x^26*y*z0^3 + 2*x^26*z0^4 - x^29 + x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 - 2*x^26*y*z0 - 2*x^26*z0^2 - x^24*z0^4 - 2*x^23*y*z0^3 - x^23*z0^4 + 2*x^26 + x^24*y*z0 + x^24*z0^2 + x^22*y*z0^3 + 2*x^22*z0^4 + x^25 - x^23*y*z0 - 2*x^23*z0^2 + 2*x^21*y*z0^3 - 2*x^21*z0^4 + x^24 + x^22*y*z0 - x^22*z0^2 - x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^21*y*z0 - x^21*z0^2 + x^20*y*z0 + x^18*z0^4 - 2*x^21 - 2*x^19*z0^2 + x^17*y*z0^3 - x^17*z0^4 - x^20 + x^18*y*z0 + x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^16*z0^4 - x^19 - x^17*y*z0 - x^17*z0^2 - 2*x^15*y*z0^3 - x^15*z0^4 - 2*x^16*z0^2 - 2*x^14*y*z0^3 + x^14*z0^4 + x^17 + x^15*y*z0 - 2*x^13*y*z0^3 + 2*x^13*z0^4 + x^14*y*z0 - x^14*z0^2 - 2*x^12*y*z0^3 + 2*x^15 - x^13*z0^2 + x^11*y*z0^3 - x^12*y*z0 - 2*x^12*z0^2 + x^10*z0^4 + 2*x^13 - 2*x^11*y*z0 - 2*x^9*y*z0^3 - x^9*z0^4 + 2*x^12 + x^10*y*z0 - 2*x^10*z0^2 + x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 + x^9*z0^2 - x^7*z0^4 - x^10 + x^8*y*z0 - 2*x^8*z0^2 - x^6*y*z0^3 - 2*x^9 + 2*x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 - x^5*z0^4 + 2*x^8 + x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - x^7 + x^5*y*z0 + x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^6 - 2*x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 - 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 + 2*x^2*y*z0 - x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^60*z0^4 + x^61*z0^2 + x^57*y^2*z0^4 - 2*x^60*z0^2 - x^58*y^2*z0^2 - x^61 + 2*x^57*y^2*z0^2 + x^57*z0^4 + x^58*y^2 - x^58*z0^2 + 2*x^57*z0^2 + x^58 - x^54*z0^4 + x^55*z0^2 - 2*x^54*z0^2 - x^55 + x^51*z0^4 - x^52*z0^2 + 2*x^51*z0^2 + x^52 - x^48*z0^4 + x^49*z0^2 - 2*x^48*z0^2 - x^49 + x^45*z0^4 - x^46*z0^2 + 2*x^45*z0^2 + x^46 - x^42*z0^4 + x^43*z0^2 + 2*x^41*z0^4 - 2*x^42*z0^2 - 2*x^40*z0^4 - x^43 + x^41*z0^2 + x^39*y*z0^3 + 2*x^39*z0^4 - 2*x^40*y*z0 + x^40*z0^2 + 2*x^38*y*z0^3 - x^38*z0^4 + x^41 + x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 - 2*x^37*z0^4 - x^40 + x^38*y^2 + x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 + 2*x^37*z0^2 - x^35*y*z0^3 - x^35*z0^4 - x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 - 2*x^37 - x^35*y*z0 + 2*x^35*z0^2 - 2*x^33*y*z0^3 + x^33*z0^4 + x^36 + 2*x^34*y*z0 + x^34*z0^2 + 2*x^32*y*z0^3 - 2*x^32*z0^4 + 2*x^35 + 2*x^33*y*z0 + x^31*y*z0^3 - 2*x^31*z0^4 - x^34 + 2*x^32*y*z0 - 2*x^32*z0^2 + x^30*y*z0^3 + 2*x^33 - 2*x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^32 + 2*x^30*y*z0 + x^30*z0^2 - 2*x^28*y*z0^3 + x^31 - x^29*y*z0 + x^29*z0^2 + 2*x^27*y*z0^3 + 2*x^27*z0^4 + x^28*y*z0 - x^28*z0^2 + x^26*y*z0^3 + 2*x^26*z0^4 - x^29 - 2*x^27*y*z0 + x^27*z0^2 + 2*x^25*y*z0^3 + x^25*z0^4 - x^28 - 2*x^26*z0^2 + x^24*y*z0^3 + x^24*z0^4 + x^27 + x^25*y*z0 - 2*x^25*z0^2 + 2*x^23*y*z0^3 - x^23*z0^4 - x^26 - 2*x^24*y*z0 + 2*x^24*z0^2 - x^22*y*z0^3 + x^22*z0^4 - x^25 - x^23*y*z0 + 2*x^23*z0^2 - x^21*z0^4 - 2*x^22*z0^2 - 2*x^20*y*z0^3 + x^20*z0^4 + 2*x^23 - x^21*y*z0 - x^21*z0^2 - 2*x^19*z0^4 - 2*x^22 + x^20*y*z0 + x^20*z0^2 - x^18*y*z0^3 - x^18*z0^4 + x^19*y*z0 + x^19*z0^2 + x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^20 + x^18*y*z0 + 2*x^18*z0^2 + 2*x^16*y*z0^3 - 2*x^19 - 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 - x^18 + 2*x^16*z0^2 + x^14*y*z0^3 - x^14*z0^4 + x^17 - 2*x^15*y*z0 - 2*x^13*y*z0^3 - 2*x^13*z0^4 + x^16 + 2*x^14*y*z0 + 2*x^12*y*z0^3 - 2*x^15 - 2*x^13*z0^2 - x^11*y*z0^3 - x^11*z0^4 - x^14 + 2*x^12*y*z0 - x^10*y*z0^3 + x^11*z0^2 + 2*x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 - 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 + x^10 + x^8*y*z0 - 2*x^8*z0^2 - x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 + 2*x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + 2*x^8 - x^6*y*z0 + 2*x^4*y*z0^3 + x^4*z0^4 - x^5*y*z0 + 2*x^3*y*z0^3 + x^3*z0^4 - x^6 + x^4*y*z0 + 2*x^4*z0^2 + 2*x^5 - x^3*y*z0 + 2*x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 + x^3 + x^2)/y) * dx, - ((-x^61*z0^3 - x^60*z0^3 + x^58*y^2*z0^3 + 2*x^61*z0 + x^59*z0^3 + x^57*y^2*z0^3 - 2*x^58*y^2*z0 - 2*x^58*z0^3 - x^56*y^2*z0^3 - x^59*z0 + x^57*z0^3 - 2*x^55*y^2*z0^3 - 2*x^58*z0 + x^56*y^2*z0 - x^56*z0^3 + 2*x^55*z0^3 + x^56*z0 - x^54*z0^3 + 2*x^55*z0 + x^53*z0^3 - 2*x^52*z0^3 - x^53*z0 + x^51*z0^3 - 2*x^52*z0 - x^50*z0^3 + 2*x^49*z0^3 + x^50*z0 - x^48*z0^3 + 2*x^49*z0 + x^47*z0^3 - 2*x^46*z0^3 - x^47*z0 + x^45*z0^3 - 2*x^46*z0 - x^44*z0^3 + 2*x^43*z0^3 + x^44*z0 - x^42*z0^3 + 2*x^43*z0 - x^39*y*z0^4 + 2*x^40*y*z0^2 + x^38*y*z0^4 + 2*x^39*y*z0^2 - 2*x^39*z0^3 - 2*x^37*y*z0^4 + x^40*y - 2*x^40*z0 + x^38*y^2*z0 + 2*x^38*y*z0^2 - 2*x^38*z0^3 - x^36*y*z0^4 + x^39*y + x^39*z0 + 2*x^37*y*z0^2 + 2*x^37*z0^3 + 2*x^35*y*z0^4 - x^38*y - x^36*y*z0^2 - 2*x^34*y*z0^4 + 2*x^37*y - x^37*z0 + 2*x^35*y*z0^2 + 2*x^35*z0^3 + x^33*y*z0^4 + x^36*z0 + x^34*y*z0^2 - 2*x^34*z0^3 - x^32*y*z0^4 + 2*x^35*y - x^35*z0 + 2*x^33*y*z0^2 - x^33*z0^3 - 2*x^31*y*z0^4 - 2*x^34*y - x^34*z0 + x^32*z0^3 + x^30*y*z0^4 + 2*x^33*y + x^33*z0 - x^31*y*z0^2 - x^31*z0^3 - x^29*y*z0^4 + 2*x^32*y + x^32*z0 + 2*x^30*z0^3 + 2*x^28*y*z0^4 + x^31*y - 2*x^31*z0 - 2*x^29*y*z0^2 + x^29*z0^3 + x^27*y*z0^4 + 2*x^30*y + x^30*z0 + 2*x^28*z0^3 + x^26*y*z0^4 + 2*x^29*y - 2*x^29*z0 + 2*x^27*y*z0^2 + 2*x^27*z0^3 + x^25*y*z0^4 - 2*x^28*z0 - 2*x^26*y*z0^2 - x^26*z0^3 - x^27*y - 2*x^25*y*z0^2 - 2*x^25*z0^3 + x^23*y*z0^4 + x^26*y + 2*x^26*z0 - 2*x^24*y*z0^2 - 2*x^24*z0^3 + 2*x^22*y*z0^4 - 2*x^25*y + 2*x^25*z0 - 2*x^23*y*z0^2 + 2*x^23*z0^3 - 2*x^21*y*z0^4 - x^24*y + x^24*z0 + 2*x^22*y*z0^2 + 2*x^22*z0^3 + x^20*y*z0^4 + x^23*y - x^23*z0 + 2*x^21*y*z0^2 + 2*x^21*z0^3 - 2*x^22*y + 2*x^22*z0 + x^20*y*z0^2 + 2*x^20*z0^3 - 2*x^18*y*z0^4 + x^21*z0 + 2*x^19*y*z0^2 - 2*x^19*z0^3 - x^17*y*z0^4 + 2*x^18*y*z0^2 - x^18*z0^3 - 2*x^16*y*z0^4 - x^19*y - x^17*y*z0^2 + x^15*y*z0^4 + 2*x^18*y - x^18*z0 + 2*x^16*y*z0^2 + x^16*z0^3 + 2*x^14*y*z0^4 + 2*x^17*y + 2*x^17*z0 - x^15*y*z0^2 + 2*x^13*y*z0^4 - x^16*y - 2*x^16*z0 + x^14*y*z0^2 - 2*x^12*y*z0^4 - 2*x^15*y + 2*x^13*z0^3 + 2*x^14*y + x^14*z0 + x^12*y*z0^2 - x^12*z0^3 + 2*x^13*y + x^13*z0 + x^11*y*z0^2 + 2*x^11*z0^3 + x^9*y*z0^4 + 2*x^12*y - x^10*y*z0^2 - x^10*z0^3 + x^11*y + x^9*y*z0^2 - x^9*z0^3 + x^10*y + 2*x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 + x^6*y*z0^4 + 2*x^9*y - 2*x^9*z0 + 2*x^7*y*z0^2 - x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - 2*x^8*z0 + 2*x^6*y*z0^2 - x^4*y*z0^4 + 2*x^7*y - 2*x^7*z0 - 2*x^5*y*z0^2 - 2*x^5*z0^3 + 2*x^3*y*z0^4 + x^6*y - x^6*z0 - x^4*z0^3 + 2*x^2*y*z0^4 + x^5*y + 2*x^3*y*z0^2 + x^4*y - 2*x^4*z0 - 2*x^2*y*z0^2 - 2*x^3*y + x^3*z0 + 2*x^2*y - x^2*z0)/y) * dx, - ((x^61*z0^4 - x^60*z0^4 - x^58*y^2*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 - x^58*z0^4 + 2*x^61 - x^57*y^2*z0^2 + x^57*z0^4 + x^60 - 2*x^58*y^2 - x^57*y^2 - x^57*z0^2 + x^55*z0^4 - 2*x^58 - x^54*z0^4 - x^57 + x^54*z0^2 - x^52*z0^4 + 2*x^55 + x^51*z0^4 + x^54 - x^51*z0^2 + x^49*z0^4 - 2*x^52 - x^48*z0^4 - x^51 + x^48*z0^2 - x^46*z0^4 + 2*x^49 + x^45*z0^4 + x^48 - x^45*z0^2 + x^43*z0^4 - 2*x^46 - x^42*z0^4 - x^45 + 2*x^41*z0^4 + x^42*z0^2 - 2*x^40*y*z0^3 - 2*x^40*z0^4 + 2*x^43 - x^41*z0^2 + x^42 + x^40*z0^2 + x^38*y^2*z0^2 + x^38*y*z0^3 - x^38*z0^4 + 2*x^41 + x^39*y*z0 - x^39*z0^2 - 2*x^37*y*z0^3 - 2*x^37*z0^4 + 2*x^40 + x^38*z0^2 - x^36*z0^4 - 2*x^39 - x^37*y*z0 - x^37*z0^2 + x^35*z0^4 - x^38 + x^36*z0^2 + x^34*y*z0^3 + x^37 - 2*x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 - 2*x^34*z0^2 + 2*x^32*y*z0^3 + x^32*z0^4 + 2*x^33*y*z0 - 2*x^33*z0^2 + x^31*y*z0^3 - x^31*z0^4 - x^34 + 2*x^32*y*z0 + x^30*y*z0^3 + x^30*z0^4 - x^31*z0^2 + x^29*z0^4 - 2*x^32 + x^30*y*z0 - 2*x^28*z0^4 - 2*x^31 - x^29*y*z0 - x^30 + 2*x^28*y*z0 - x^28*z0^2 + 2*x^26*y*z0^3 - 2*x^26*z0^4 - x^29 + 2*x^27*y*z0 - x^27*z0^2 + 2*x^25*z0^4 - x^26*y*z0 + 2*x^24*y*z0^3 + x^24*z0^4 - 2*x^27 - x^25*z0^2 + x^23*y*z0^3 + x^26 - x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^22*z0^4 - x^25 + 2*x^23*y*z0 + 2*x^23*z0^2 - 2*x^21*y*z0^3 - x^21*z0^4 - 2*x^24 + x^22*y*z0 + x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^23 + x^21*y*z0 + x^21*z0^2 - x^19*y*z0^3 - x^19*z0^4 + x^22 + x^20*y*z0 - 2*x^20*z0^2 + 2*x^18*y*z0^3 + x^18*z0^4 + 2*x^21 - x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 - x^20 - x^18*y*z0 - 2*x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^16*z0^4 + x^19 - 2*x^17*y*z0 + 2*x^17*z0^2 + 2*x^15*y*z0^3 + 2*x^15*z0^4 - 2*x^18 - 2*x^16*y*z0 + 2*x^14*y*z0^3 + x^17 - 2*x^15*y*z0 - 2*x^15*z0^2 + x^13*y*z0^3 + 2*x^13*z0^4 + x^16 + 2*x^14*y*z0 - x^14*z0^2 - 2*x^12*y*z0^3 + x^12*z0^4 + x^15 - x^13*y*z0 + 2*x^13*z0^2 - 2*x^11*y*z0^3 + 2*x^14 + x^12*y*z0 - 2*x^10*y*z0^3 - 2*x^10*z0^4 + 2*x^13 - x^11*y*z0 - 2*x^11*z0^2 - 2*x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 - 2*x^8*y*z0^3 - x^8*z0^4 + x^11 - x^9*y*z0 + x^9*z0^2 - 2*x^7*y*z0^3 - x^7*z0^4 - 2*x^10 + x^8*y*z0 + 2*x^6*y*z0^3 + x^6*z0^4 + 2*x^9 - 2*x^7*y*z0 - 2*x^7*z0^2 - x^5*y*z0^3 - 2*x^5*z0^4 + x^8 - x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 + 2*x^5*y*z0 + x^5*z0^2 - x^3*z0^4 - x^6 + 2*x^4*y*z0 - x^4*z0^2 - x^2*z0^4 - x^5 + 2*x^3*y*z0 + 2*x^3*z0^2 + x^2*z0^2 + x^3 - x^2)/y) * dx, - ((-2*x^61*z0^3 - x^60*z0^3 + 2*x^58*y^2*z0^3 + x^61*z0 - x^59*z0^3 + x^57*y^2*z0^3 - x^60*z0 - x^58*y^2*z0 - 2*x^58*z0^3 + x^56*y^2*z0^3 + x^57*y^2*z0 - x^57*z0^3 - x^55*y^2*z0^3 - x^58*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 + x^57*z0 + 2*x^55*z0^3 + x^54*z0^3 + x^55*z0 - x^53*z0^3 - x^54*z0 - 2*x^52*z0^3 - x^51*z0^3 - x^52*z0 + x^50*z0^3 + x^51*z0 + 2*x^49*z0^3 + x^48*z0^3 + x^49*z0 - x^47*z0^3 - x^48*z0 - 2*x^46*z0^3 - x^45*z0^3 - x^46*z0 + x^44*z0^3 + x^45*z0 + 2*x^43*z0^3 + x^42*z0^3 + x^43*z0 + x^41*z0^3 - 2*x^39*y*z0^4 - x^42*z0 - x^40*y*z0^2 - 2*x^40*z0^3 + x^38*y^2*z0^3 - x^38*y*z0^4 + x^41*z0 + x^39*y*z0^2 - x^39*z0^3 - 2*x^40*y - x^40*z0 + 2*x^38*y*z0^2 + 2*x^38*z0^3 + 2*x^36*y*z0^4 - 2*x^37*z0^3 + x^38*y + 2*x^38*z0 - 2*x^36*y*z0^2 - 2*x^36*z0^3 + 2*x^34*y*z0^4 + x^37*y + x^35*y*z0^2 - x^35*z0^3 + 2*x^33*y*z0^4 - 2*x^36*y - x^34*y*z0^2 - x^35*z0 + x^33*y*z0^2 + x^33*z0^3 - 2*x^31*y*z0^4 + 2*x^34*y + x^34*z0 + x^32*y*z0^2 + 2*x^32*z0^3 - 2*x^30*y*z0^4 - 2*x^33*y + x^33*z0 - 2*x^31*y*z0^2 + 2*x^31*z0^3 + 2*x^29*y*z0^4 + 2*x^32*y - 2*x^32*z0 + x^30*y*z0^2 - x^28*y*z0^4 - 2*x^31*z0 + 2*x^29*y*z0^2 - 2*x^29*z0^3 - x^27*y*z0^4 - x^30*y + 2*x^30*z0 + x^28*y*z0^2 + x^28*z0^3 + 2*x^29*y - x^29*z0 + 2*x^27*y*z0^2 - x^27*z0^3 + x^25*y*z0^4 + 2*x^28*y - x^28*z0 - 2*x^27*y + x^27*z0 + 2*x^25*y*z0^2 + 2*x^25*z0^3 - 2*x^23*y*z0^4 + x^26*z0 - 2*x^24*y*z0^2 - 2*x^24*z0^3 + x^22*y*z0^4 - 2*x^25*z0 + x^23*y*z0^2 + x^23*z0^3 + x^21*y*z0^4 + x^24*y - x^24*z0 - 2*x^22*y*z0^2 + 2*x^20*y*z0^4 + x^23*y + 2*x^21*y*z0^2 + 2*x^21*z0^3 + 2*x^19*y*z0^4 + x^22*y - x^22*z0 - 2*x^20*y*z0^2 - 2*x^20*z0^3 - x^18*y*z0^4 - 2*x^21*y - 2*x^21*z0 - 2*x^19*y*z0^2 - 2*x^19*z0^3 + x^20*y + x^18*z0^3 + x^19*y - 2*x^19*z0 + x^17*z0^3 - 2*x^15*y*z0^4 - 2*x^18*z0 + x^16*z0^3 - x^14*y*z0^4 + 2*x^17*y - 2*x^17*z0 - 2*x^15*y*z0^2 + x^15*z0^3 - 2*x^16*y + x^16*z0 - x^14*z0^3 + x^12*y*z0^4 - x^15*y + x^13*y*z0^2 + x^13*z0^3 + x^11*y*z0^4 + x^14*y - x^14*z0 + x^12*y*z0^2 - 2*x^12*z0^3 + x^10*y*z0^4 - 2*x^13*y - 2*x^11*y*z0^2 - 2*x^11*z0^3 - 2*x^9*y*z0^4 - 2*x^12*y + x^12*z0 - x^10*y*z0^2 + x^10*z0^3 + 2*x^8*y*z0^4 + 2*x^11*y - 2*x^9*y*z0^2 + x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y - 2*x^10*z0 + 2*x^8*z0^3 + x^6*y*z0^4 - x^9*y - 2*x^9*z0 - 2*x^7*y*z0^2 + x^7*z0^3 + x^8*y - x^8*z0 + x^6*y*z0^2 - 2*x^6*z0^3 + x^4*y*z0^4 + x^7*y + 2*x^5*z0^3 + x^3*y*z0^4 + x^6*y + x^6*z0 - 2*x^4*y*z0^2 + 2*x^2*y*z0^4 + 2*x^5*y - x^5*z0 + 2*x^3*y*z0^2 - x^3*z0^3 - 2*x^4*y - x^4*z0 - x^2*z0^3 - x^3*y - x^3*z0 + 2*x^2*z0)/y) * dx, - ((-x^60*z0^4 + x^61*z0^2 - x^59*z0^4 + x^57*y^2*z0^4 - 2*x^60*z0^2 - x^58*y^2*z0^2 + x^56*y^2*z0^4 + x^61 + 2*x^57*y^2*z0^2 + x^57*z0^4 + 2*x^60 - x^58*y^2 - x^58*z0^2 + x^56*z0^4 - 2*x^57*y^2 + 2*x^57*z0^2 - x^58 - x^54*z0^4 - 2*x^57 + x^55*z0^2 - x^53*z0^4 - 2*x^54*z0^2 + x^55 + x^51*z0^4 + 2*x^54 - x^52*z0^2 + x^50*z0^4 + 2*x^51*z0^2 - x^52 - x^48*z0^4 - 2*x^51 + x^49*z0^2 - x^47*z0^4 - 2*x^48*z0^2 + x^49 + x^45*z0^4 + 2*x^48 - x^46*z0^2 + x^44*z0^4 + 2*x^45*z0^2 - x^46 - x^42*z0^4 - 2*x^45 + x^43*z0^2 + x^41*z0^4 - 2*x^42*z0^2 - 2*x^40*z0^4 + x^38*y^2*z0^4 + x^43 + x^41*z0^2 + x^39*y*z0^3 + 2*x^39*z0^4 + 2*x^42 - 2*x^40*y*z0 - x^40*z0^2 + x^38*y*z0^3 + 2*x^38*z0^4 - 2*x^41 - 2*x^39*y*z0 + x^39*z0^2 - 2*x^37*z0^4 + 2*x^40 - x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - 2*x^36*z0^4 - x^37*y*z0 + 2*x^37*z0^2 - x^35*y*z0^3 + x^35*z0^4 - x^38 - x^36*y*z0 - x^36*z0^2 - 2*x^34*y*z0^3 - x^37 - x^35*y*z0 + x^35*z0^2 - 2*x^33*y*z0^3 + 2*x^36 + 2*x^34*z0^2 - x^32*z0^4 - x^35 - 2*x^33*z0^2 + x^31*y*z0^3 + 2*x^31*z0^4 - x^34 + 2*x^32*y*z0 + x^32*z0^2 + 2*x^30*y*z0^3 + x^30*z0^4 - x^31*y*z0 + 2*x^31*z0^2 - x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 - x^30*z0^2 + 2*x^28*y*z0^3 + 2*x^31 - x^29*y*z0 + x^29*z0^2 + 2*x^27*y*z0^3 + x^30 - x^28*z0^2 + x^26*y*z0^3 + x^26*z0^4 + x^29 - x^27*y*z0 + 2*x^27*z0^2 - x^25*y*z0^3 + 2*x^25*z0^4 - x^26*y*z0 + x^24*y*z0^3 + x^24*z0^4 - x^27 - x^25*z0^2 + 2*x^23*y*z0^3 + 2*x^23*z0^4 - x^26 + x^24*y*z0 + 2*x^24*z0^2 + 2*x^22*y*z0^3 - 2*x^22*z0^4 - x^25 + 2*x^23*y*z0 + 2*x^23*z0^2 + x^21*y*z0^3 + 2*x^24 + x^22*y*z0 + x^22*z0^2 + x^20*y*z0^3 - 2*x^20*z0^4 + x^23 - 2*x^21*y*z0 - 2*x^20*y*z0 - x^18*y*z0^3 - 2*x^18*z0^4 - x^21 - x^19*y*z0 - 2*x^19*z0^2 - 2*x^17*y*z0^3 - x^17*z0^4 + 2*x^20 + 2*x^18*y*z0 + x^18*z0^2 + x^16*z0^4 + 2*x^19 + x^17*y*z0 - 2*x^15*z0^4 - x^18 + x^16*y*z0 + 2*x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 - x^17 + x^15*y*z0 + 2*x^15*z0^2 - 2*x^13*y*z0^3 + x^16 + x^14*z0^2 - 2*x^13*y*z0 + 2*x^14 - 2*x^12*y*z0 + x^10*y*z0^3 - 2*x^10*z0^4 - x^13 - 2*x^11*y*z0 + x^9*y*z0^3 + x^9*z0^4 + 2*x^10*z0^2 + x^8*z0^4 - 2*x^11 + x^9*y*z0 + x^9*z0^2 + 2*x^7*y*z0^3 - x^10 - x^8*z0^2 - x^6*y*z0^3 - 2*x^6*z0^4 + x^9 - x^7*y*z0 - x^7*z0^2 + 2*x^5*y*z0^3 + 2*x^5*z0^4 - 2*x^8 - 2*x^6*y*z0 + x^6*z0^2 + 2*x^4*z0^4 - x^7 + 2*x^5*y*z0 + 2*x^5*z0^2 + x^3*y*z0^3 + 2*x^6 + x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - x^2*z0^4 + 2*x^5 + x^3*y*z0 - x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 + x^3)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 + x^58*y^2*z0^4 + x^61*z0^2 + x^59*z0^4 + 2*x^60*z0^2 - x^58*y^2*z0^2 + x^58*z0^4 - x^56*y^2*z0^4 + 2*x^61 - 2*x^57*y^2*z0^2 - x^60 - 2*x^58*y^2 - x^58*z0^2 - x^56*z0^4 + x^57*y^2 - 2*x^57*z0^2 - x^55*z0^4 - 2*x^58 + x^57 + x^55*z0^2 + x^53*z0^4 + 2*x^54*z0^2 + x^52*z0^4 + 2*x^55 - x^54 - x^52*z0^2 - x^50*z0^4 - 2*x^51*z0^2 - x^49*z0^4 - 2*x^52 + x^51 + x^49*z0^2 + x^47*z0^4 + 2*x^48*z0^2 + x^46*z0^4 + 2*x^49 - x^48 - x^46*z0^2 - x^44*z0^4 - 2*x^45*z0^2 - x^43*z0^4 - 2*x^46 + x^45 + x^43*z0^2 + x^41*z0^4 + 2*x^42*z0^2 + 2*x^40*y*z0^3 + 2*x^43 + x^41*z0^2 + x^39*y*z0^3 - x^39*z0^4 - 2*x^42 - 2*x^40*y*z0 + x^38*y*z0^3 + x^39*y^2 + 2*x^39*z0^2 + 2*x^40 + 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - 2*x^39 - x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 + 2*x^38 + 2*x^36*y*z0 - 2*x^36*z0^2 + 2*x^34*y*z0^3 - x^34*z0^4 + 2*x^37 - 2*x^35*y*z0 - 2*x^35*z0^2 - 2*x^33*y*z0^3 + x^33*z0^4 - 2*x^34*y*z0 - 2*x^34*z0^2 - 2*x^32*y*z0^3 + 2*x^32*z0^4 - 2*x^35 + 2*x^33*y*z0 - 2*x^31*z0^4 - 2*x^34 + x^32*y*z0 - x^30*y*z0^3 - 2*x^33 - 2*x^31*y*z0 - 2*x^31*z0^2 - x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^32 + 2*x^30*y*z0 + x^30*z0^2 + x^28*y*z0^3 - x^28*z0^4 + x^29*y*z0 - 2*x^29*z0^2 + 2*x^27*y*z0^3 - x^27*z0^4 + 2*x^30 - 2*x^28*z0^2 + x^26*z0^4 + 2*x^29 + x^27*y*z0 + 2*x^27*z0^2 + x^25*y*z0^3 - 2*x^25*z0^4 - x^26*z0^2 - x^24*y*z0^3 - 2*x^24*z0^4 + x^27 - x^25*y*z0 - 2*x^25*z0^2 + x^23*y*z0^3 - x^23*z0^4 - 2*x^26 - x^24*y*z0 + x^24*z0^2 - x^22*y*z0^3 + 2*x^22*z0^4 - 2*x^23*y*z0 - x^23*z0^2 + x^21*y*z0^3 - x^24 - x^22*y*z0 + x^22*z0^2 - x^20*y*z0^3 + 2*x^20*z0^4 - 2*x^21*y*z0 - x^19*y*z0^3 + x^22 + x^20*y*z0 + 2*x^20*z0^2 + 2*x^18*y*z0^3 + x^18*z0^4 + 2*x^21 + x^19*y*z0 + 2*x^19*z0^2 - x^17*z0^4 - x^18*y*z0 + 2*x^18*z0^2 + x^16*y*z0^3 + 2*x^16*z0^4 + 2*x^19 + x^17*y*z0 - x^18 - 2*x^16*y*z0 - x^16*z0^2 - 2*x^14*y*z0^3 - 2*x^14*z0^4 + x^17 + 2*x^15*y*z0 - 2*x^15*z0^2 + x^13*y*z0^3 - 2*x^13*z0^4 + x^16 - 2*x^14*y*z0 - x^14*z0^2 + 2*x^12*y*z0^3 + 2*x^12*z0^4 + x^15 - 2*x^13*y*z0 - x^13*z0^2 + 2*x^11*y*z0^3 + x^11*z0^4 - 2*x^14 - x^12*y*z0 + 2*x^12*z0^2 + 2*x^10*y*z0^3 + 2*x^10*z0^4 + x^13 + x^11*y*z0 + 2*x^9*y*z0^3 - 2*x^9*z0^4 - x^12 + x^10*y*z0 + x^10*z0^2 - x^8*y*z0^3 - x^8*z0^4 - x^11 + x^9*y*z0 + x^7*y*z0^3 - x^7*z0^4 - 2*x^8*z0^2 - x^9 + x^7*z0^2 - x^8 + 2*x^6*y*z0 + 2*x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 + x^7 + 2*x^5*y*z0 - x^5*z0^2 + x^3*y*z0^3 + 2*x^3*z0^4 + x^6 + x^4*y*z0 + 2*x^4*z0^2 + 2*x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 - 2*x^2*y*z0 + 2*x^2*z0^2 + 2*x^3)/y) * dx, - ((-2*x^61*z0^3 + x^60*z0^3 + 2*x^58*y^2*z0^3 - 2*x^61*z0 + x^59*z0^3 - x^57*y^2*z0^3 - x^60*z0 + 2*x^58*y^2*z0 - x^56*y^2*z0^3 + x^57*y^2*z0 + 2*x^57*z0^3 + 2*x^55*y^2*z0^3 + 2*x^58*z0 - x^56*z0^3 + 2*x^54*y^2*z0^3 + x^57*z0 - 2*x^54*z0^3 - 2*x^55*z0 + x^53*z0^3 - x^54*z0 + 2*x^51*z0^3 + 2*x^52*z0 - x^50*z0^3 + x^51*z0 - 2*x^48*z0^3 - 2*x^49*z0 + x^47*z0^3 - x^48*z0 + 2*x^45*z0^3 + 2*x^46*z0 - x^44*z0^3 + x^45*z0 - 2*x^42*z0^3 - 2*x^43*z0 - x^41*z0^3 - 2*x^39*y*z0^4 - 2*x^42*z0 - x^40*y*z0^2 + x^40*z0^3 + x^38*y*z0^4 - 2*x^41*z0 + x^39*y^2*z0 - 2*x^39*y*z0^2 + x^39*z0^3 - 2*x^37*y*z0^4 - x^40*y + 2*x^38*y*z0^2 + x^38*z0^3 + x^36*y*z0^4 + x^39*y - x^39*z0 - x^37*y*z0^2 + x^38*y + x^38*z0 - x^36*y*z0^2 + 2*x^36*z0^3 + 2*x^34*y*z0^4 - 2*x^37*y - x^37*z0 - 2*x^35*y*z0^2 + x^35*z0^3 + 2*x^36*y + x^36*z0 - x^34*y*z0^2 - 2*x^34*z0^3 + x^35*z0 + 2*x^33*y*z0^2 - 2*x^33*z0^3 + x^31*y*z0^4 + x^34*y + 2*x^32*z0^3 + 2*x^30*y*z0^4 + 2*x^33*y + 2*x^33*z0 + x^31*y*z0^2 + x^29*y*z0^4 - x^32*y - 2*x^32*z0 - 2*x^30*y*z0^2 - 2*x^30*z0^3 + 2*x^28*y*z0^4 + x^31*z0 + 2*x^29*y*z0^2 + x^30*y - x^30*z0 - 2*x^28*y*z0^2 - 2*x^26*y*z0^4 - 2*x^29*y + x^29*z0 + x^27*y*z0^2 + x^27*z0^3 - x^25*y*z0^4 + x^28*y + 2*x^28*z0 - 2*x^26*z0^3 - 2*x^24*y*z0^4 - x^27*y - 2*x^27*z0 + x^25*z0^3 - 2*x^23*y*z0^4 + x^26*y + 2*x^26*z0 - 2*x^24*y*z0^2 - x^24*z0^3 - 2*x^22*y*z0^4 - x^25*y - 2*x^25*z0 - x^23*y*z0^2 + 2*x^23*z0^3 - 2*x^21*y*z0^4 - x^24*y - x^24*z0 - x^22*y*z0^2 + 2*x^22*z0^3 - x^23*y + x^23*z0 - 2*x^21*z0^3 - x^19*y*z0^4 + x^22*y - 2*x^22*z0 - x^20*y*z0^2 + x^20*z0^3 + 2*x^18*y*z0^4 + 2*x^21*y + 2*x^19*y*z0^2 - 2*x^19*z0^3 + x^17*y*z0^4 + x^20*y + x^18*y*z0^2 - 2*x^18*z0^3 - x^16*y*z0^4 + x^19*y + x^17*y*z0^2 - 2*x^17*z0^3 - 2*x^15*y*z0^4 + x^18*y - 2*x^18*z0 + x^16*z0^3 - x^14*y*z0^4 + 2*x^17*z0 + x^15*z0^3 - x^13*y*z0^4 + 2*x^16*y + x^16*z0 + x^14*y*z0^2 - x^14*z0^3 + x^12*y*z0^4 - x^13*y*z0^2 - 2*x^13*z0^3 + 2*x^11*y*z0^4 - x^14*y + x^14*z0 - x^12*y*z0^2 - x^12*z0^3 + 2*x^13*z0 - 2*x^11*z0^3 - x^9*y*z0^4 - x^12*y - x^10*y*z0^2 + x^10*z0^3 + 2*x^8*y*z0^4 + 2*x^11*y - x^11*z0 + 2*x^9*y*z0^2 + x^9*z0^3 + 2*x^7*y*z0^4 - x^10*y + 2*x^10*z0 + 2*x^8*z0^3 + x^6*y*z0^4 - x^9*y - x^9*z0 - x^7*y*z0^2 - 2*x^7*z0^3 - x^5*y*z0^4 + 2*x^8*z0 + x^6*y*z0^2 - 2*x^7*y + 2*x^7*z0 + x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^6*y - 2*x^4*z0^3 - 2*x^2*y*z0^4 + 2*x^3*y*z0^2 - 2*x^3*z0^3 + 2*x^4*y - 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^3*y - x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((2*x^61*z0^2 - 2*x^59*z0^4 + 2*x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^56*y^2*z0^4 + x^61 - 2*x^57*y^2*z0^2 + 2*x^60 - x^58*y^2 - 2*x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 - 2*x^57*z0^2 - x^58 - 2*x^57 + 2*x^55*z0^2 - 2*x^53*z0^4 + 2*x^54*z0^2 + x^55 + 2*x^54 - 2*x^52*z0^2 + 2*x^50*z0^4 - 2*x^51*z0^2 - x^52 - 2*x^51 + 2*x^49*z0^2 - 2*x^47*z0^4 + 2*x^48*z0^2 + x^49 + 2*x^48 - 2*x^46*z0^2 + 2*x^44*z0^4 - 2*x^45*z0^2 - x^46 - 2*x^45 + 2*x^43*z0^2 + x^41*z0^4 + x^42*z0^2 - 2*x^40*z0^4 + x^43 + 2*x^41*z0^2 + x^39*y^2*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 + 2*x^42 + x^40*y*z0 - x^38*y*z0^3 + x^38*z0^4 - 2*x^41 + x^39*y*z0 + 2*x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 - 2*x^36*z0^4 - 2*x^37*z0^2 - x^35*y*z0^3 + 2*x^38 - x^36*y*z0 - 2*x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^34*z0^4 - x^37 + 2*x^35*y*z0 - x^33*y*z0^3 - 2*x^33*z0^4 - x^36 - x^34*y*z0 - 2*x^34*z0^2 + x^32*y*z0^3 + x^35 + 2*x^31*y*z0^3 - 2*x^31*z0^4 - 2*x^34 - 2*x^32*y*z0 + x^32*z0^2 + x^30*y*z0^3 - 2*x^30*z0^4 - x^33 - 2*x^31*y*z0 + x^29*y*z0^3 - 2*x^29*z0^4 + 2*x^32 + x^30*y*z0 + 2*x^30*z0^2 - x^28*y*z0^3 - x^28*z0^4 - 2*x^31 + x^29*y*z0 - 2*x^29*z0^2 - x^27*z0^4 - 2*x^30 + 2*x^28*y*z0 - 2*x^28*z0^2 + 2*x^26*y*z0^3 - 2*x^26*z0^4 - 2*x^29 - x^27*y*z0 - 2*x^27*z0^2 - x^25*y*z0^3 + 2*x^25*z0^4 - x^28 - 2*x^26*y*z0 - 2*x^26*z0^2 - x^24*y*z0^3 - x^24*z0^4 - x^27 - 2*x^25*y*z0 + 2*x^25*z0^2 + x^23*y*z0^3 - 2*x^23*z0^4 + 2*x^26 + 2*x^24*y*z0 - 2*x^24*z0^2 + 2*x^22*z0^4 - x^25 + 2*x^23*y*z0 + 2*x^21*y*z0^3 - x^21*z0^4 + x^24 - 2*x^22*y*z0 + x^22*z0^2 - x^20*y*z0^3 - x^20*z0^4 + 2*x^21*y*z0 + 2*x^21*z0^2 - x^19*z0^4 + 2*x^22 + x^20*y*z0 + x^20*z0^2 + 2*x^18*z0^4 - x^21 + x^19*y*z0 - 2*x^19*z0^2 + 2*x^17*y*z0^3 - x^17*z0^4 - 2*x^20 - x^18*y*z0 - x^16*y*z0^3 - x^19 - 2*x^17*y*z0 - x^15*y*z0^3 + x^15*z0^4 + x^18 - 2*x^16*z0^2 + x^14*y*z0^3 + 2*x^14*z0^4 - x^17 + x^15*y*z0 + x^15*z0^2 - 2*x^13*y*z0^3 + 2*x^13*z0^4 + 2*x^16 + x^14*y*z0 + x^14*z0^2 - 2*x^12*z0^4 - 2*x^13*y*z0 - 2*x^13*z0^2 + 2*x^11*z0^4 + 2*x^14 + x^12*y*z0 + 2*x^12*z0^2 - x^10*y*z0^3 + 2*x^10*z0^4 + 2*x^13 + x^11*y*z0 - x^11*z0^2 + 2*x^9*y*z0^3 - 2*x^12 - x^8*y*z0^3 - x^8*z0^4 - 2*x^11 + 2*x^9*z0^2 + x^7*y*z0^3 - 2*x^7*z0^4 + 2*x^10 - 2*x^8*y*z0 - 2*x^8*z0^2 + 2*x^6*y*z0^3 - x^9 - x^7*y*z0 - x^7*z0^2 - 2*x^5*z0^4 + 2*x^6*y*z0 + x^6*z0^2 - 2*x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^7 + x^5*z0^2 - 2*x^3*y*z0^3 + x^3*z0^4 + x^6 - 2*x^4*y*z0 - x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 - 2*x^3*y*z0 - x^3*z0^2 + x^2*z0^2 + 2*x^3)/y) * dx, - ((-2*x^60*z0^3 - 2*x^59*z0^3 + 2*x^57*y^2*z0^3 - x^58*z0^3 + 2*x^56*y^2*z0^3 + 2*x^59*z0 + 2*x^57*z0^3 + x^55*y^2*z0^3 - 2*x^56*y^2*z0 + 2*x^56*z0^3 + x^55*z0^3 - 2*x^56*z0 - 2*x^54*z0^3 - 2*x^53*z0^3 - x^52*z0^3 + 2*x^53*z0 + 2*x^51*z0^3 + 2*x^50*z0^3 + x^49*z0^3 - 2*x^50*z0 - 2*x^48*z0^3 - 2*x^47*z0^3 - x^46*z0^3 + 2*x^47*z0 + 2*x^45*z0^3 + 2*x^44*z0^3 + x^43*z0^3 - 2*x^44*z0 + 2*x^42*z0^3 - 2*x^41*z0^3 + x^39*y^2*z0^3 + x^38*y*z0^4 + 2*x^41*z0 + x^39*z0^3 - 2*x^40*z0 + x^36*y*z0^4 - x^39*y - x^39*z0 + x^37*y*z0^2 + x^37*z0^3 - 2*x^35*y*z0^4 - 2*x^38*y - x^36*y*z0^2 - 2*x^36*z0^3 + x^35*y*z0^2 - 2*x^35*z0^3 - x^33*y*z0^4 + x^36*y + 2*x^36*z0 - 2*x^34*y*z0^2 + x^34*z0^3 + 2*x^32*y*z0^4 - x^35*z0 - 2*x^33*y*z0^2 + x^33*z0^3 - 2*x^31*y*z0^4 + x^34*y + x^34*z0 - 2*x^32*y*z0^2 - 2*x^32*z0^3 - 2*x^30*y*z0^4 + x^33*y + 2*x^33*z0 + 2*x^31*y*z0^2 + 2*x^31*z0^3 + 2*x^29*y*z0^4 - x^32*y + 2*x^32*z0 - x^30*z0^3 - x^28*y*z0^4 - 2*x^31*z0 - x^29*y*z0^2 - 2*x^29*z0^3 + 2*x^27*y*z0^4 - 2*x^30*z0 - 2*x^26*y*z0^4 - x^29*y - x^27*y*z0^2 - 2*x^27*z0^3 + 2*x^25*y*z0^4 + x^28*y + 2*x^28*z0 - 2*x^26*y*z0^2 + x^26*z0^3 + 2*x^24*y*z0^4 - 2*x^27*z0 + 2*x^25*y*z0^2 - 2*x^25*z0^3 - x^23*y*z0^4 + x^26*y - 2*x^26*z0 - x^24*y*z0^2 + x^24*z0^3 - x^22*y*z0^4 + x^25*y + x^23*y*z0^2 + x^23*z0^3 - x^21*y*z0^4 + 2*x^24*y - x^24*z0 - x^22*y*z0^2 - 2*x^23*y - 2*x^23*z0 - 2*x^21*y*z0^2 + 2*x^21*z0^3 + 2*x^19*y*z0^4 + x^20*y*z0^2 - 2*x^20*z0^3 - 2*x^18*y*z0^4 + x^19*y*z0^2 + x^19*z0^3 - 2*x^17*y*z0^4 - 2*x^20*z0 + x^18*y*z0^2 + 2*x^16*y*z0^4 + 2*x^19*z0 - 2*x^17*y*z0^2 - x^17*z0^3 - 2*x^15*y*z0^4 - x^18*y - x^18*z0 - 2*x^16*z0^3 + x^14*y*z0^4 - 2*x^17*z0 + 2*x^15*y*z0^2 - x^15*z0^3 + 2*x^13*y*z0^4 + 2*x^16*y - 2*x^16*z0 + x^14*y*z0^2 + x^12*y*z0^4 + 2*x^15*y + x^15*z0 - x^13*z0^3 + 2*x^11*y*z0^4 + 2*x^14*y + x^14*z0 - x^12*y*z0^2 - 2*x^12*z0^3 - 2*x^10*y*z0^4 + 2*x^13*y + x^13*z0 + x^9*y*z0^4 + 2*x^12*y - x^12*z0 + x^10*y*z0^2 - 2*x^11*y - 2*x^9*y*z0^2 + 2*x^9*z0^3 + x^7*y*z0^4 + 2*x^10*y - 2*x^10*z0 - 2*x^8*z0^3 - x^9*y - x^9*z0 - 2*x^7*y*z0^2 - 2*x^8*z0 - 2*x^6*y*z0^2 - 2*x^6*z0^3 + 2*x^4*y*z0^4 + 2*x^7*y + 2*x^7*z0 + 2*x^5*y*z0^2 + 2*x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y - x^5*z0 - 2*x^4*y - x^4*z0 - 2*x^2*y*z0^2 + x^2*z0^3 - x^3*y - x^3*z0 + x^2*y)/y) * dx, - ((-2*x^61*z0^4 + x^60*z0^4 + 2*x^58*y^2*z0^4 - x^61*z0^2 + 2*x^59*z0^4 - x^57*y^2*z0^4 - 2*x^60*z0^2 + x^58*y^2*z0^2 + 2*x^58*z0^4 - 2*x^56*y^2*z0^4 + 2*x^61 + 2*x^57*y^2*z0^2 - x^57*z0^4 - 2*x^58*y^2 + x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*z0^2 - 2*x^55*z0^4 - 2*x^58 + x^54*z0^4 - x^55*z0^2 + 2*x^53*z0^4 - 2*x^54*z0^2 + 2*x^52*z0^4 + 2*x^55 - x^51*z0^4 + x^52*z0^2 - 2*x^50*z0^4 + 2*x^51*z0^2 - 2*x^49*z0^4 - 2*x^52 + x^48*z0^4 - x^49*z0^2 + 2*x^47*z0^4 - 2*x^48*z0^2 + 2*x^46*z0^4 + 2*x^49 - x^45*z0^4 + x^46*z0^2 - 2*x^44*z0^4 + 2*x^45*z0^2 - 2*x^43*z0^4 - 2*x^46 - x^43*z0^2 + x^41*z0^4 + x^39*y^2*z0^4 - 2*x^42*z0^2 - x^40*y*z0^3 + x^40*z0^4 + 2*x^43 - x^41*z0^2 - x^39*y*z0^3 - x^39*z0^4 + 2*x^40*y*z0 + 2*x^40*z0^2 - 2*x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + x^39*y*z0 - 2*x^39*z0^2 - x^37*y*z0^3 + x^40 + x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + 2*x^36*z0^4 + 2*x^37*z0^2 - x^35*y*z0^3 + 2*x^38 + 2*x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 - x^37 - 2*x^35*y*z0 - x^33*y*z0^3 - x^33*z0^4 - x^36 + x^34*y*z0 + 2*x^34*z0^2 - x^32*y*z0^3 + x^32*z0^4 + x^33*y*z0 - x^33*z0^2 - x^31*y*z0^3 + x^31*z0^4 - x^34 - 2*x^32*y*z0 - x^32*z0^2 + x^30*y*z0^3 - x^30*z0^4 + 2*x^31*y*z0 - x^31*z0^2 + x^32 + x^30*y*z0 + 2*x^30*z0^2 + x^28*y*z0^3 + x^28*z0^4 - 2*x^29*y*z0 + 2*x^27*y*z0^3 + 2*x^27*z0^4 - 2*x^30 + 2*x^28*z0^2 + x^26*y*z0^3 - 2*x^26*z0^4 - 2*x^27*z0^2 + 2*x^25*y*z0^3 + x^28 + 2*x^26*y*z0 + x^26*z0^2 + x^24*y*z0^3 + x^24*z0^4 + 2*x^27 + x^25*y*z0 - x^25*z0^2 + 2*x^23*y*z0^3 + x^26 - x^24*y*z0 + 2*x^24*z0^2 - x^22*y*z0^3 + x^25 - 2*x^23*y*z0 - 2*x^23*z0^2 - 2*x^21*y*z0^3 + x^21*z0^4 - x^24 + x^22*y*z0 - x^22*z0^2 + x^20*z0^4 - 2*x^23 - 2*x^21*z0^2 + x^22 + 2*x^20*y*z0 - x^20*z0^2 + 2*x^18*y*z0^3 + x^21 - x^19*y*z0 + 2*x^17*y*z0^3 + 2*x^17*z0^4 - x^20 - 2*x^18*y*z0 + 2*x^18*z0^2 + x^16*y*z0^3 + x^16*z0^4 - 2*x^19 + x^17*y*z0 - x^17*z0^2 + 2*x^15*y*z0^3 - x^18 - x^16*y*z0 + 2*x^16*z0^2 + 2*x^14*y*z0^3 - x^14*z0^4 - 2*x^17 - x^15*y*z0 - 2*x^15*z0^2 + 2*x^13*y*z0^3 + 2*x^16 - 2*x^14*y*z0 + x^14*z0^2 - 2*x^12*y*z0^3 + x^12*z0^4 - x^15 - x^13*y*z0 - x^11*y*z0^3 - x^11*z0^4 - 2*x^14 - 2*x^12*y*z0 + 2*x^12*z0^2 - x^11*y*z0 - x^11*z0^2 + x^9*y*z0^3 + x^9*z0^4 + 2*x^12 + x^10*y*z0 + x^10*z0^2 + 2*x^8*z0^4 - x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 - x^7*y*z0^3 - x^7*z0^4 + 2*x^8*y*z0 - x^8*z0^2 + 2*x^6*y*z0^3 - 2*x^9 - x^7*y*z0 + x^7*z0^2 + x^5*z0^4 - x^8 + x^6*y*z0 - x^4*z0^4 - 2*x^7 - 2*x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*y*z0^3 + x^6 - 2*x^4*y*z0 + x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 - 2*x^3*z0^2 + x^2*y*z0 + 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((2*x^61*z0^4 - 2*x^60*z0^4 - 2*x^58*y^2*z0^4 - 2*x^61*z0^2 + x^59*z0^4 + 2*x^57*y^2*z0^4 - x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^58*z0^4 - x^56*y^2*z0^4 - x^61 + x^57*y^2*z0^2 + 2*x^57*z0^4 + x^60 + x^58*y^2 + 2*x^58*z0^2 - x^56*z0^4 - x^57*y^2 + x^57*z0^2 + 2*x^55*z0^4 + x^58 - 2*x^54*z0^4 - x^57 - 2*x^55*z0^2 + x^53*z0^4 - x^54*z0^2 - 2*x^52*z0^4 - x^55 + 2*x^51*z0^4 + x^54 + 2*x^52*z0^2 - x^50*z0^4 + x^51*z0^2 + 2*x^49*z0^4 + x^52 - 2*x^48*z0^4 - x^51 - 2*x^49*z0^2 + x^47*z0^4 - x^48*z0^2 - 2*x^46*z0^4 - x^49 + 2*x^45*z0^4 + x^48 + 2*x^46*z0^2 - x^44*z0^4 + x^45*z0^2 + 2*x^43*z0^4 + x^46 - 2*x^42*z0^4 - x^45 - 2*x^43*z0^2 - x^42*z0^2 + x^40*y*z0^3 - 2*x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^42 + x^40*y^2 - x^40*y*z0 - x^40*z0^2 - 2*x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + 2*x^39*y*z0 - 2*x^39*z0^2 - 2*x^37*y*z0^3 - x^37*z0^4 + x^40 - 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 + x^39 + x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 - 2*x^35*z0^4 + 2*x^36*y*z0 + 2*x^36*z0^2 - x^34*y*z0^3 + 2*x^34*z0^4 + 2*x^37 - 2*x^35*y*z0 - 2*x^35*z0^2 - x^33*z0^4 + 2*x^36 - x^34*y*z0 - 2*x^34*z0^2 - 2*x^32*y*z0^3 + x^32*z0^4 - x^35 - x^33*z0^2 + 2*x^31*y*z0^3 - x^31*z0^4 + 2*x^34 + 2*x^32*y*z0 + x^32*z0^2 - 2*x^30*y*z0^3 - x^31*y*z0 - 2*x^31*z0^2 - 2*x^29*y*z0^3 - 2*x^29*z0^4 + x^32 + x^30*y*z0 - x^30*z0^2 - x^28*y*z0^3 - 2*x^31 + 2*x^29*y*z0 + x^29*z0^2 + x^27*y*z0^3 - 2*x^30 + x^28*y*z0 + 2*x^28*z0^2 - 2*x^26*y*z0^3 + x^26*z0^4 - 2*x^27*z0^2 - 2*x^25*y*z0^3 - 2*x^25*z0^4 + 2*x^26*z0^2 - 2*x^24*y*z0^3 + x^24*z0^4 + 2*x^27 - 2*x^25*y*z0 - 2*x^25*z0^2 + 2*x^23*y*z0^3 + x^23*z0^4 - x^24*y*z0 + 2*x^24*z0^2 + x^22*y*z0^3 + x^22*z0^4 - 2*x^25 - 2*x^23*y*z0 - 2*x^21*z0^4 - 2*x^24 - x^22*y*z0 - x^20*y*z0^3 - x^20*z0^4 + 2*x^23 - x^21*y*z0 + x^21*z0^2 + x^22 + x^20*y*z0 + 2*x^20*z0^2 - 2*x^18*y*z0^3 - 2*x^18*z0^4 + x^21 - 2*x^19*y*z0 + x^19*z0^2 - 2*x^17*y*z0^3 + 2*x^18*y*z0 - 2*x^18*z0^2 + x^16*y*z0^3 + x^16*z0^4 - x^19 - 2*x^17*y*z0 + x^17*z0^2 + x^15*z0^4 + 2*x^18 + 2*x^16*y*z0 - 2*x^14*y*z0^3 + 2*x^14*z0^4 - x^17 + 2*x^15*y*z0 - 2*x^15*z0^2 + 2*x^13*z0^4 - 2*x^16 + 2*x^14*y*z0 - 2*x^14*z0^2 - x^12*z0^4 + 2*x^15 - x^13*y*z0 + 2*x^13*z0^2 - 2*x^11*z0^4 + x^14 + x^12*y*z0 + 2*x^10*y*z0^3 - x^10*z0^4 - x^13 + 2*x^11*y*z0 + x^11*z0^2 + x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^12 - 2*x^10*z0^2 + x^8*z0^4 - 2*x^11 - x^9*y*z0 - x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 + 2*x^8*y*z0 - x^8*z0^2 - 2*x^6*y*z0^3 - x^6*z0^4 - 2*x^9 - x^7*y*z0 + x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 - 2*x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 - x^4*z0^4 - x^5*y*z0 + x^5*z0^2 + 2*x^3*y*z0^3 + x^6 + x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - x^5 + x^3*y*z0 - 2*x^3*z0^2 + x^2*y*z0 + x^2*z0^2 - 2*x^3 + 2*x^2)/y) * dx, - ((-2*x^61*z0^3 + x^60*z0^3 + 2*x^58*y^2*z0^3 - 2*x^61*z0 + 2*x^59*z0^3 - x^57*y^2*z0^3 + 2*x^60*z0 + 2*x^58*y^2*z0 - 2*x^56*y^2*z0^3 - 2*x^59*z0 - 2*x^57*y^2*z0 - x^57*z0^3 + 2*x^55*y^2*z0^3 + 2*x^58*z0 + 2*x^56*y^2*z0 - 2*x^56*z0^3 - 2*x^57*z0 + 2*x^56*z0 + x^54*z0^3 - 2*x^55*z0 + 2*x^53*z0^3 + 2*x^54*z0 - 2*x^53*z0 - x^51*z0^3 + 2*x^52*z0 - 2*x^50*z0^3 - 2*x^51*z0 + 2*x^50*z0 + x^48*z0^3 - 2*x^49*z0 + 2*x^47*z0^3 + 2*x^48*z0 - 2*x^47*z0 - x^45*z0^3 + 2*x^46*z0 - 2*x^44*z0^3 - 2*x^45*z0 + 2*x^44*z0 + x^42*z0^3 + 2*x^43*z0 - 2*x^39*y*z0^4 + 2*x^42*z0 + x^40*y^2*z0 - x^40*y*z0^2 + x^41*z0 - 2*x^39*y*z0^2 - 2*x^39*z0^3 + 2*x^37*y*z0^4 - x^40*y + 2*x^40*z0 - 2*x^38*y*z0^2 + x^38*z0^3 - 2*x^36*y*z0^4 + x^39*y + x^39*z0 + x^37*z0^3 - 2*x^35*y*z0^4 - 2*x^38*y + x^38*z0 - 2*x^36*z0^3 - x^34*y*z0^4 - 2*x^37*y + 2*x^37*z0 + x^33*y*z0^4 + x^36*y - 2*x^36*z0 - x^34*y*z0^2 - 2*x^34*z0^3 + 2*x^32*y*z0^4 + 2*x^35*y - 2*x^35*z0 + 2*x^33*z0^3 + x^31*y*z0^4 + 2*x^34*y - x^34*z0 - x^32*z0^3 - x^30*y*z0^4 + x^33*y - 2*x^33*z0 - x^31*y*z0^2 + 2*x^29*y*z0^4 - x^32*y + x^30*y*z0^2 + 2*x^30*z0^3 - x^31*y + x^31*z0 + 2*x^29*y*z0^2 - 2*x^29*z0^3 - 2*x^27*y*z0^4 - x^30*z0 + 2*x^28*y*z0^2 + 2*x^28*z0^3 + x^26*y*z0^4 + 2*x^29*z0 + 2*x^27*y*z0^2 + 2*x^27*z0^3 - x^25*y*z0^4 - 2*x^28*y + x^28*z0 - x^26*y*z0^2 - x^26*z0^3 + x^24*y*z0^4 + 2*x^27*y + 2*x^27*z0 - 2*x^25*y*z0^2 - x^25*z0^3 - 2*x^23*y*z0^4 + 2*x^26*z0 - x^24*z0^3 + 2*x^22*y*z0^4 - 2*x^25*y - x^23*z0^3 - 2*x^21*y*z0^4 - 2*x^24*y + x^24*z0 + x^22*y*z0^2 + x^22*z0^3 - 2*x^20*y*z0^4 + x^23*y - 2*x^23*z0 + x^21*y*z0^2 + x^21*z0^3 + x^19*y*z0^4 - 2*x^20*y*z0^2 - x^20*z0^3 - 2*x^18*y*z0^4 + x^21*y - x^21*z0 - 2*x^19*y*z0^2 + 2*x^19*z0^3 - 2*x^17*y*z0^4 + x^20*y + x^20*z0 - 2*x^18*y*z0^2 - x^16*y*z0^4 - 2*x^19*y - 2*x^19*z0 + 2*x^17*y*z0^2 - 2*x^17*z0^3 + x^15*y*z0^4 + x^18*z0 - 2*x^16*y*z0^2 + 2*x^14*y*z0^4 - x^17*y - x^17*z0 - x^15*y*z0^2 - 2*x^15*z0^3 + x^13*y*z0^4 - x^16*y - x^14*y*z0^2 + 2*x^14*z0^3 - x^15*y - x^15*z0 + 2*x^13*y*z0^2 + 2*x^13*z0^3 - x^11*y*z0^4 + 2*x^14*y - 2*x^14*z0 + 2*x^13*y + 2*x^13*z0 - x^11*z0^3 - x^9*y*z0^4 - x^12*y - x^12*z0 + x^10*y*z0^2 + 2*x^8*y*z0^4 + 2*x^11*y - 2*x^11*z0 - 2*x^9*y*z0^2 + x^9*z0^3 + 2*x^7*y*z0^4 + x^10*y - 2*x^10*z0 - x^8*y*z0^2 + x^8*z0^3 + 2*x^6*y*z0^4 + 2*x^9*y + x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 + 2*x^5*y*z0^4 + 2*x^8*y - x^6*z0^3 - 2*x^7*z0 + 2*x^5*y*z0^2 - x^5*z0^3 + x^3*y*z0^4 + x^6*y - x^6*z0 - 2*x^4*y*z0^2 - 2*x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - 2*x^3*y*z0^2 - x^3*z0^3 - 2*x^4*y + x^4*z0 + x^2*z0^3 + x^3*y - x^3*z0 + 2*x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + x^60*z0^4 + 2*x^58*y^2*z0^4 - 2*x^59*z0^4 - x^57*y^2*z0^4 - 2*x^60*z0^2 + 2*x^58*z0^4 + 2*x^56*y^2*z0^4 + 2*x^57*y^2*z0^2 - x^57*z0^4 + x^60 + 2*x^56*z0^4 - x^57*y^2 + 2*x^57*z0^2 - 2*x^55*z0^4 + x^54*z0^4 - x^57 - 2*x^53*z0^4 - 2*x^54*z0^2 + 2*x^52*z0^4 - x^51*z0^4 + x^54 + 2*x^50*z0^4 + 2*x^51*z0^2 - 2*x^49*z0^4 + x^48*z0^4 - x^51 - 2*x^47*z0^4 - 2*x^48*z0^2 + 2*x^46*z0^4 - x^45*z0^4 + x^48 + 2*x^44*z0^4 + 2*x^45*z0^2 - 2*x^43*z0^4 + x^42*z0^4 - x^45 - x^43*z0^2 + x^41*z0^4 - 2*x^42*z0^2 + x^40*y^2*z0^2 - x^40*y*z0^3 + 2*x^40*z0^4 - x^39*z0^4 + x^42 + x^40*z0^2 - 2*x^38*y*z0^3 + x^38*z0^4 - 2*x^41 - x^39*y*z0 + 2*x^39*z0^2 + x^37*y*z0^3 - 2*x^37*z0^4 - 2*x^40 + 2*x^38*y*z0 - x^36*z0^4 - x^39 - x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 + 2*x^35*z0^4 + 2*x^38 + x^36*y*z0 - 2*x^36*z0^2 - 2*x^34*y*z0^3 + 2*x^34*z0^4 - 2*x^37 - x^35*y*z0 - 2*x^35*z0^2 - 2*x^33*y*z0^3 - 2*x^33*z0^4 + x^34*y*z0 - x^34*z0^2 - 2*x^32*y*z0^3 - 2*x^33*y*z0 - x^33*z0^2 + 2*x^31*y*z0^3 + 2*x^31*z0^4 - x^34 - 2*x^32*y*z0 + 2*x^32*z0^2 - 2*x^30*y*z0^3 + 2*x^30*z0^4 + 2*x^33 + x^31*y*z0 + 2*x^31*z0^2 - x^29*y*z0^3 + x^32 + x^30*y*z0 - x^30*z0^2 - x^28*y*z0^3 + x^28*z0^4 + 2*x^31 + x^29*y*z0 + x^29*z0^2 - 2*x^27*y*z0^3 - 2*x^27*z0^4 + 2*x^30 - 2*x^28*y*z0 - x^28*z0^2 - 2*x^26*y*z0^3 + x^26*z0^4 + x^29 - x^27*y*z0 - 2*x^27*z0^2 - x^25*z0^4 - 2*x^28 - x^26*y*z0 + x^26*z0^2 + x^24*y*z0^3 + 2*x^24*z0^4 - x^25*y*z0 - 2*x^25*z0^2 + x^23*y*z0^3 + x^23*z0^4 - x^26 + 2*x^24*y*z0 + 2*x^24*z0^2 + 2*x^22*z0^4 - 2*x^25 + x^23*y*z0 + 2*x^21*y*z0^3 - 2*x^21*z0^4 - x^24 + 2*x^22*y*z0 - x^22*z0^2 - 2*x^20*y*z0^3 + 2*x^20*z0^4 + 2*x^23 + x^21*y*z0 + 2*x^21*z0^2 - 2*x^19*z0^4 - 2*x^22 + x^20*y*z0 + 2*x^20*z0^2 + 2*x^18*y*z0^3 - x^19*y*z0 + 2*x^19*z0^2 - 2*x^17*y*z0^3 + x^17*z0^4 - x^20 - x^18*y*z0 + 2*x^16*z0^4 - 2*x^19 - x^15*y*z0^3 + x^15*z0^4 - 2*x^18 - 2*x^16*y*z0 - 2*x^14*y*z0^3 - 2*x^14*z0^4 - x^17 + 2*x^15*z0^2 + x^13*y*z0^3 - 2*x^13*z0^4 - 2*x^16 - 2*x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 + x^15 + 2*x^13*y*z0 - 2*x^13*z0^2 + x^11*y*z0^3 - x^11*z0^4 - x^14 + x^12*y*z0 - 2*x^12*z0^2 - x^10*y*z0^3 - 2*x^10*z0^4 + x^13 + x^11*y*z0 - x^11*z0^2 - 2*x^9*y*z0^3 - 2*x^9*z0^4 + x^10*y*z0 - x^10*z0^2 + x^8*y*z0^3 - x^8*z0^4 - x^11 + x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 + 2*x^8*y*z0 - 2*x^6*y*z0^3 + x^6*z0^4 - x^9 - x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 - 2*x^5*z0^4 + x^8 + x^6*y*z0 + 2*x^4*y*z0^3 - 2*x^4*z0^4 + x^7 - 2*x^5*y*z0 - 2*x^5*z0^2 + x^3*z0^4 + 2*x^6 - x^4*y*z0 - x^4*z0^2 + x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 - 2*x^3*z0^2 + x^2*y*z0 + x^2*z0^2 - x^3 + 2*x^2)/y) * dx, - ((x^61*z0^3 - x^58*y^2*z0^3 + x^59*z0^3 + 2*x^60*z0 - 2*x^58*z0^3 - x^56*y^2*z0^3 - x^59*z0 - 2*x^57*y^2*z0 + x^55*y^2*z0^3 + x^56*y^2*z0 - x^56*z0^3 - 2*x^57*z0 + 2*x^55*z0^3 + x^56*z0 + x^53*z0^3 + 2*x^54*z0 - 2*x^52*z0^3 - x^53*z0 - x^50*z0^3 - 2*x^51*z0 + 2*x^49*z0^3 + x^50*z0 + x^47*z0^3 + 2*x^48*z0 - 2*x^46*z0^3 - x^47*z0 - x^44*z0^3 - 2*x^45*z0 + x^43*z0^3 + x^44*z0 + x^40*y^2*z0^3 + 2*x^41*z0^3 + x^39*y*z0^4 + 2*x^42*z0 - 2*x^40*y*z0^2 - 2*x^40*z0^3 + x^38*y*z0^4 - x^41*z0 + x^37*y*z0^4 - x^40*z0 + 2*x^38*y*z0^2 + 2*x^38*z0^3 + x^39*y + x^39*z0 + 2*x^37*y*z0^2 - 2*x^37*z0^3 - 2*x^36*y*z0^2 - 2*x^36*z0^3 - x^34*y*z0^4 + 2*x^37*z0 + 2*x^35*y*z0^2 - 2*x^35*z0^3 + x^33*y*z0^4 - 2*x^36*y + x^36*z0 - 2*x^34*y*z0^2 - x^34*z0^3 - x^35*y + 2*x^35*z0 - x^33*y*z0^2 - 2*x^33*z0^3 - x^34*z0 - x^32*z0^3 - x^30*y*z0^4 - 2*x^33*y + 2*x^33*z0 - 2*x^31*y*z0^2 + 2*x^31*z0^3 - 2*x^29*y*z0^4 + x^32*y - 2*x^32*z0 + 2*x^30*y*z0^2 + x^28*y*z0^4 + x^31*y - x^31*z0 - 2*x^29*y*z0^2 + 2*x^29*z0^3 - 2*x^30*y + 2*x^30*z0 - x^26*y*z0^4 - x^29*y + 2*x^29*z0 + x^27*y*z0^2 - x^27*z0^3 + 2*x^25*y*z0^4 - 2*x^28*y + 2*x^26*y*z0^2 + 2*x^24*y*z0^4 + x^27*z0 + x^25*y*z0^2 + x^25*z0^3 - 2*x^23*y*z0^4 + x^26*y - 2*x^26*z0 + 2*x^24*y*z0^2 - x^24*z0^3 + x^25*y - 2*x^25*z0 + 2*x^23*z0^3 - 2*x^21*y*z0^4 - x^24*y + 2*x^24*z0 + x^22*y*z0^2 - 2*x^22*z0^3 - x^20*y*z0^4 + 2*x^23*z0 - 2*x^21*z0^3 + x^19*y*z0^4 + 2*x^22*y - 2*x^20*z0^3 - x^21*y + 2*x^21*z0 + x^19*z0^3 - x^17*y*z0^4 - 2*x^20*y - 2*x^20*z0 - x^18*y*z0^2 - 2*x^16*y*z0^4 - x^19*y - x^19*z0 - 2*x^17*y*z0^2 - x^17*z0^3 - 2*x^18*y + 2*x^16*y*z0^2 - 2*x^16*z0^3 - x^14*y*z0^4 + 2*x^17*z0 - x^15*z0^3 - 2*x^13*y*z0^4 + x^16*z0 - x^14*y*z0^2 - x^14*z0^3 + x^12*y*z0^4 - 2*x^15*z0 - 2*x^13*y*z0^2 - 2*x^13*z0^3 - 2*x^11*y*z0^4 + 2*x^14*y - 2*x^14*z0 + 2*x^12*y*z0^2 + 2*x^12*z0^3 - 2*x^10*y*z0^4 - x^13*y + 2*x^11*y*z0^2 - x^11*z0^3 - x^9*y*z0^4 + 2*x^12*z0 - x^8*y*z0^4 + x^11*y + 2*x^11*z0 - 2*x^9*y*z0^2 + 2*x^7*y*z0^4 - x^10*y - x^10*z0 + 2*x^8*y*z0^2 + 2*x^6*y*z0^4 + 2*x^9*y - 2*x^9*z0 - x^7*y*z0^2 - x^7*z0^3 + 2*x^5*y*z0^4 + 2*x^8*z0 + x^6*y*z0^2 - 2*x^6*z0^3 + 2*x^4*y*z0^4 - x^7*y + 2*x^7*z0 + 2*x^3*y*z0^4 + 2*x^6*y + x^6*z0 - 2*x^4*y*z0^2 - x^2*y*z0^4 - 2*x^5*z0 + x^3*y*z0^2 + x^3*z0^3 + 2*x^4*y - 2*x^4*z0 - 2*x^2*y*z0^2 - 2*x^3*y - x^3*z0 - 2*x^2*y + x^2*z0)/y) * dx, - ((-x^61*z0^4 - x^60*z0^4 + x^58*y^2*z0^4 - 2*x^59*z0^4 + x^57*y^2*z0^4 - 2*x^60*z0^2 + x^58*z0^4 + 2*x^56*y^2*z0^4 - x^61 + 2*x^57*y^2*z0^2 + x^57*z0^4 - 2*x^60 + x^58*y^2 + 2*x^56*z0^4 + 2*x^57*y^2 + 2*x^57*z0^2 - x^55*z0^4 + x^58 - x^54*z0^4 + 2*x^57 - 2*x^53*z0^4 - 2*x^54*z0^2 + x^52*z0^4 - x^55 + x^51*z0^4 - 2*x^54 + 2*x^50*z0^4 + 2*x^51*z0^2 - x^49*z0^4 + x^52 - x^48*z0^4 + 2*x^51 - 2*x^47*z0^4 - 2*x^48*z0^2 + x^46*z0^4 - x^49 + x^45*z0^4 - 2*x^48 + 2*x^44*z0^4 + 2*x^45*z0^2 - 2*x^43*z0^4 + x^46 - x^42*z0^4 + x^40*y^2*z0^4 + 2*x^45 - x^41*z0^4 - 2*x^42*z0^2 + 2*x^40*y*z0^3 + x^40*z0^4 - x^43 - 2*x^42 - 2*x^40*z0^2 - 2*x^38*y*z0^3 + 2*x^38*z0^4 + x^41 - x^39*y*z0 + 2*x^39*z0^2 + 2*x^37*y*z0^3 + 2*x^37*z0^4 + x^40 + 2*x^38*y*z0 + x^36*z0^4 + 2*x^39 - x^37*y*z0 + x^37*z0^2 - 2*x^35*y*z0^3 - x^35*z0^4 - 2*x^38 - 2*x^36*z0^2 - 2*x^34*y*z0^3 - x^35*y*z0 + 2*x^35*z0^2 + 2*x^33*z0^4 + 2*x^36 + 2*x^34*y*z0 + x^34*z0^2 + 2*x^32*y*z0^3 + 2*x^32*z0^4 + x^35 - x^33*y*z0 - x^33*z0^2 - x^31*y*z0^3 - x^31*z0^4 - 2*x^34 + 2*x^32*y*z0 + 2*x^32*z0^2 - 2*x^30*y*z0^3 - 2*x^30*z0^4 + x^33 - 2*x^31*z0^2 + 2*x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^30*z0^2 + 2*x^28*y*z0^3 - 2*x^28*z0^4 - 2*x^31 - 2*x^29*y*z0 - x^29*z0^2 + 2*x^27*y*z0^3 + x^27*z0^4 - 2*x^30 - x^28*y*z0 + 2*x^28*z0^2 + 2*x^26*y*z0^3 - x^29 + x^27*z0^2 + x^25*z0^4 - x^28 - 2*x^26*z0^2 + x^24*y*z0^3 + 2*x^24*z0^4 - x^25*z0^2 + x^23*y*z0^3 - 2*x^23*z0^4 + x^26 + 2*x^24*y*z0 + x^24*z0^2 - x^22*y*z0^3 + x^22*z0^4 - 2*x^25 + x^23*y*z0 + 2*x^23*z0^2 + x^21*y*z0^3 - x^21*z0^4 - x^24 - 2*x^22*y*z0 + 2*x^22*z0^2 + x^20*y*z0^3 - x^20*z0^4 - x^23 + x^21*z0^2 - x^19*y*z0^3 - 2*x^19*z0^4 + x^22 - 2*x^20*y*z0 - 2*x^20*z0^2 + x^18*y*z0^3 - x^18*z0^4 - x^21 + x^19*y*z0 - x^19*z0^2 + 2*x^17*y*z0^3 + 2*x^20 - x^18*y*z0 - 2*x^18*z0^2 + x^17*y*z0 - 2*x^17*z0^2 - 2*x^15*y*z0^3 - 2*x^15*z0^4 + 2*x^18 + 2*x^16*y*z0 + 2*x^14*y*z0^3 - x^14*z0^4 - 2*x^17 - x^15*y*z0 - 2*x^13*y*z0^3 - 2*x^13*z0^4 - 2*x^16 + x^14*y*z0 - 2*x^12*y*z0^3 - 2*x^15 + 2*x^13*y*z0 + 2*x^11*y*z0^3 + x^14 + 2*x^12*y*z0 - x^12*z0^2 - 2*x^10*z0^4 + 2*x^13 - x^11*z0^2 + 2*x^9*y*z0^3 + x^9*z0^4 + x^12 + x^10*y*z0 + x^10*z0^2 + x^8*z0^4 - x^9*z0^2 + 2*x^7*y*z0^3 + 2*x^7*z0^4 - x^10 - x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 + x^9 + 2*x^7*y*z0 - 2*x^7*z0^2 + x^5*z0^4 + x^8 + x^6*y*z0 - x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 + x^5*y*z0 + x^5*z0^2 - 2*x^3*z0^4 - x^6 - 2*x^4*y*z0 - x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^3*y*z0 + 2*x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 + x^3 - 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-2*x^60*z0^4 + x^61*z0^2 + x^59*z0^4 + 2*x^57*y^2*z0^4 - x^58*y^2*z0^2 - x^56*y^2*z0^4 + 2*x^57*z0^4 + 2*x^60 - x^58*z0^2 - x^56*z0^4 - 2*x^57*y^2 - 2*x^54*z0^4 - 2*x^57 + x^55*z0^2 + x^53*z0^4 + 2*x^51*z0^4 + 2*x^54 - x^52*z0^2 - x^50*z0^4 - 2*x^48*z0^4 - 2*x^51 + x^49*z0^2 + x^47*z0^4 + 2*x^45*z0^4 + 2*x^48 - x^46*z0^2 - x^44*z0^4 - 2*x^42*z0^4 - 2*x^45 + x^43*z0^2 + x^41*z0^4 - x^44 + 2*x^40*z0^4 + x^41*y^2 + x^41*z0^2 + x^39*y*z0^3 - 2*x^39*z0^4 + 2*x^42 - 2*x^40*y*z0 + x^40*z0^2 + x^38*y*z0^3 + x^41 - x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 + x^37*z0^4 - x^40 - x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - 2*x^37*y*z0 + x^37*z0^2 - x^35*y*z0^3 - 2*x^35*z0^4 + x^38 - 2*x^36*y*z0 + x^36*z0^2 + 2*x^34*z0^4 + 2*x^37 + x^35*y*z0 - 2*x^33*y*z0^3 + 2*x^33*z0^4 + 2*x^36 - x^32*z0^4 - x^33*y*z0 + 2*x^33*z0^2 + x^31*y*z0^3 + x^31*z0^4 + x^34 + x^32*z0^2 - x^30*z0^4 + 2*x^33 - 2*x^31*z0^2 + x^29*y*z0^3 - 2*x^29*z0^4 - 2*x^30*y*z0 + x^28*y*z0^3 - x^31 - 2*x^29*y*z0 + x^29*z0^2 + x^27*y*z0^3 - 2*x^27*z0^4 - x^30 + x^28*y*z0 + 2*x^28*z0^2 + x^29 + x^27*y*z0 - 2*x^27*z0^2 - 2*x^25*y*z0^3 + x^25*z0^4 + x^28 - x^26*y*z0 + 2*x^26*z0^2 - 2*x^24*z0^4 + 2*x^27 - x^25*y*z0 + 2*x^23*y*z0^3 + 2*x^23*z0^4 + x^26 + x^24*y*z0 + 2*x^24*z0^2 - 2*x^22*y*z0^3 - x^22*z0^4 - 2*x^25 - x^23*y*z0 + 2*x^23*z0^2 + 2*x^21*y*z0^3 - 2*x^22*y*z0 - 2*x^20*z0^4 - 2*x^23 + x^21*y*z0 - 2*x^21*z0^2 - 2*x^19*y*z0^3 + 2*x^19*z0^4 - x^22 + x^20*z0^2 + 2*x^18*y*z0^3 - x^18*z0^4 + x^19*y*z0 + x^19*z0^2 + 2*x^17*y*z0^3 - x^20 + x^18*z0^2 - x^16*y*z0^3 - 2*x^16*z0^4 - 2*x^17*y*z0 + 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^18 - 2*x^16*z0^2 + 2*x^14*y*z0^3 + 2*x^14*z0^4 - x^17 - x^15*y*z0 + x^13*z0^4 + 2*x^16 - x^14*y*z0 - 2*x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 - x^15 - 2*x^13*y*z0 - x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 + x^12*y*z0 + x^12*z0^2 + 2*x^13 + x^11*y*z0 + 2*x^11*z0^2 + 2*x^9*y*z0^3 - x^12 + 2*x^10*y*z0 - 2*x^10*z0^2 - x^8*y*z0^3 + 2*x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 - x^7*z0^4 - 2*x^10 + x^8*y*z0 + x^6*y*z0^3 - 2*x^9 - 2*x^7*y*z0 + 2*x^7*z0^2 + 2*x^5*z0^4 + x^8 - x^6*y*z0 - x^6*z0^2 - 2*x^4*y*z0^3 - x^4*z0^4 - x^7 - 2*x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*y*z0^3 + x^3*z0^4 - x^6 + x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 - x^5 + x^3*y*z0 + x^3*z0^2 + x^2*z0^2 + 2*x^3 - x^2)/y) * dx, - ((-2*x^61*z0^3 - 2*x^60*z0^3 + 2*x^58*y^2*z0^3 + 2*x^61*z0 + x^59*z0^3 + 2*x^57*y^2*z0^3 - 2*x^60*z0 - 2*x^58*y^2*z0 + x^58*z0^3 - x^56*y^2*z0^3 + 2*x^57*y^2*z0 + 2*x^57*z0^3 + x^55*y^2*z0^3 - 2*x^58*z0 - x^56*z0^3 + 2*x^57*z0 - x^55*z0^3 - 2*x^54*z0^3 + 2*x^55*z0 + x^53*z0^3 - 2*x^54*z0 + x^52*z0^3 + 2*x^51*z0^3 - 2*x^52*z0 - x^50*z0^3 + 2*x^51*z0 - x^49*z0^3 - 2*x^48*z0^3 + 2*x^49*z0 + x^47*z0^3 - 2*x^48*z0 + x^46*z0^3 + 2*x^45*z0^3 - 2*x^46*z0 - x^44*z0^3 + 2*x^45*z0 - x^43*z0^3 - x^44*z0 - 2*x^42*z0^3 + 2*x^43*z0 + x^41*y^2*z0 - x^41*z0^3 - 2*x^39*y*z0^4 - 2*x^42*z0 - x^40*y*z0^2 + 2*x^40*z0^3 - 2*x^38*y*z0^4 - 2*x^41*z0 + 2*x^39*y*z0^2 + x^39*z0^3 + 2*x^37*y*z0^4 + x^40*y - 2*x^40*z0 + x^38*z0^3 + x^36*y*z0^4 + 2*x^39*y - x^37*y*z0^2 - x^37*z0^3 - 2*x^38*z0 + x^36*y*z0^2 + 2*x^36*z0^3 + 2*x^34*y*z0^4 + 2*x^37*y + 2*x^37*z0 + x^35*y*z0^2 - 2*x^35*z0^3 - x^33*y*z0^4 - 2*x^34*y*z0^2 - x^34*z0^3 - x^32*y*z0^4 + 2*x^35*y - x^35*z0 + 2*x^33*y*z0^2 + x^33*z0^3 + x^31*y*z0^4 + x^34*y - x^34*z0 + 2*x^32*y*z0^2 - 2*x^30*y*z0^4 - 2*x^33*y - x^33*z0 - x^31*z0^3 + x^29*y*z0^4 + x^32*y - 2*x^32*z0 + 2*x^30*y*z0^2 + 2*x^30*z0^3 - 2*x^28*y*z0^4 - x^31*y + x^31*z0 - x^29*y*z0^2 + x^29*z0^3 + 2*x^30*y - x^30*z0 + x^28*y*z0^2 - x^28*z0^3 - x^26*y*z0^4 - 2*x^29*y - x^29*z0 - 2*x^27*y*z0^2 - 2*x^27*z0^3 - 2*x^25*y*z0^4 + 2*x^28*y - 2*x^28*z0 - 2*x^26*y*z0^2 + 2*x^26*z0^3 - 2*x^24*y*z0^4 - 2*x^27*y - x^27*z0 - 2*x^25*y*z0^2 + 2*x^23*y*z0^4 + 2*x^26*y - 2*x^26*z0 + x^24*y*z0^2 + x^24*z0^3 + x^22*y*z0^4 - x^25*y - 2*x^25*z0 - x^23*y*z0^2 - 2*x^23*z0^3 + 2*x^21*y*z0^4 - x^24*y - x^24*z0 + 2*x^22*y*z0^2 - x^22*z0^3 + 2*x^20*y*z0^4 + 2*x^23*y + 2*x^21*y*z0^2 - x^21*z0^3 - x^22*y - 2*x^22*z0 - 2*x^20*y*z0^2 - x^20*z0^3 - 2*x^21*y - 2*x^21*z0 + x^19*y*z0^2 - 2*x^19*z0^3 - 2*x^20*y - x^20*z0 + 2*x^18*y*z0^2 + x^18*z0^3 - x^16*y*z0^4 - 2*x^19*y - x^19*z0 - 2*x^17*y*z0^2 + 2*x^17*z0^3 + 2*x^15*y*z0^4 + x^18*y - 2*x^18*z0 + x^16*y*z0^2 - 2*x^16*z0^3 - x^14*y*z0^4 - 2*x^17*y - 2*x^17*z0 - 2*x^15*y*z0^2 + x^13*y*z0^4 + 2*x^16*y - 2*x^14*y*z0^2 - x^15*y + x^15*z0 + x^13*y*z0^2 - x^13*z0^3 + 2*x^11*y*z0^4 + 2*x^14*y + x^14*z0 - x^12*y*z0^2 + x^10*y*z0^4 - x^13*y + 2*x^13*z0 - x^11*y*z0^2 - 2*x^11*z0^3 + x^9*y*z0^4 + 2*x^12*y - x^12*z0 + x^10*z0^3 - 2*x^11*y - x^11*z0 + 2*x^9*y*z0^2 + 2*x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y + x^10*z0 + 2*x^8*z0^3 - x^6*y*z0^4 - 2*x^9*y + x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 + x^8*y + x^8*z0 - 2*x^6*y*z0^2 + 2*x^6*z0^3 + x^4*y*z0^4 - x^7*y - x^7*z0 - 2*x^5*y*z0^2 + x^5*z0^3 + x^3*y*z0^4 + x^6*y - x^6*z0 + 2*x^4*y*z0^2 - 2*x^4*z0^3 - x^2*y*z0^4 + 2*x^3*z0^3 - x^4*y + 2*x^4*z0 - x^2*y*z0^2 + x^2*z0^3 + 2*x^3*y - 2*x^3*z0 - x^2*y - 2*x^2*z0)/y) * dx, - ((2*x^61*z0^4 - 2*x^58*y^2*z0^4 - 2*x^61*z0^2 - x^59*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 - x^61 - x^57*y^2*z0^2 + x^58*y^2 + 2*x^58*z0^2 + x^56*z0^4 - x^57*z0^2 + 2*x^55*z0^4 + x^58 - 2*x^55*z0^2 - x^53*z0^4 + x^54*z0^2 - 2*x^52*z0^4 - x^55 + 2*x^52*z0^2 + x^50*z0^4 - x^51*z0^2 + 2*x^49*z0^4 + x^52 - 2*x^49*z0^2 - x^47*z0^4 + x^48*z0^2 - 2*x^46*z0^4 - x^49 + 2*x^46*z0^2 + x^44*z0^4 - x^45*z0^2 + 2*x^43*z0^4 + x^46 - x^44*z0^2 - 2*x^43*z0^2 + x^41*y^2*z0^2 - 2*x^41*z0^4 + x^42*z0^2 + x^40*y*z0^3 - x^43 - x^41*z0^2 - 2*x^39*y*z0^3 + 2*x^39*z0^4 - x^40*y*z0 + 2*x^40*z0^2 - x^38*y*z0^3 - 2*x^38*z0^4 - x^41 - 2*x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 - 2*x^40 - 2*x^38*y*z0 - x^36*y*z0^3 - x^39 - x^37*y*z0 - x^37*z0^2 - x^35*y*z0^3 + 2*x^35*z0^4 + x^38 + 2*x^36*y*z0 - x^36*z0^2 + x^34*y*z0^3 - x^35*y*z0 + x^35*z0^2 - x^33*y*z0^3 - x^33*z0^4 + 2*x^36 + x^34*y*z0 - 2*x^34*z0^2 + x^32*y*z0^3 + x^32*z0^4 - 2*x^35 - 2*x^33*y*z0 + 2*x^33*z0^2 - x^34 - 2*x^32*y*z0 + x^32*z0^2 + x^30*y*z0^3 - x^30*z0^4 - 2*x^33 + 2*x^31*z0^2 + x^29*y*z0^3 - 2*x^32 - x^28*y*z0^3 + 2*x^28*z0^4 - x^31 - 2*x^29*y*z0 + x^27*y*z0^3 - x^27*z0^4 - 2*x^30 + x^28*y*z0 - x^28*z0^2 + 2*x^27*y*z0 + x^25*y*z0^3 - 2*x^25*z0^4 - x^28 + x^26*y*z0 - x^26*z0^2 + 2*x^24*y*z0^3 + 2*x^27 - 2*x^25*y*z0 - 2*x^25*z0^2 - 2*x^23*y*z0^3 + 2*x^23*z0^4 - 2*x^26 - x^24*y*z0 + x^22*y*z0^3 - 2*x^22*z0^4 - x^23*z0^2 + x^21*y*z0^3 - x^21*z0^4 + 2*x^24 - 2*x^22*z0^2 - 2*x^20*y*z0^3 + 2*x^20*z0^4 + 2*x^23 + x^21*y*z0 - x^21*z0^2 + 2*x^19*y*z0^3 + 2*x^19*z0^4 - 2*x^22 - x^20*y*z0 + x^18*y*z0^3 + x^18*z0^4 + x^21 + x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 + x^20 - 2*x^16*z0^4 - x^17*y*z0 - 2*x^17*z0^2 - x^15*y*z0^3 - 2*x^15*z0^4 - x^18 - x^16*y*z0 - 2*x^14*y*z0^3 + 2*x^14*z0^4 + x^17 - x^15*y*z0 + 2*x^15*z0^2 - 2*x^13*y*z0^3 + x^13*z0^4 + 2*x^16 - 2*x^14*y*z0 + x^14*z0^2 - x^12*y*z0^3 - 2*x^12*z0^4 - 2*x^13*y*z0 - 2*x^13*z0^2 - x^11*y*z0^3 + x^11*z0^4 - 2*x^14 + 2*x^12*y*z0 - x^12*z0^2 - x^10*y*z0^3 - 2*x^10*z0^4 + x^13 + x^11*y*z0 - 2*x^11*z0^2 - x^9*y*z0^3 - x^9*z0^4 + 2*x^12 - x^10*y*z0 + 2*x^10*z0^2 - x^8*y*z0^3 + 2*x^11 + x^9*y*z0 + x^9*z0^2 - 2*x^7*z0^4 - x^10 - 2*x^8*y*z0 - x^6*z0^4 - 2*x^9 + x^7*y*z0 - 2*x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 - x^8 + 2*x^6*y*z0 - 2*x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 + x^5*y*z0 + x^5*z0^2 + x^3*z0^4 + 2*x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 + x^2*y*z0^3 + x^2*z0^4 - 2*x^3*y*z0 + 2*x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 + 2*x^3 + 2*x^2)/y) * dx, - ((-x^61*z0^3 - 2*x^60*z0^3 + x^58*y^2*z0^3 + x^61*z0 - x^59*z0^3 + 2*x^57*y^2*z0^3 - 2*x^60*z0 - x^58*y^2*z0 - 2*x^58*z0^3 + x^56*y^2*z0^3 + 2*x^57*y^2*z0 - 2*x^55*y^2*z0^3 - x^58*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 + 2*x^57*z0 + 2*x^55*z0^3 + x^55*z0 - x^53*z0^3 - 2*x^54*z0 - 2*x^52*z0^3 - x^52*z0 + x^50*z0^3 + 2*x^51*z0 + 2*x^49*z0^3 + x^49*z0 - x^47*z0^3 - 2*x^48*z0 - 2*x^46*z0^3 - x^46*z0 + 2*x^45*z0 + 2*x^43*z0^3 + x^41*y^2*z0^3 + x^43*z0 - x^41*z0^3 - x^39*y*z0^4 - 2*x^42*z0 + 2*x^40*y*z0^2 + x^40*z0^3 - x^38*y*z0^4 + x^41*z0 + x^39*y*z0^2 - x^39*z0^3 + x^37*y*z0^4 - 2*x^40*y + x^40*z0 - 2*x^38*y*z0^2 + 2*x^38*z0^3 - 2*x^39*y + x^39*z0 - x^37*y*z0^2 - x^37*z0^3 + x^35*y*z0^4 - x^38*y + 2*x^38*z0 - 2*x^36*y*z0^2 - 2*x^36*z0^3 + x^34*y*z0^4 + x^37*y - x^37*z0 + 2*x^35*y*z0^2 + 2*x^35*z0^3 + x^33*y*z0^4 - x^36*y - x^36*z0 - 2*x^34*y*z0^2 - x^34*z0^3 + 2*x^32*y*z0^4 - 2*x^35*y + 2*x^35*z0 - x^33*y*z0^2 + 2*x^31*y*z0^4 - x^34*z0 + 2*x^33*y - 2*x^31*y*z0^2 - 2*x^31*z0^3 - 2*x^29*y*z0^4 + x^32*y + x^32*z0 + x^30*y*z0^2 - 2*x^30*z0^3 - 2*x^31*y + x^31*z0 - x^29*y*z0^2 - 2*x^29*z0^3 - 2*x^27*y*z0^4 - 2*x^30*y + 2*x^30*z0 + x^28*y*z0^2 + 2*x^28*z0^3 - x^26*y*z0^4 - x^29*z0 - 2*x^27*y*z0^2 + 2*x^27*z0^3 - 2*x^25*y*z0^4 - 2*x^28*z0 - 2*x^26*y*z0^2 + x^26*z0^3 - 2*x^24*y*z0^4 + x^27*y - 2*x^27*z0 - 2*x^25*y*z0^2 - 2*x^25*z0^3 + 2*x^23*y*z0^4 - 2*x^26*y + x^26*z0 + x^24*y*z0^2 + x^24*z0^3 - x^22*y*z0^4 - x^25*y - x^25*z0 + x^23*y*z0^2 + 2*x^23*z0^3 + 2*x^21*y*z0^4 + x^24*y - x^24*z0 - x^20*y*z0^4 + 2*x^23*y + 2*x^23*z0 + 2*x^21*y*z0^2 + 2*x^21*z0^3 - x^22*y - 2*x^22*z0 - x^20*y*z0^2 + 2*x^20*z0^3 - x^18*y*z0^4 + 2*x^21*y + 2*x^21*z0 + x^19*y*z0^2 - x^19*z0^3 + 2*x^17*y*z0^4 + 2*x^20*y - x^20*z0 + 2*x^18*y*z0^2 + 2*x^19*y + x^17*y*z0^2 + x^17*z0^3 - x^15*y*z0^4 + x^18*y + 2*x^18*z0 - 2*x^16*y*z0^2 - 2*x^16*z0^3 + x^14*y*z0^4 + 2*x^15*y*z0^2 + 2*x^15*z0^3 + 2*x^16*y - x^14*y*z0^2 - 2*x^14*z0^3 + x^12*y*z0^4 + x^15*y - 2*x^15*z0 + x^13*y*z0^2 + x^11*y*z0^4 + 2*x^14*y - 2*x^14*z0 + x^12*y*z0^2 + x^12*z0^3 + 2*x^10*y*z0^4 - 2*x^13*y + x^13*z0 + 2*x^11*y*z0^2 - x^11*z0^3 + x^9*y*z0^4 - x^10*y*z0^2 - x^10*z0^3 + 2*x^8*y*z0^4 + 2*x^11*z0 - x^9*z0^3 - 2*x^8*y*z0^2 - 2*x^8*z0^3 - x^6*y*z0^4 + 2*x^9*y + x^9*z0 + x^7*y*z0^2 + x^7*z0^3 + 2*x^5*y*z0^4 - x^8*y + 2*x^6*z0^3 - 2*x^4*y*z0^4 - 2*x^7*y + 2*x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^3*y*z0^4 - x^6*y + x^6*z0 + x^4*y*z0^2 - x^4*z0^3 + x^5*y - x^5*z0 + 2*x^4*z0 + 2*x^2*y*z0^2 - x^2*z0^3 + 2*x^3*y + x^3*z0 - 2*x^2*y + x^2*z0)/y) * dx, - ((-x^61*z0^4 + 2*x^60*z0^4 + x^58*y^2*z0^4 + 2*x^61*z0^2 + x^59*z0^4 - 2*x^57*y^2*z0^4 - 2*x^58*y^2*z0^2 + x^58*z0^4 - x^56*y^2*z0^4 - 2*x^61 - 2*x^57*z0^4 - x^60 + 2*x^58*y^2 - 2*x^58*z0^2 - x^56*z0^4 + x^57*y^2 - x^55*z0^4 + 2*x^58 + 2*x^54*z0^4 + x^57 + 2*x^55*z0^2 + x^53*z0^4 + x^52*z0^4 - 2*x^55 - 2*x^51*z0^4 - x^54 - 2*x^52*z0^2 - x^50*z0^4 - x^49*z0^4 + 2*x^52 + 2*x^48*z0^4 + x^51 + 2*x^49*z0^2 + x^47*z0^4 + x^46*z0^4 - 2*x^49 - 2*x^45*z0^4 - x^48 - 2*x^46*z0^2 - 2*x^44*z0^4 - x^43*z0^4 + x^41*y^2*z0^4 + 2*x^46 + 2*x^42*z0^4 + x^45 + 2*x^43*z0^2 + 2*x^40*y*z0^3 - x^40*z0^4 - 2*x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + x^39*z0^4 - x^42 + x^40*y*z0 + x^40*z0^2 + x^38*y*z0^3 - 2*x^41 + 2*x^39*y*z0 - 2*x^39*z0^2 - x^37*y*z0^3 + x^37*z0^4 + x^40 - x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 - 2*x^36*z0^4 + x^39 + 2*x^37*y*z0 + x^37*z0^2 - 2*x^35*y*z0^3 + x^35*z0^4 - 2*x^38 - x^36*y*z0 + 2*x^36*z0^2 + x^34*z0^4 + 2*x^37 - x^35*y*z0 + 2*x^33*y*z0^3 + x^33*z0^4 - x^36 - x^34*y*z0 - x^34*z0^2 - 2*x^32*y*z0^3 - 2*x^32*z0^4 - 2*x^35 + x^33*y*z0 - x^33*z0^2 - x^31*y*z0^3 - 2*x^31*z0^4 - x^34 - 2*x^32*y*z0 + x^30*y*z0^3 + x^30*z0^4 - x^33 + x^31*y*z0 + x^31*z0^2 - 2*x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^30*y*z0 + x^30*z0^2 - 2*x^28*y*z0^3 + x^31 - x^29*y*z0 - 2*x^29*z0^2 + 2*x^30 - x^28*y*z0 + 2*x^28*z0^2 + x^26*y*z0^3 - x^26*z0^4 - 2*x^29 + 2*x^27*y*z0 + 2*x^27*z0^2 + x^25*y*z0^3 + x^25*z0^4 - 2*x^28 + x^26*y*z0 - x^26*z0^2 + 2*x^24*z0^4 + x^27 - x^25*y*z0 + x^25*z0^2 - 2*x^23*y*z0^3 + x^26 - 2*x^24*y*z0 + x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^22*z0^4 + x^25 + x^23*z0^2 - x^21*y*z0^3 + 2*x^21*z0^4 - x^24 - 2*x^22*z0^2 + x^20*y*z0^3 + 2*x^20*z0^4 - x^23 - x^21*y*z0 + x^21*z0^2 - 2*x^19*y*z0^3 - 2*x^19*z0^4 + x^22 + x^20*z0^2 + 2*x^18*y*z0^3 + x^18*z0^4 - 2*x^21 - 2*x^19*z0^2 - 2*x^17*y*z0^3 + 2*x^18*y*z0 + 2*x^18*z0^2 - x^16*y*z0^3 - 2*x^16*z0^4 - x^19 - x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^15*z0^4 - 2*x^18 - 2*x^16*y*z0 - 2*x^16*z0^2 + 2*x^14*y*z0^3 + 2*x^17 + 2*x^15*z0^2 + 2*x^13*y*z0^3 - x^13*z0^4 - x^16 - 2*x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 - 2*x^12*z0^4 + x^15 + 2*x^13*y*z0 - x^11*y*z0^3 - 2*x^14 - x^12*y*z0 - x^12*z0^2 - x^10*y*z0^3 + 2*x^10*z0^4 + x^13 + x^11*y*z0 - x^9*y*z0^3 - x^9*z0^4 - x^12 - x^10*z0^2 + x^8*y*z0^3 - x^8*z0^4 + x^11 + x^9*y*z0 + x^9*z0^2 - 2*x^10 + x^8*y*z0 - 2*x^8*z0^2 + x^6*y*z0^3 - 2*x^6*z0^4 - x^9 + 2*x^7*z0^2 - x^5*y*z0^3 + x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 - x^5*z0^2 - 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 - 2*x^4*y*z0 + 2*x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^3*y*z0 - 2*x^3 - 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 + x^58*y^2*z0^4 + x^61*z0^2 - 2*x^60*z0^2 - x^58*y^2*z0^2 + x^58*z0^4 - 2*x^61 + 2*x^57*y^2*z0^2 - 2*x^60 + 2*x^58*y^2 - x^58*z0^2 + 2*x^57*y^2 + 2*x^57*z0^2 - x^55*z0^4 + 2*x^58 + 2*x^57 + x^55*z0^2 - 2*x^54*z0^2 + x^52*z0^4 - 2*x^55 - 2*x^54 - x^52*z0^2 + 2*x^51*z0^2 - x^49*z0^4 + 2*x^52 + 2*x^51 + x^49*z0^2 - 2*x^48*z0^2 + x^46*z0^4 - 2*x^49 - 2*x^48 - x^46*z0^2 + 2*x^45*z0^2 - x^43*z0^4 + 2*x^46 + x^45 + x^43*z0^2 - 2*x^41*z0^4 + x^42*y^2 - 2*x^42*z0^2 + 2*x^40*y*z0^3 - 2*x^40*z0^4 - 2*x^43 + x^41*z0^2 + x^39*y*z0^3 - x^39*z0^4 - x^42 - 2*x^40*y*z0 - x^38*y*z0^3 + x^38*z0^4 - 2*x^41 + x^39*y*z0 + x^39*z0^2 - 2*x^37*y*z0^3 + 2*x^37*z0^4 - x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - 2*x^37*y*z0 + 2*x^35*y*z0^3 + x^38 - 2*x^36*y*z0 - x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 + x^37 - 2*x^35*y*z0 - 2*x^35*z0^2 - x^33*y*z0^3 - x^33*z0^4 + x^36 - 2*x^34*y*z0 + x^34*z0^2 + 2*x^32*y*z0^3 + x^32*z0^4 + 2*x^33*y*z0 + 2*x^33*z0^2 - 2*x^31*y*z0^3 - 2*x^31*z0^4 + x^34 - x^32*y*z0 + x^32*z0^2 + 2*x^30*z0^4 + x^31*y*z0 + x^31*z0^2 - 2*x^29*y*z0^3 + x^29*z0^4 + x^32 - x^30*y*z0 - x^30*z0^2 + x^28*y*z0^3 + x^28*z0^4 - x^31 - 2*x^29*y*z0 + x^29*z0^2 - 2*x^27*y*z0^3 + 2*x^27*z0^4 - 2*x^30 - x^28*y*z0 + x^28*z0^2 + 2*x^26*y*z0^3 - x^26*z0^4 + x^29 - x^27*y*z0 - 2*x^27*z0^2 - 2*x^25*y*z0^3 - x^25*z0^4 + 2*x^28 - 2*x^26*y*z0 - x^26*z0^2 + x^24*y*z0^3 + x^24*z0^4 + 2*x^27 - 2*x^25*z0^2 + x^23*y*z0^3 + 2*x^23*z0^4 + x^24*y*z0 - x^24*z0^2 + 2*x^25 + x^23*y*z0 - x^23*z0^2 - x^21*z0^4 + x^22*z0^2 + x^20*y*z0^3 + 2*x^20*z0^4 - 2*x^21*y*z0 - x^21*z0^2 + 2*x^19*y*z0^3 + 2*x^22 - 2*x^20*y*z0 + 2*x^20*z0^2 - x^18*y*z0^3 - x^18*z0^4 + x^21 + 2*x^19*y*z0 + x^19*z0^2 - x^17*y*z0^3 - 2*x^18*y*z0 + 2*x^18*z0^2 - x^16*z0^4 - 2*x^19 - x^17*y*z0 + x^17*z0^2 - x^15*y*z0^3 + 2*x^15*z0^4 + 2*x^16*y*z0 - x^14*y*z0^3 + x^17 - x^15*y*z0 + 2*x^15*z0^2 + x^13*y*z0^3 + x^13*z0^4 - x^16 - x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 - x^15 - x^13*y*z0 + 2*x^13*z0^2 + 2*x^11*y*z0^3 + 2*x^11*z0^4 + 2*x^14 - 2*x^12*y*z0 + x^12*z0^2 - x^10*y*z0^3 + x^10*z0^4 - x^13 + x^11*z0^2 - 2*x^9*y*z0^3 - 2*x^12 + x^10*y*z0 + 2*x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^11 - x^9*y*z0 + 2*x^9*z0^2 + 2*x^7*y*z0^3 + 2*x^7*z0^4 + 2*x^10 + x^8*y*z0 + 2*x^8*z0^2 - x^6*y*z0^3 + 2*x^6*z0^4 - x^9 - x^7*y*z0 + 2*x^5*y*z0^3 - 2*x^5*z0^4 - x^6*y*z0 - 2*x^6*z0^2 + 2*x^4*y*z0^3 + x^5*y*z0 + 2*x^3*z0^4 - x^6 + x^4*y*z0 + x^4*z0^2 + x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^3*y*z0 - x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - 2*x^3 + x^2)/y) * dx, - ((x^60*z0^3 - x^57*y^2*z0^3 - x^60*z0 + x^58*z0^3 - 2*x^59*z0 + x^57*y^2*z0 - 2*x^57*z0^3 - x^55*y^2*z0^3 + 2*x^56*y^2*z0 + x^54*y^2*z0^3 + x^57*z0 - x^55*z0^3 + 2*x^56*z0 + 2*x^54*z0^3 - x^54*z0 + x^52*z0^3 - 2*x^53*z0 - 2*x^51*z0^3 + x^51*z0 - x^49*z0^3 + 2*x^50*z0 + 2*x^48*z0^3 - x^48*z0 + x^46*z0^3 - 2*x^47*z0 - 2*x^45*z0^3 - x^43*z0^3 + 2*x^44*z0 + x^42*y^2*z0 + 2*x^42*z0^3 - x^38*y*z0^4 - 2*x^41*z0 + x^39*z0^3 - x^37*y*z0^4 - x^40*z0 - 2*x^38*y*z0^2 - 2*x^39*y + x^39*z0 - x^37*y*z0^2 + x^37*z0^3 - 2*x^35*y*z0^4 - 2*x^38*y + x^36*y*z0^2 - x^36*z0^3 + 2*x^34*y*z0^4 + x^37*z0 - 2*x^35*y*z0^2 + x^35*z0^3 - x^33*y*z0^4 - 2*x^36*z0 + x^34*y*z0^2 - x^34*z0^3 - x^32*y*z0^4 - x^35*z0 - 2*x^33*z0^3 - x^34*y - x^34*z0 + x^32*y*z0^2 + x^32*z0^3 + 2*x^30*y*z0^4 - x^33*y - 2*x^33*z0 - 2*x^31*z0^3 + 2*x^29*y*z0^4 + 2*x^32*y - x^32*z0 - 2*x^30*y*z0^2 - 2*x^30*z0^3 + 2*x^28*y*z0^4 + 2*x^31*y - 2*x^29*y*z0^2 - x^29*z0^3 - 2*x^27*y*z0^4 - x^30*y - 2*x^30*z0 - x^28*y*z0^2 + x^26*y*z0^4 - x^29*y + 2*x^27*y*z0^2 + 2*x^27*z0^3 - 2*x^25*y*z0^4 - x^28*z0 + x^26*y*z0^2 - x^24*y*z0^4 + x^27*y - 2*x^25*y*z0^2 - x^25*z0^3 + x^23*y*z0^4 + 2*x^26*y + 2*x^26*z0 - x^24*y*z0^2 + 2*x^24*z0^3 - 2*x^22*y*z0^4 - 2*x^25*z0 + 2*x^23*y*z0^2 + x^23*z0^3 - x^21*y*z0^4 - x^24*z0 - 2*x^22*z0^3 - x^20*y*z0^4 - x^23*z0 - x^21*y*z0^2 - x^21*z0^3 - 2*x^19*y*z0^4 + 2*x^22*y - 2*x^22*z0 + 2*x^20*z0^3 + x^18*y*z0^4 + 2*x^21*y - 2*x^21*z0 + 2*x^19*z0^3 - 2*x^17*y*z0^4 + 2*x^20*y + 2*x^18*y*z0^2 - 2*x^18*z0^3 - x^16*y*z0^4 - 2*x^19*y + x^19*z0 - x^17*z0^3 + 2*x^15*y*z0^4 - 2*x^18*y - 2*x^18*z0 + x^16*y*z0^2 - x^17*y + x^17*z0 + 2*x^15*y*z0^2 - 2*x^15*z0^3 + x^13*y*z0^4 + 2*x^16*y - 2*x^14*z0^3 - x^12*y*z0^4 + x^15*y - x^15*z0 - x^13*y*z0^2 - 2*x^11*y*z0^4 + x^14*y - 2*x^14*z0 + x^12*y*z0^2 - x^12*z0^3 - 2*x^10*y*z0^4 + x^13*y + 2*x^13*z0 + 2*x^11*y*z0^2 + x^11*z0^3 + x^9*y*z0^4 - 2*x^12*y + 2*x^12*z0 - x^10*y*z0^2 - 2*x^10*z0^3 - 2*x^8*y*z0^4 - x^11*z0 + x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y - x^10*z0 + 2*x^6*y*z0^4 - 2*x^9*y + x^9*z0 - 2*x^7*y*z0^2 - 2*x^7*z0^3 + x^5*y*z0^4 - 2*x^8*y + 2*x^6*z0^3 + x^4*y*z0^4 + 2*x^7*y + x^5*y*z0^2 - 2*x^5*z0^3 - x^6*y - 2*x^6*z0 - x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^2*y*z0^4 - x^5*y + 2*x^3*y*z0^2 - x^3*z0^3 - x^2*y*z0^2 - x^2*z0^3 + x^3*z0 - 2*x^2*y + 2*x^2*z0)/y) * dx, - ((x^61*z0^4 + 2*x^60*z0^4 - x^58*y^2*z0^4 - 2*x^61*z0^2 - x^59*z0^4 - 2*x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 - x^58*z0^4 + x^56*y^2*z0^4 + 2*x^61 - x^57*y^2*z0^2 - 2*x^57*z0^4 + x^60 - 2*x^58*y^2 + 2*x^58*z0^2 + x^56*z0^4 - x^57*y^2 - x^57*z0^2 + x^55*z0^4 - 2*x^58 + 2*x^54*z0^4 - x^57 - 2*x^55*z0^2 - x^53*z0^4 + x^54*z0^2 - x^52*z0^4 + 2*x^55 - 2*x^51*z0^4 + x^54 + 2*x^52*z0^2 + x^50*z0^4 - x^51*z0^2 + x^49*z0^4 - 2*x^52 + 2*x^48*z0^4 - x^51 - 2*x^49*z0^2 - x^47*z0^4 + x^48*z0^2 - x^46*z0^4 + 2*x^49 - 2*x^45*z0^4 + x^48 + 2*x^46*z0^2 + x^44*z0^4 - 2*x^45*z0^2 + x^43*z0^4 - 2*x^46 + x^42*y^2*z0^2 + 2*x^42*z0^4 - x^45 - 2*x^43*z0^2 + x^41*z0^4 + 2*x^42*z0^2 - 2*x^40*y*z0^3 + 2*x^40*z0^4 + 2*x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^42 - x^40*y*z0 + x^38*y*z0^3 - x^38*z0^4 + 2*x^41 - 2*x^37*y*z0^3 - x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + x^36*z0^4 + 2*x^39 + x^37*y*z0 + 2*x^35*y*z0^3 + 2*x^38 - x^36*y*z0 + x^34*y*z0^3 + x^35*y*z0 + 2*x^35*z0^2 + x^33*y*z0^3 - x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 + x^32*y*z0^3 + 2*x^33*y*z0 - 2*x^31*y*z0^3 - 2*x^31*z0^4 + 2*x^34 + 2*x^32*z0^2 - 2*x^30*y*z0^3 + x^30*z0^4 + 2*x^33 + x^31*y*z0 + 2*x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 + 2*x^30*y*z0 - x^30*z0^2 + 2*x^28*y*z0^3 + 2*x^28*z0^4 - 2*x^31 - 2*x^29*y*z0 + x^27*y*z0^3 - 2*x^27*z0^4 + x^30 - x^28*z0^2 + x^26*z0^4 + 2*x^29 + x^27*y*z0 + x^27*z0^2 - x^25*y*z0^3 - x^26*y*z0 + 2*x^24*y*z0^3 + x^27 + x^25*y*z0 - 2*x^25*z0^2 - x^23*z0^4 + 2*x^26 - x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^22*z0^4 - x^25 - x^23*y*z0 - x^21*y*z0^3 - 2*x^24 + x^22*y*z0 - x^22*z0^2 + 2*x^20*y*z0^3 - 2*x^23 + 2*x^21*y*z0 - 2*x^21*z0^2 - 2*x^19*y*z0^3 + 2*x^19*z0^4 + 2*x^22 + 2*x^20*z0^2 - x^18*y*z0^3 - x^21 + 2*x^19*z0^2 - 2*x^20 + 2*x^18*z0^2 + 2*x^16*z0^4 - 2*x^19 + x^17*y*z0 + x^17*z0^2 - 2*x^15*y*z0^3 - x^16*y*z0 + x^16*z0^2 + x^14*y*z0^3 - 2*x^17 - x^15*y*z0 - x^15*z0^2 - 2*x^13*y*z0^3 + x^13*z0^4 - x^16 - x^14*z0^2 + x^12*y*z0^3 + x^12*z0^4 + 2*x^15 - x^13*y*z0 + 2*x^13*z0^2 + 2*x^11*y*z0^3 + x^11*z0^4 - x^14 - 2*x^12*y*z0 + x^12*z0^2 - 2*x^10*y*z0^3 - 2*x^13 - x^11*y*z0 - 2*x^11*z0^2 + x^9*y*z0^3 - x^9*z0^4 - 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 + x^10 - x^6*y*z0^3 + x^9 + x^7*y*z0 - x^7*z0^2 + x^5*y*z0^3 + x^5*z0^4 - x^8 + 2*x^6*y*z0 + 2*x^6*z0^2 + x^4*y*z0^3 + x^7 - 2*x^5*z0^2 - x^3*y*z0^3 + x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + x^2*z0^4 + 2*x^3*z0^2 - 2*x^2*y*z0 - 2*x^2*z0^2)/y) * dx, - ((x^61*z0^3 - 2*x^60*z0^3 - x^58*y^2*z0^3 - x^61*z0 + 2*x^57*y^2*z0^3 + x^60*z0 + x^58*y^2*z0 - x^58*z0^3 - 2*x^59*z0 - x^57*y^2*z0 + x^58*z0 + 2*x^56*y^2*z0 + 2*x^54*y^2*z0^3 - x^57*z0 + x^55*z0^3 + 2*x^56*z0 - x^55*z0 + x^54*z0 - x^52*z0^3 - 2*x^53*z0 + x^52*z0 - x^51*z0 + x^49*z0^3 + 2*x^50*z0 - x^49*z0 + x^48*z0 - x^46*z0^3 - 2*x^47*z0 - x^45*z0^3 + x^46*z0 + x^42*y^2*z0^3 - x^45*z0 + x^43*z0^3 + 2*x^44*z0 + x^42*z0^3 - x^43*z0 + x^41*z0^3 + x^39*y*z0^4 + x^42*z0 - 2*x^40*y*z0^2 + 2*x^41*z0 - x^39*y*z0^2 + x^39*z0^3 + x^37*y*z0^4 + 2*x^40*y - 2*x^40*z0 + 2*x^38*z0^3 - 2*x^36*y*z0^4 + x^39*z0 + x^37*y*z0^2 - x^37*z0^3 - 2*x^35*y*z0^4 - 2*x^38*y - 2*x^38*z0 - 2*x^36*y*z0^2 - x^36*z0^3 - x^37*y - 2*x^37*z0 + x^35*y*z0^2 - 2*x^35*z0^3 - 2*x^33*y*z0^4 - 2*x^36*z0 - 2*x^34*y*z0^2 + 2*x^34*z0^3 + x^32*y*z0^4 - 2*x^35*y + 2*x^35*z0 + x^33*y*z0^2 - x^34*z0 + x^32*y*z0^2 + x^32*z0^3 + x^30*y*z0^4 - x^33*y + 2*x^31*z0^3 - 2*x^29*y*z0^4 + 2*x^32*y - 2*x^32*z0 - 2*x^30*y*z0^2 - x^30*z0^3 + 2*x^28*y*z0^4 + x^31*z0 - x^29*y*z0^2 - 2*x^29*z0^3 + 2*x^27*y*z0^4 + 2*x^30*y - 2*x^30*z0 - 2*x^28*y*z0^2 + x^28*z0^3 + x^26*y*z0^4 + x^29*y - 2*x^27*y*z0^2 - x^25*y*z0^4 + x^28*y - x^26*y*z0^2 - 2*x^26*z0^3 - 2*x^27*y + x^27*z0 + x^25*y*z0^2 - 2*x^25*z0^3 - x^23*y*z0^4 + x^26*y - x^26*z0 - 2*x^24*y*z0^2 - 2*x^24*z0^3 - 2*x^22*y*z0^4 + 2*x^25*y + 2*x^23*y*z0^2 + x^23*z0^3 - x^21*y*z0^4 - x^22*y*z0^2 - 2*x^22*z0^3 + x^23*y + x^23*z0 - 2*x^21*y*z0^2 - 2*x^21*z0^3 + x^19*y*z0^4 + x^22*y - x^22*z0 - 2*x^20*z0^3 + x^18*y*z0^4 - 2*x^21*y - 2*x^21*z0 - 2*x^19*z0^3 - x^17*y*z0^4 - 2*x^20*y - x^20*z0 - 2*x^18*y*z0^2 - 2*x^18*z0^3 + x^16*y*z0^4 - 2*x^19*y + x^19*z0 + 2*x^17*y*z0^2 - x^15*y*z0^4 - 2*x^18*y + x^18*z0 - x^16*y*z0^2 + x^16*z0^3 - x^14*y*z0^4 + x^17*y - x^17*z0 - x^15*y*z0^2 - 2*x^15*z0^3 - x^13*y*z0^4 + 2*x^16*y - x^14*y*z0^2 + x^12*y*z0^4 - 2*x^15*y + 2*x^15*z0 - x^13*y*z0^2 + 2*x^13*z0^3 - x^11*y*z0^4 + 2*x^12*y*z0^2 + x^12*z0^3 + 2*x^10*y*z0^4 + x^13*y - 2*x^13*z0 - x^11*z0^3 + x^9*y*z0^4 + x^12*y - x^10*y*z0^2 + 2*x^10*z0^3 - x^8*y*z0^4 - x^11*z0 - x^9*y*z0^2 + 2*x^9*z0^3 + 2*x^7*y*z0^4 - x^10*z0 - 2*x^8*z0^3 + 2*x^6*y*z0^4 + 2*x^9*z0 + 2*x^7*y*z0^2 - 2*x^5*y*z0^4 + 2*x^8*y + 2*x^8*z0 + 2*x^6*y*z0^2 - 2*x^6*z0^3 + 2*x^4*y*z0^4 - 2*x^6*y - x^6*z0 + 2*x^2*y*z0^4 - 2*x^5*y - 2*x^5*z0 - 2*x^3*y*z0^2 - 2*x^3*z0^3 + 2*x^4*y - x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - x^3*y - x^2*y - x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + x^60*z0^4 + 2*x^58*y^2*z0^4 + 2*x^61*z0^2 + 2*x^59*z0^4 - x^57*y^2*z0^4 + x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^58*z0^4 - 2*x^56*y^2*z0^4 - x^57*y^2*z0^2 - x^57*z0^4 - 2*x^58*z0^2 - 2*x^56*z0^4 - x^57*z0^2 - 2*x^55*z0^4 + x^54*z0^4 + 2*x^55*z0^2 + 2*x^53*z0^4 + x^54*z0^2 + 2*x^52*z0^4 - x^51*z0^4 - 2*x^52*z0^2 - 2*x^50*z0^4 - x^51*z0^2 - 2*x^49*z0^4 + x^48*z0^4 + 2*x^49*z0^2 + 2*x^47*z0^4 + x^48*z0^2 + 2*x^46*z0^4 - 2*x^45*z0^4 - 2*x^46*z0^2 - 2*x^44*z0^4 + x^42*y^2*z0^4 - x^45*z0^2 - 2*x^43*z0^4 + 2*x^42*z0^4 + 2*x^43*z0^2 + x^42*z0^2 - x^40*y*z0^3 - 2*x^40*z0^4 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 + x^40*y*z0 + 2*x^40*z0^2 + x^38*y*z0^3 + x^38*z0^4 - 2*x^41 - x^39*y*z0 + 2*x^39*z0^2 - x^37*y*z0^3 - 2*x^40 - x^38*z0^2 + x^36*y*z0^3 + 2*x^36*z0^4 + 2*x^37*y*z0 - 2*x^35*y*z0^3 + x^35*z0^4 - x^36*y*z0 - 2*x^36*z0^2 + x^34*y*z0^3 + 2*x^34*z0^4 - x^35*z0^2 - x^33*y*z0^3 + x^33*z0^4 - x^36 + x^34*y*z0 - 2*x^34*z0^2 - 2*x^32*y*z0^3 - x^32*z0^4 + 2*x^35 + 2*x^33*y*z0 + 2*x^31*y*z0^3 - 2*x^34 + 2*x^32*z0^2 - 2*x^30*y*z0^3 - 2*x^30*z0^4 + 2*x^33 + x^31*y*z0 + x^31*z0^2 - x^29*y*z0^3 + 2*x^29*z0^4 - x^32 - x^30*y*z0 + 2*x^30*z0^2 + 2*x^28*y*z0^3 - x^28*z0^4 - x^27*y*z0^3 - 2*x^27*z0^4 + x^28*y*z0 + 2*x^28*z0^2 - 2*x^26*y*z0^3 + x^26*z0^4 - 2*x^29 - 2*x^25*y*z0^3 - x^28 + 2*x^26*z0^2 + 2*x^24*y*z0^3 + x^24*z0^4 + x^27 + 2*x^25*y*z0 - x^25*z0^2 + 2*x^23*y*z0^3 - 2*x^23*z0^4 - 2*x^26 - x^24*y*z0 + 2*x^24*z0^2 + x^22*y*z0^3 - x^25 - x^23*y*z0 + 2*x^23*z0^2 + x^21*y*z0^3 + 2*x^24 - x^22*z0^2 - x^20*z0^4 - x^23 + 2*x^21*y*z0 + x^21*z0^2 - x^19*z0^4 + 2*x^22 + 2*x^20*y*z0 - 2*x^20*z0^2 - x^18*y*z0^3 - x^18*z0^4 - x^19*y*z0 - 2*x^17*y*z0^3 + x^20 + 2*x^18*y*z0 - x^18*z0^2 + x^16*y*z0^3 + x^16*z0^4 - 2*x^17*y*z0 + 2*x^17*z0^2 - x^15*y*z0^3 - x^18 + x^16*z0^2 - x^14*z0^4 + 2*x^17 - x^15*y*z0 - x^15*z0^2 + x^13*y*z0^3 + 2*x^16 - 2*x^14*y*z0 - x^14*z0^2 - 2*x^12*y*z0^3 - x^12*z0^4 - 2*x^15 + x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 + 2*x^12*y*z0 + 2*x^12*z0^2 + x^10*z0^4 - x^13 + x^11*z0^2 - x^9*y*z0^3 + x^9*z0^4 - 2*x^12 - x^10*z0^2 - 2*x^8*y*z0^3 + x^8*z0^4 + x^11 + x^9*y*z0 + x^9*z0^2 + x^7*y*z0^3 - 2*x^7*z0^4 + x^10 - x^8*y*z0 - x^8*z0^2 - x^6*z0^4 + x^7*z0^2 + x^5*z0^4 + 2*x^8 + x^6*y*z0 + x^6*z0^2 + x^4*y*z0^3 - 2*x^4*z0^4 - x^7 + 2*x^5*y*z0 + 2*x^5*z0^2 + x^3*y*z0^3 - x^3*z0^4 - x^6 + 2*x^4*y*z0 + x^4*z0^2 + 2*x^2*z0^4 + x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 + 2*x^2*z0^2 + 2*x^3 + 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 - x^59*z0^4 - 2*x^60*z0^2 - x^58*z0^4 + x^56*y^2*z0^4 + x^61 + 2*x^57*y^2*z0^2 + x^60 - x^58*y^2 + x^56*z0^4 - x^57*y^2 + 2*x^57*z0^2 + x^55*z0^4 - x^58 - x^57 - x^53*z0^4 - 2*x^54*z0^2 - x^52*z0^4 + x^55 + x^54 + x^50*z0^4 + 2*x^51*z0^2 + x^49*z0^4 - x^52 - x^51 - x^47*z0^4 - 2*x^48*z0^2 - x^46*z0^4 + x^49 + x^48 + x^44*z0^4 + 2*x^45*z0^2 + x^43*z0^4 - 2*x^46 - x^45 + x^43*y^2 - 2*x^41*z0^4 - 2*x^42*z0^2 - 2*x^40*y*z0^3 + x^40*z0^4 + 2*x^43 - 2*x^39*z0^4 + x^42 + x^38*y*z0^3 - 2*x^38*z0^4 - x^41 - 2*x^39*y*z0 + 2*x^39*z0^2 - 2*x^37*y*z0^3 - 2*x^37*z0^4 + 2*x^40 + x^38*y*z0 - 2*x^36*z0^4 - 2*x^39 + x^37*y*z0 - 2*x^37*z0^2 - x^35*y*z0^3 + x^38 + 2*x^36*y*z0 - 2*x^36*z0^2 - 2*x^34*y*z0^3 + 2*x^37 + x^35*y*z0 - 2*x^35*z0^2 + 2*x^33*y*z0^3 - x^33*z0^4 - x^36 + 2*x^34*y*z0 - x^34*z0^2 + x^32*z0^4 - 2*x^33*y*z0 - x^33*z0^2 - 2*x^31*y*z0^3 + x^31*z0^4 - x^34 - 2*x^32*y*z0 + x^32*z0^2 + 2*x^30*y*z0^3 - 2*x^31*z0^2 - 2*x^29*y*z0^3 + x^29*z0^4 + 2*x^32 - 2*x^30*y*z0 + 2*x^30*z0^2 - x^31 - x^29*z0^2 - x^27*z0^4 - 2*x^30 + 2*x^28*y*z0 - x^28*z0^2 - 2*x^26*y*z0^3 - x^27*y*z0 - x^27*z0^2 + x^25*y*z0^3 + 2*x^25*z0^4 + 2*x^26*y*z0 + x^26*z0^2 + x^24*y*z0^3 + x^24*z0^4 + 2*x^27 - x^25*y*z0 - 2*x^25*z0^2 + x^23*y*z0^3 + x^23*z0^4 + x^24*y*z0 - 2*x^24*z0^2 + 2*x^22*y*z0^3 - x^22*z0^4 - 2*x^25 + 2*x^23*z0^2 - 2*x^21*y*z0^3 - x^21*z0^4 - x^24 + 2*x^22*y*z0 + 2*x^22*z0^2 - 2*x^20*y*z0^3 + 2*x^23 + x^21*y*z0 + 2*x^21*z0^2 + x^19*y*z0^3 - 2*x^19*z0^4 - x^20*y*z0 + 2*x^18*y*z0^3 - x^21 + 2*x^19*y*z0 - 2*x^19*z0^2 + 2*x^17*z0^4 + 2*x^20 + 2*x^18*y*z0 + 2*x^18*z0^2 + 2*x^16*y*z0^3 + x^16*z0^4 - 2*x^19 + 2*x^15*y*z0^3 + 2*x^15*z0^4 + x^18 - 2*x^16*y*z0 + x^16*z0^2 - 2*x^14*y*z0^3 + x^14*z0^4 - x^17 + x^15*y*z0 - 2*x^15*z0^2 - 2*x^13*y*z0^3 + x^13*z0^4 + x^14*y*z0 + 2*x^14*z0^2 - 2*x^12*y*z0^3 - 2*x^12*z0^4 - x^15 + 2*x^13*y*z0 + 2*x^13*z0^2 + 2*x^11*z0^4 + 2*x^12*y*z0 + x^12*z0^2 - x^10*y*z0^3 + x^10*z0^4 + x^13 - 2*x^11*y*z0 + 2*x^11*z0^2 + 2*x^9*y*z0^3 - x^9*z0^4 - x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 + x^9*y*z0 + 2*x^9*z0^2 - x^7*z0^4 - x^6*y*z0^3 + 2*x^6*z0^4 + x^7*z0^2 - 2*x^5*z0^4 - x^8 - x^4*z0^4 - 2*x^7 + 2*x^5*y*z0 - x^5*z0^2 - 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 + x^4*y*z0 - x^2*y*z0^3 + x^2*z0^4 - x^3*y*z0 - 2*x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 - x^3)/y) * dx, - ((-x^61*z0^3 + x^58*y^2*z0^3 - 2*x^59*z0^3 + x^60*z0 - x^58*z0^3 + 2*x^56*y^2*z0^3 - 2*x^59*z0 - x^57*y^2*z0 + x^57*z0^3 + 2*x^55*y^2*z0^3 + 2*x^56*y^2*z0 + 2*x^56*z0^3 - x^54*y^2*z0^3 - x^57*z0 + x^55*z0^3 + 2*x^56*z0 - x^54*z0^3 - 2*x^53*z0^3 + x^54*z0 - x^52*z0^3 - 2*x^53*z0 + x^51*z0^3 + 2*x^50*z0^3 - x^51*z0 + x^49*z0^3 + 2*x^50*z0 - x^48*z0^3 - 2*x^47*z0^3 + x^48*z0 - x^46*z0^3 - 2*x^47*z0 + x^45*z0^3 - x^46*z0 + 2*x^44*z0^3 - x^45*z0 + x^43*y^2*z0 + x^43*z0^3 + 2*x^44*z0 - x^42*z0^3 + x^43*z0 + 2*x^41*z0^3 - x^39*y*z0^4 + x^42*z0 + 2*x^40*y*z0^2 - x^40*z0^3 - 2*x^38*y*z0^4 - 2*x^41*z0 + x^39*z0^3 + x^40*z0 - x^38*y*z0^2 - 2*x^38*z0^3 - 2*x^36*y*z0^4 - x^39*y - x^37*y*z0^2 + x^37*z0^3 + x^36*y*z0^2 - 2*x^36*z0^3 + x^34*y*z0^4 + 2*x^35*z0^3 - x^36*y - x^36*z0 - 2*x^34*y*z0^2 + x^34*z0^3 + x^35*y - 2*x^35*z0 + 2*x^33*y*z0^2 - x^33*z0^3 - 2*x^31*y*z0^4 - 2*x^34*y + 2*x^32*y*z0^2 - x^32*z0^3 + x^30*y*z0^4 - x^33*y - x^31*y*z0^2 - x^31*z0^3 + x^29*y*z0^4 - 2*x^32*y - x^32*z0 - x^30*y*z0^2 - x^30*z0^3 - 2*x^28*y*z0^4 + x^31*y - 2*x^31*z0 + 2*x^29*y*z0^2 - x^29*z0^3 - 2*x^27*y*z0^4 - x^30*y + 2*x^30*z0 + 2*x^28*y*z0^2 - x^28*z0^3 - x^26*y*z0^4 + x^29*y + x^29*z0 - 2*x^27*y*z0^2 - 2*x^27*z0^3 - 2*x^25*y*z0^4 + 2*x^28*y - 2*x^28*z0 + x^26*y*z0^2 + 2*x^26*z0^3 - x^24*y*z0^4 - 2*x^27*y - 2*x^27*z0 + x^25*z0^3 - x^23*y*z0^4 - x^26*y + x^26*z0 - 2*x^24*y*z0^2 - 2*x^24*z0^3 + x^22*y*z0^4 - x^25*y - 2*x^25*z0 - x^23*y*z0^2 - 2*x^23*z0^3 + 2*x^21*y*z0^4 + 2*x^24*y + x^24*z0 + x^22*y*z0^2 - x^20*y*z0^4 - x^23*y + x^21*y*z0^2 - x^21*z0^3 + 2*x^19*y*z0^4 - x^22*y + 2*x^22*z0 + 2*x^20*y*z0^2 - 2*x^20*z0^3 + x^18*y*z0^4 + x^21*y + x^21*z0 - x^19*y*z0^2 + x^19*z0^3 + 2*x^17*y*z0^4 - x^20*y + 2*x^20*z0 + 2*x^18*y*z0^2 - x^18*z0^3 + 2*x^16*y*z0^4 - x^19*y - x^19*z0 + 2*x^17*z0^3 - x^15*y*z0^4 + x^18*y - 2*x^18*z0 - 2*x^16*y*z0^2 - 2*x^16*z0^3 + 2*x^14*y*z0^4 - 2*x^17*y + 2*x^17*z0 + 2*x^15*y*z0^2 - x^15*z0^3 + x^13*y*z0^4 + x^16*y + 2*x^16*z0 - x^14*y*z0^2 + x^12*y*z0^4 - x^15*y + 2*x^15*z0 + x^13*y*z0^2 + 2*x^11*y*z0^4 - 2*x^14*y - 2*x^14*z0 + 2*x^12*z0^3 + x^10*y*z0^4 + x^9*y*z0^4 - 2*x^12*y + x^12*z0 - 2*x^10*y*z0^2 + 2*x^10*z0^3 + x^8*y*z0^4 + 2*x^11*z0 - x^9*y*z0^2 + x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y + 2*x^10*z0 + x^8*y*z0^2 + x^8*z0^3 - 2*x^6*y*z0^4 - x^7*y*z0^2 - 2*x^7*z0^3 + 2*x^5*y*z0^4 - 2*x^8*y + x^6*y*z0^2 - 2*x^6*z0^3 + 2*x^4*y*z0^4 - x^7*y - 2*x^7*z0 - 2*x^5*z0^3 + x^3*y*z0^4 + x^6*y - 2*x^6*z0 + x^4*y*z0^2 - 2*x^4*z0^3 - x^2*y*z0^4 + 2*x^5*y - 2*x^5*z0 + x^3*y*z0^2 - x^3*z0^3 + x^4*y - 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 - 2*x^3*y + 2*x^3*z0 - 2*x^2*y - 2*x^2*z0)/y) * dx, - ((2*x^61*z0^4 + x^60*z0^4 - 2*x^58*y^2*z0^4 + 2*x^59*z0^4 - x^57*y^2*z0^4 - 2*x^58*z0^4 - 2*x^56*y^2*z0^4 - 2*x^61 - x^57*z0^4 + 2*x^60 + 2*x^58*y^2 - 2*x^56*z0^4 - 2*x^57*y^2 + 2*x^55*z0^4 + 2*x^58 + x^54*z0^4 - 2*x^57 + 2*x^53*z0^4 - 2*x^52*z0^4 - 2*x^55 - x^51*z0^4 + 2*x^54 - 2*x^50*z0^4 + 2*x^49*z0^4 + 2*x^52 + x^48*z0^4 - 2*x^51 + 2*x^47*z0^4 - 2*x^46*z0^4 - 2*x^49 - x^45*z0^4 + 2*x^48 - x^46*z0^2 - 2*x^44*z0^4 + x^43*y^2*z0^2 + 2*x^43*z0^4 + 2*x^46 + x^42*z0^4 - 2*x^45 + x^43*z0^2 - 2*x^41*z0^4 + x^40*y*z0^3 + x^40*z0^4 - 2*x^43 + 2*x^39*z0^4 + 2*x^42 - x^40*z0^2 - x^38*y*z0^3 + 2*x^38*z0^4 + x^41 + 2*x^40 - 2*x^38*y*z0 + 2*x^36*z0^4 + x^39 - x^37*z0^2 - 2*x^35*z0^4 + x^38 + 2*x^36*y*z0 - 2*x^34*z0^4 + 2*x^37 + 2*x^35*y*z0 - x^35*z0^2 + x^33*z0^4 - 2*x^34*y*z0 + 2*x^34*z0^2 - 2*x^32*y*z0^3 + 2*x^32*z0^4 - 2*x^35 + x^33*y*z0 - x^31*y*z0^3 - 2*x^31*z0^4 + x^34 - x^30*y*z0^3 + 2*x^30*z0^4 - 2*x^33 - 2*x^31*y*z0 - 2*x^31*z0^2 + x^29*y*z0^3 - x^29*z0^4 - x^32 + 2*x^30*y*z0 - x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 - x^29*y*z0 + x^27*z0^4 - x^30 - x^28*y*z0 + x^28*z0^2 - x^26*y*z0^3 + 2*x^26*z0^4 + 2*x^29 - x^27*y*z0 - 2*x^27*z0^2 - x^25*y*z0^3 - x^25*z0^4 - x^28 - 2*x^26*y*z0 - x^26*z0^2 + x^27 - x^25*y*z0 - 2*x^25*z0^2 + x^23*y*z0^3 + x^23*z0^4 - 2*x^26 - 2*x^24*y*z0 - x^22*z0^4 + 2*x^25 - x^23*y*z0 + 2*x^23*z0^2 + x^21*z0^4 + x^24 + 2*x^22*y*z0 - 2*x^22*z0^2 + x^20*y*z0^3 - x^23 - x^21*y*z0 + 2*x^19*y*z0^3 - x^19*z0^4 + x^22 + 2*x^20*y*z0 - x^20*z0^2 - 2*x^18*y*z0^3 + 2*x^18*z0^4 + x^21 - 2*x^19*y*z0 - x^19*z0^2 + 2*x^17*y*z0^3 - x^17*z0^4 - x^20 + 2*x^18*y*z0 + 2*x^18*z0^2 - 2*x^16*y*z0^3 - x^16*z0^4 - x^19 + x^17*y*z0 - 2*x^17*z0^2 + 2*x^15*y*z0^3 - 2*x^15*z0^4 - x^16*y*z0 + x^14*z0^4 - x^17 - x^13*y*z0^3 - 2*x^13*z0^4 + 2*x^16 - 2*x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 - 2*x^15 + x^13*y*z0 + 2*x^11*y*z0^3 - x^11*z0^4 - x^14 + 2*x^12*z0^2 + 2*x^10*y*z0^3 + 2*x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^10*y*z0 - x^10*z0^2 + 2*x^8*y*z0^3 + x^8*z0^4 + 2*x^9*y*z0 + x^7*y*z0^3 - 2*x^7*z0^4 - x^10 + 2*x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 + 2*x^6*z0^4 + 2*x^9 + 2*x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 - x^5*z0^4 + 2*x^8 - x^6*y*z0 + x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 + 2*x^5*y*z0 + x^5*z0^2 + x^3*z0^4 + x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + x^5 + x^3*y*z0 - x^3*z0^2 - 2*x^2*y*z0 + 2*x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((x^61*z0^3 - x^60*z0^3 - x^58*y^2*z0^3 + 2*x^61*z0 + 2*x^59*z0^3 + x^57*y^2*z0^3 + x^60*z0 - 2*x^58*y^2*z0 + x^58*z0^3 - 2*x^56*y^2*z0^3 + 2*x^59*z0 - x^57*y^2*z0 + x^57*z0^3 - 2*x^55*y^2*z0^3 - 2*x^58*z0 - 2*x^56*y^2*z0 - 2*x^56*z0^3 - x^57*z0 - x^55*z0^3 - 2*x^56*z0 - x^54*z0^3 + 2*x^55*z0 + 2*x^53*z0^3 + x^54*z0 + x^52*z0^3 + 2*x^53*z0 + x^51*z0^3 - 2*x^52*z0 - 2*x^50*z0^3 - x^51*z0 - x^49*z0^3 - 2*x^50*z0 - x^48*z0^3 + 2*x^49*z0 + 2*x^47*z0^3 + x^48*z0 + 2*x^47*z0 + x^45*z0^3 + x^43*y^2*z0^3 - 2*x^46*z0 - 2*x^44*z0^3 - x^45*z0 - 2*x^44*z0 - x^42*z0^3 + 2*x^43*z0 - 2*x^41*z0^3 + x^39*y*z0^4 + x^42*z0 - 2*x^40*y*z0^2 + x^40*z0^3 - x^38*y*z0^4 - x^41*z0 + 2*x^39*y*z0^2 + x^39*z0^3 - 2*x^37*y*z0^4 + x^40*y + 2*x^38*z0^3 + 2*x^36*y*z0^4 - 2*x^39*y + x^39*z0 + x^37*y*z0^2 - x^37*z0^3 + x^35*y*z0^4 + 2*x^38*y - x^38*z0 + 2*x^34*y*z0^4 + 2*x^37*y - 2*x^35*y*z0^2 - 2*x^35*z0^3 + x^33*y*z0^4 + x^36*y - x^34*y*z0^2 + 2*x^34*z0^3 + x^32*y*z0^4 - 2*x^35*z0 - x^33*y*z0^2 + x^33*z0^3 - x^31*y*z0^4 - 2*x^34*y - x^34*z0 + 2*x^32*y*z0^2 + x^32*z0^3 + x^30*y*z0^4 + 2*x^33*y - 2*x^33*z0 + x^31*y*z0^2 + 2*x^31*z0^3 - x^29*y*z0^4 + 2*x^32*y + x^32*z0 - 2*x^30*y*z0^2 + x^30*z0^3 + 2*x^31*y - 2*x^31*z0 + x^29*z0^3 + x^30*y - 2*x^28*y*z0^2 + 2*x^26*y*z0^4 + 2*x^29*y + x^29*z0 + 2*x^27*y*z0^2 - x^27*z0^3 - x^25*y*z0^4 - 2*x^28*y - 2*x^28*z0 + 2*x^26*z0^3 + 2*x^24*y*z0^4 + 2*x^27*y - 2*x^27*z0 - 2*x^25*y*z0^2 + x^25*z0^3 - x^23*y*z0^4 + x^26*y + 2*x^26*z0 + x^24*y*z0^2 - 2*x^24*z0^3 + x^22*y*z0^4 + 2*x^25*y + 2*x^25*z0 - 2*x^23*y*z0^2 - 2*x^23*z0^3 - 2*x^21*y*z0^4 - 2*x^24*y + 2*x^24*z0 - x^22*y*z0^2 + 2*x^22*z0^3 + x^20*y*z0^4 + 2*x^23*y - x^23*z0 - 2*x^21*y*z0^2 - 2*x^21*z0^3 + x^19*y*z0^4 + x^22*y + x^22*z0 + x^20*y*z0^2 + 2*x^20*z0^3 - x^18*y*z0^4 + 2*x^21*y + x^19*z0^3 + x^17*y*z0^4 + 2*x^20*y - x^20*z0 + 2*x^18*y*z0^2 - x^18*z0^3 - x^16*y*z0^4 - x^19*y + x^19*z0 - x^17*y*z0^2 + 2*x^17*z0^3 + x^15*y*z0^4 - 2*x^18*y - 2*x^18*z0 + x^16*y*z0^2 + x^16*z0^3 - 2*x^17*y - x^17*z0 - x^15*y*z0^2 - 2*x^15*z0^3 - 2*x^13*y*z0^4 + x^16*y + x^16*z0 + x^14*y*z0^2 + x^14*z0^3 - 2*x^12*y*z0^4 - x^15*y - 2*x^13*y*z0^2 - 2*x^11*y*z0^4 + x^14*y - x^12*z0^3 - x^10*y*z0^4 + x^11*y*z0^2 - 2*x^11*z0^3 - x^9*y*z0^4 - 2*x^12*z0 + x^10*y*z0^2 - x^8*y*z0^4 - 2*x^11*y + x^9*z0^3 - 2*x^10*y - 2*x^10*z0 - 2*x^8*y*z0^2 - x^8*z0^3 - x^6*y*z0^4 + x^9*z0 - 2*x^7*y*z0^2 - x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - 2*x^6*y*z0^2 - 2*x^6*z0^3 - 2*x^4*y*z0^4 + x^7*y + x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y - x^6*z0 - 2*x^4*y*z0^2 + x^4*z0^3 - x^2*y*z0^4 + x^5*y + 2*x^5*z0 - x^3*y*z0^2 - 2*x^3*z0^3 + 2*x^2*y*z0^2 - x^2*z0^3 - 2*x^3*z0 - x^2*y)/y) * dx, - ((-x^60*z0^4 + x^61*z0^2 + 2*x^59*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 - x^58*y^2*z0^2 - 2*x^56*y^2*z0^4 - x^61 - x^57*y^2*z0^2 + x^57*z0^4 + 2*x^60 + x^58*y^2 - x^58*z0^2 - 2*x^56*z0^4 - 2*x^57*y^2 - x^57*z0^2 + x^58 - x^54*z0^4 - 2*x^57 + x^55*z0^2 + 2*x^53*z0^4 + x^54*z0^2 - x^55 + x^51*z0^4 + 2*x^54 - x^52*z0^2 - 2*x^50*z0^4 - x^51*z0^2 + x^52 - x^48*z0^4 - 2*x^51 + x^49*z0^2 + 2*x^47*z0^4 + x^48*z0^2 - x^46*z0^4 - x^49 + x^45*z0^4 + x^43*y^2*z0^4 + 2*x^48 - x^46*z0^2 - 2*x^44*z0^4 - x^45*z0^2 + x^43*z0^4 + x^46 - x^42*z0^4 - 2*x^45 + x^43*z0^2 - x^41*z0^4 + x^42*z0^2 + x^40*z0^4 - x^43 + x^41*z0^2 + x^39*y*z0^3 + 2*x^42 - 2*x^40*y*z0 - 2*x^40*z0^2 - x^38*y*z0^3 - x^38*z0^4 + 2*x^41 + x^39*y*z0 - 2*x^39*z0^2 - 2*x^37*y*z0^3 + 2*x^40 + 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - x^36*z0^4 + x^39 - x^37*y*z0 - x^37*z0^2 - 2*x^35*y*z0^3 - x^35*z0^4 - 2*x^38 - x^36*y*z0 + 2*x^36*z0^2 + x^34*y*z0^3 - x^34*z0^4 - x^37 + 2*x^35*y*z0 + 2*x^35*z0^2 + x^33*y*z0^3 - 2*x^36 + 2*x^34*y*z0 - 2*x^34*z0^2 - x^32*y*z0^3 - 2*x^32*z0^4 + x^35 + 2*x^33*y*z0 + x^33*z0^2 + x^31*z0^4 - 2*x^34 + 2*x^32*y*z0 - 2*x^32*z0^2 + x^30*z0^4 + 2*x^33 + x^31*z0^2 - x^29*z0^4 - x^32 + 2*x^30*y*z0 + 2*x^28*y*z0^3 - x^28*z0^4 + 2*x^31 - x^29*y*z0 + x^29*z0^2 + 2*x^27*y*z0^3 + 2*x^27*z0^4 - 2*x^30 - 2*x^28*y*z0 - x^28*z0^2 + 2*x^26*y*z0^3 + x^26*z0^4 - 2*x^29 + 2*x^27*z0^2 - x^25*z0^4 + 2*x^28 + 2*x^24*y*z0^3 - x^24*z0^4 + 2*x^27 + 2*x^25*y*z0 - 2*x^25*z0^2 - 2*x^23*y*z0^3 - 2*x^23*z0^4 - 2*x^26 - x^24*y*z0 - 2*x^24*z0^2 - x^22*y*z0^3 + 2*x^22*z0^4 + 2*x^25 - x^23*y*z0 + x^23*z0^2 + x^21*z0^4 - 2*x^24 - x^22*y*z0 + 2*x^22*z0^2 + x^20*y*z0^3 - 2*x^20*z0^4 + 2*x^23 + 2*x^21*y*z0 - x^21*z0^2 + x^19*y*z0^3 + x^19*z0^4 + x^20*y*z0 - x^20*z0^2 + 2*x^18*y*z0^3 - x^18*z0^4 - x^21 - x^19*y*z0 - 2*x^17*y*z0^3 + x^17*z0^4 - x^20 - x^18*y*z0 - x^18*z0^2 - 2*x^16*y*z0^3 + x^16*z0^4 - x^17*y*z0 - x^17*z0^2 + 2*x^15*y*z0^3 + x^18 + x^16*y*z0 - x^16*z0^2 - x^14*y*z0^3 - 2*x^14*z0^4 + 2*x^17 + 2*x^15*y*z0 + x^15*z0^2 + 2*x^13*y*z0^3 + 2*x^16 + 2*x^14*y*z0 - x^12*y*z0^3 - 2*x^12*z0^4 + 2*x^15 + 2*x^13*y*z0 + x^13*z0^2 + x^10*z0^4 - 2*x^13 + 2*x^11*y*z0 - 2*x^11*z0^2 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 + 2*x^10*z0^2 - x^11 - x^9*z0^2 + 2*x^7*y*z0^3 + x^7*z0^4 - 2*x^10 + 2*x^8*y*z0 + 2*x^6*y*z0^3 + 2*x^9 - x^7*y*z0 + x^7*z0^2 - x^5*y*z0^3 + 2*x^5*z0^4 + x^6*y*z0 + 2*x^6*z0^2 + 2*x^4*y*z0^3 + x^7 + x^5*y*z0 + x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^6 - x^4*z0^2 - 2*x^2*y*z0^3 + x^2*z0^4 - x^5 + 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 + x^2*z0^2 + 2*x^3)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((2*x^61*z0^4 + 2*x^60*z0^4 - 2*x^58*y^2*z0^4 - x^61*z0^2 - 2*x^57*y^2*z0^4 + 2*x^60*z0^2 + x^58*y^2*z0^2 - 2*x^58*z0^4 + 2*x^61 - 2*x^57*y^2*z0^2 - 2*x^57*z0^4 + x^60 - 2*x^58*y^2 + x^58*z0^2 - x^57*y^2 - 2*x^57*z0^2 + 2*x^55*z0^4 - 2*x^58 + 2*x^54*z0^4 - x^57 - x^55*z0^2 + 2*x^54*z0^2 - 2*x^52*z0^4 + 2*x^55 - 2*x^51*z0^4 + x^54 + x^52*z0^2 - 2*x^51*z0^2 + 2*x^49*z0^4 - 2*x^52 + 2*x^48*z0^4 - x^51 - x^49*z0^2 + 2*x^48*z0^2 - 2*x^46*z0^4 + 2*x^49 - 2*x^45*z0^4 + x^48 + x^46*z0^2 - x^47 - 2*x^45*z0^2 + 2*x^43*z0^4 - 2*x^46 + x^44*y^2 + 2*x^42*z0^4 - x^45 - x^43*z0^2 - 2*x^41*z0^4 + x^44 + 2*x^42*z0^2 + x^40*y*z0^3 - 2*x^40*z0^4 + 2*x^43 - x^41*z0^2 - x^39*y*z0^3 + x^39*z0^4 + x^42 + 2*x^40*y*z0 - x^40*z0^2 + x^38*y*z0^3 + x^38*z0^4 + 2*x^41 + 2*x^39*y*z0 - x^39*z0^2 - 2*x^37*y*z0^3 + 2*x^37*z0^4 + 2*x^40 - 2*x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 + 2*x^37*y*z0 - 2*x^37*z0^2 + 2*x^38 + 2*x^36*y*z0 + x^36*z0^2 + 2*x^34*y*z0^3 - x^34*z0^4 - x^37 - x^35*y*z0 + 2*x^33*y*z0^3 - 2*x^33*z0^4 + x^36 + 2*x^34*y*z0 + 2*x^32*y*z0^3 + x^33*z0^2 - 2*x^31*y*z0^3 + 2*x^31*z0^4 + 2*x^34 + 2*x^32*z0^2 + 2*x^30*y*z0^3 - x^30*z0^4 - 2*x^33 - 2*x^31*y*z0 - x^29*z0^4 + x^32 + 2*x^28*y*z0^3 + x^28*z0^4 + x^31 - 2*x^29*y*z0 + x^29*z0^2 + 2*x^27*y*z0^3 + 2*x^27*z0^4 - 2*x^30 + x^28*y*z0 - 2*x^26*y*z0^3 + 2*x^26*z0^4 - x^27*y*z0 + 2*x^27*z0^2 + x^25*y*z0^3 + x^28 - 2*x^26*y*z0 - x^26*z0^2 - x^24*y*z0^3 + 2*x^24*z0^4 + 2*x^25*y*z0 + 2*x^25*z0^2 + x^23*y*z0^3 + x^23*z0^4 - 2*x^26 - 2*x^24*y*z0 + 2*x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^22*z0^4 - 2*x^23*y*z0 - x^23*z0^2 + 2*x^21*y*z0^3 + 2*x^21*z0^4 - 2*x^24 - 2*x^22*y*z0 - 2*x^22*z0^2 - 2*x^20*y*z0^3 + 2*x^20*z0^4 + 2*x^23 - x^21*z0^2 - 2*x^19*y*z0^3 + 2*x^19*z0^4 - 2*x^20*y*z0 + x^20*z0^2 - x^18*y*z0^3 - x^18*z0^4 + 2*x^21 + 2*x^19*y*z0 + 2*x^19*z0^2 + 2*x^17*y*z0^3 + 2*x^17*z0^4 + 2*x^20 - x^18*y*z0 + x^18*z0^2 - x^16*y*z0^3 + x^19 + x^17*z0^2 - 2*x^15*y*z0^3 + x^15*z0^4 + x^18 - 2*x^16*y*z0 - 2*x^16*z0^2 + x^14*y*z0^3 - x^14*z0^4 - x^17 - 2*x^15*y*z0 - x^13*y*z0^3 + x^13*z0^4 + 2*x^16 - 2*x^14*y*z0 - 2*x^14*z0^2 + 2*x^12*y*z0^3 + 2*x^12*z0^4 + x^15 - x^13*y*z0 - 2*x^13*z0^2 + 2*x^11*y*z0^3 + x^11*z0^4 + 2*x^14 - x^12*z0^2 + x^10*z0^4 - x^11*y*z0 + x^11*z0^2 - x^9*y*z0^3 + x^10*y*z0 + x^10*z0^2 - 2*x^8*z0^4 - x^11 + 2*x^9*y*z0 - x^9*z0^2 + 2*x^7*y*z0^3 + x^7*z0^4 + x^10 - x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 - 2*x^6*z0^4 - 2*x^9 + 2*x^7*y*z0 - 2*x^7*z0^2 - 2*x^5*y*z0^3 + 2*x^5*z0^4 - x^8 + x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 + x^5*y*z0 - x^5*z0^2 - x^3*y*z0^3 + x^3*z0^4 + 2*x^6 - 2*x^4*y*z0 - x^4*z0^2 - x^2*y*z0^3 - 2*x^2*z0^4 + 2*x^5 - 2*x^3*y*z0 + 2*x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 + x^2)/y) * dx, - ((x^61*z0^3 - 2*x^60*z0^3 - x^58*y^2*z0^3 + 2*x^61*z0 + 2*x^57*y^2*z0^3 + 2*x^60*z0 - 2*x^58*y^2*z0 - 2*x^58*z0^3 + 2*x^59*z0 - 2*x^57*y^2*z0 + 2*x^57*z0^3 + x^55*y^2*z0^3 - 2*x^58*z0 - 2*x^56*y^2*z0 - 2*x^57*z0 + 2*x^55*z0^3 - 2*x^56*z0 - 2*x^54*z0^3 + 2*x^55*z0 + 2*x^54*z0 - 2*x^52*z0^3 + 2*x^53*z0 + 2*x^51*z0^3 - 2*x^52*z0 - 2*x^51*z0 + 2*x^49*z0^3 - 2*x^50*z0 - 2*x^48*z0^3 + 2*x^49*z0 + 2*x^48*z0 - 2*x^46*z0^3 + x^47*z0 + 2*x^45*z0^3 - 2*x^46*z0 + x^44*y^2*z0 - 2*x^45*z0 + 2*x^43*z0^3 - x^44*z0 - 2*x^42*z0^3 + 2*x^43*z0 + x^41*z0^3 + x^39*y*z0^4 + 2*x^42*z0 - 2*x^40*y*z0^2 - 2*x^41*z0 + 2*x^39*y*z0^2 - 2*x^39*z0^3 + 2*x^37*y*z0^4 + x^40*y + x^40*z0 + 2*x^38*y*z0^2 + 2*x^38*z0^3 - 2*x^36*y*z0^4 - 2*x^37*z0^3 + x^35*y*z0^4 + 2*x^38*y + 2*x^36*z0^3 - 2*x^34*y*z0^4 + 2*x^37*y + x^37*z0 + 2*x^35*z0^3 - x^33*y*z0^4 - x^36*y + x^36*z0 - x^34*z0^3 + 2*x^32*y*z0^4 - x^35*y - x^35*z0 - x^33*z0^3 + x^34*y - x^34*z0 - 2*x^30*y*z0^4 - 2*x^33*y + 2*x^33*z0 - 2*x^31*y*z0^2 + 2*x^31*z0^3 + x^29*y*z0^4 + x^32*y - x^32*z0 - x^30*y*z0^2 - 2*x^30*z0^3 - 2*x^31*y + x^31*z0 + 2*x^29*y*z0^2 + x^29*z0^3 + x^27*y*z0^4 - 2*x^30*y - 2*x^28*y*z0^2 - 2*x^26*y*z0^4 - 2*x^29*y - 2*x^27*y*z0^2 - 2*x^27*z0^3 + x^25*y*z0^4 - x^28*y - 2*x^28*z0 + x^26*y*z0^2 - x^26*z0^3 + x^24*y*z0^4 + x^27*z0 - 2*x^25*y*z0^2 + 2*x^25*z0^3 - x^23*y*z0^4 + 2*x^26*y + 2*x^26*z0 - x^24*z0^3 + x^25*y + x^25*z0 - x^23*y*z0^2 - 2*x^21*y*z0^4 - 2*x^24*z0 + x^22*z0^3 - 2*x^20*y*z0^4 + x^23*y + x^21*y*z0^2 + 2*x^21*z0^3 - 2*x^22*y + x^22*z0 - 2*x^20*y*z0^2 - x^20*z0^3 + x^18*y*z0^4 - x^21*y + x^21*z0 - x^19*y*z0^2 - x^19*z0^3 + 2*x^17*y*z0^4 - 2*x^20*z0 + x^18*y*z0^2 + x^18*z0^3 + 2*x^16*y*z0^4 - 2*x^19*y - 2*x^19*z0 - 2*x^17*y*z0^2 - 2*x^15*y*z0^4 - 2*x^18*y - x^18*z0 + x^16*y*z0^2 + x^16*z0^3 - 2*x^17*y + x^17*z0 - 2*x^15*y*z0^2 - x^15*z0^3 + x^13*y*z0^4 - 2*x^16*y + 2*x^14*y*z0^2 + 2*x^12*y*z0^4 + x^15*z0 + x^13*y*z0^2 - x^13*z0^3 - 2*x^11*y*z0^4 + x^14*y - 2*x^14*z0 - 2*x^12*y*z0^2 - 2*x^12*z0^3 - x^10*y*z0^4 + x^13*y - 2*x^11*y*z0^2 - 2*x^11*z0^3 - x^9*y*z0^4 + x^12*y - x^12*z0 + x^10*y*z0^2 + x^10*z0^3 + x^8*y*z0^4 + 2*x^11*y + 2*x^9*y*z0^2 - 2*x^9*z0^3 + 2*x^7*y*z0^4 - x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 + 2*x^6*y*z0^4 - x^9*y - 2*x^7*y*z0^2 - x^7*z0^3 - 2*x^8*y - 2*x^8*z0 - 2*x^6*y*z0^2 + 2*x^6*z0^3 - x^4*y*z0^4 - 2*x^7*y - x^7*z0 + 2*x^5*y*z0^2 - 2*x^3*y*z0^4 - x^6*z0 + 2*x^4*y*z0^2 + 2*x^4*z0^3 + x^2*y*z0^4 + x^5*y + 2*x^5*z0 - x^3*y*z0^2 - 2*x^3*z0^3 - x^4*z0 - 2*x^2*y*z0^2 - x^2*z0^3 - x^3*y - x^3*z0 + x^2*y - 2*x^2*z0)/y) * dx, - ((-2*x^61*z0^4 - x^60*z0^4 + 2*x^58*y^2*z0^4 - x^61*z0^2 + x^59*z0^4 + x^57*y^2*z0^4 + x^58*y^2*z0^2 + 2*x^58*z0^4 - x^56*y^2*z0^4 + 2*x^61 + x^57*z0^4 + 2*x^60 - 2*x^58*y^2 + x^58*z0^2 - x^56*z0^4 - 2*x^57*y^2 - 2*x^55*z0^4 - 2*x^58 - x^54*z0^4 - 2*x^57 - x^55*z0^2 + x^53*z0^4 + 2*x^52*z0^4 + 2*x^55 + x^51*z0^4 + 2*x^54 + x^52*z0^2 - x^50*z0^4 - 2*x^49*z0^4 - 2*x^52 - x^48*z0^4 - 2*x^51 - x^49*z0^2 + x^47*z0^4 + 2*x^46*z0^4 + 2*x^49 - x^47*z0^2 + x^45*z0^4 + 2*x^48 + x^46*z0^2 + x^44*y^2*z0^2 - x^44*z0^4 - 2*x^43*z0^4 - 2*x^46 + x^44*z0^2 - x^42*z0^4 - 2*x^45 - x^43*z0^2 - x^40*y*z0^3 - 2*x^40*z0^4 + 2*x^43 - 2*x^41*z0^2 - x^39*y*z0^3 + 2*x^39*z0^4 + 2*x^42 + 2*x^40*y*z0 - 2*x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + x^39*z0^2 - x^37*y*z0^3 + 2*x^37*z0^4 + 2*x^40 - x^38*z0^2 + 2*x^36*y*z0^3 - x^36*z0^4 - 2*x^39 - 2*x^37*y*z0 - 2*x^37*z0^2 + 2*x^35*y*z0^3 - 2*x^35*z0^4 - x^36*y*z0 - x^36*z0^2 + 2*x^34*z0^4 + 2*x^35*z0^2 + 2*x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 - 2*x^34*z0^2 + x^32*z0^4 + 2*x^33*z0^2 - 2*x^31*y*z0^3 + x^34 - 2*x^32*y*z0 - x^30*y*z0^3 + 2*x^33 - x^31*y*z0 - x^29*y*z0^3 - x^32 - 2*x^30*y*z0 - 2*x^30*z0^2 + x^28*y*z0^3 + x^28*z0^4 - 2*x^29*y*z0 - x^29*z0^2 + 2*x^27*y*z0^3 + x^27*z0^4 - x^30 + 2*x^28*y*z0 - 2*x^28*z0^2 - 2*x^26*y*z0^3 - 2*x^26*z0^4 - x^27*y*z0 - x^27*z0^2 + 2*x^25*y*z0^3 - 2*x^25*z0^4 + x^28 - 2*x^26*z0^2 + 2*x^24*y*z0^3 + 2*x^24*z0^4 - 2*x^27 - x^25*y*z0 + x^25*z0^2 - x^23*y*z0^3 - x^26 - 2*x^24*y*z0 - x^24*z0^2 + x^22*y*z0^3 - x^22*z0^4 - x^25 - x^23*z0^2 - x^21*y*z0^3 - x^21*z0^4 + 2*x^24 + 2*x^22*z0^2 + x^20*y*z0^3 + 2*x^20*z0^4 - x^23 - 2*x^21*z0^2 - 2*x^19*y*z0^3 - 2*x^19*z0^4 - x^20*z0^2 - x^18*y*z0^3 - 2*x^18*z0^4 - 2*x^21 + x^19*y*z0 + x^19*z0^2 - x^17*y*z0^3 - x^17*z0^4 - 2*x^20 + x^18*y*z0 + 2*x^18*z0^2 - 2*x^16*y*z0^3 - x^16*z0^4 + 2*x^19 - 2*x^17*y*z0 - 2*x^17*z0^2 + 2*x^15*y*z0^3 + x^18 - x^16*y*z0 - 2*x^16*z0^2 + x^14*y*z0^3 - x^14*z0^4 - 2*x^17 + 2*x^15*y*z0 + 2*x^15*z0^2 + 2*x^13*y*z0^3 - 2*x^13*z0^4 - x^14*y*z0 + x^14*z0^2 - 2*x^12*y*z0^3 + 2*x^12*z0^4 - 2*x^15 + 2*x^13*y*z0 - x^13*z0^2 - 2*x^11*y*z0^3 - x^11*z0^4 + x^14 + 2*x^12*y*z0 - x^12*z0^2 + 2*x^10*y*z0^3 - x^13 + x^11*y*z0 + x^9*y*z0^3 - x^9*z0^4 - x^12 - 2*x^10*y*z0 - 2*x^10*z0^2 - x^8*y*z0^3 + x^11 + 2*x^9*z0^2 + 2*x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 - 2*x^8*y*z0 - x^6*y*z0^3 - x^6*z0^4 + x^9 - x^7*y*z0 - x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - x^8 - 2*x^6*y*z0 - 2*x^4*z0^4 - x^7 - x^5*y*z0 + x^5*z0^2 + 2*x^3*y*z0^3 + x^3*z0^4 + x^4*y*z0 + 2*x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 - 2*x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 - x^3)/y) * dx, - ((-2*x^61*z0^3 + 2*x^58*y^2*z0^3 - 2*x^60*z0 + x^58*z0^3 - x^59*z0 + 2*x^57*y^2*z0 + x^55*y^2*z0^3 + x^56*y^2*z0 + 2*x^57*z0 - x^55*z0^3 + x^56*z0 - 2*x^54*z0 + x^52*z0^3 - x^53*z0 + 2*x^51*z0 - x^49*z0^3 + x^50*z0 - x^47*z0^3 - 2*x^48*z0 + x^46*z0^3 + x^44*y^2*z0^3 - x^47*z0 + x^44*z0^3 + 2*x^45*z0 - x^43*z0^3 + x^44*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 - 2*x^42*z0 - x^40*y*z0^2 - x^40*z0^3 - x^38*y*z0^4 - x^41*z0 + x^39*z0^3 + x^40*z0 + 2*x^38*z0^3 - x^36*y*z0^4 - 2*x^39*y + 2*x^37*y*z0^2 - x^35*y*z0^4 + x^38*y - 2*x^36*y*z0^2 - x^36*z0^3 - 2*x^37*z0 - x^35*z0^3 + 2*x^33*y*z0^4 - x^36*y + 2*x^36*z0 - x^34*y*z0^2 + x^34*z0^3 + x^32*y*z0^4 + 2*x^35*y - x^35*z0 - 2*x^33*y*z0^2 + 2*x^33*z0^3 - x^31*y*z0^4 + x^34*z0 + 2*x^32*y*z0^2 + 2*x^32*z0^3 + x^30*y*z0^4 + 2*x^33*z0 - x^31*y*z0^2 + x^31*z0^3 - 2*x^29*y*z0^4 + x^32*y + 2*x^32*z0 - x^30*z0^3 - 2*x^28*y*z0^4 - 2*x^31*y - 2*x^31*z0 - 2*x^29*y*z0^2 + 2*x^29*z0^3 + 2*x^27*y*z0^4 + x^30*y - 2*x^30*z0 + x^28*y*z0^2 - x^28*z0^3 - x^29*y + x^27*y*z0^2 - x^27*z0^3 - 2*x^25*y*z0^4 + x^28*y - 2*x^28*z0 - 2*x^26*y*z0^2 + x^26*z0^3 + 2*x^24*y*z0^4 + x^27*z0 - 2*x^25*y*z0^2 - 2*x^25*z0^3 + 2*x^26*y - 2*x^26*z0 - x^24*y*z0^2 - 2*x^24*z0^3 - x^25*y - 2*x^25*z0 + x^23*y*z0^2 - 2*x^23*z0^3 + x^21*y*z0^4 + x^24*z0 + x^22*y*z0^2 - 2*x^22*z0^3 + 2*x^23*y + x^21*y*z0^2 + 2*x^21*z0^3 + 2*x^19*y*z0^4 + x^22*y - 2*x^22*z0 - 2*x^20*y*z0^2 - x^21*y - x^21*z0 + 2*x^19*y*z0^2 - 2*x^19*z0^3 - 2*x^17*y*z0^4 + x^20*z0 - x^18*y*z0^2 - 2*x^16*y*z0^4 + x^19*y + x^19*z0 + x^17*y*z0^2 - x^17*z0^3 - 2*x^15*y*z0^4 - 2*x^18*y + 2*x^18*z0 - x^16*y*z0^2 + 2*x^16*z0^3 - x^17*y + 2*x^17*z0 - x^15*y*z0^2 + 2*x^15*z0^3 + x^16*y - 2*x^14*y*z0^2 + x^14*z0^3 - 2*x^12*y*z0^4 + x^15*z0 - 2*x^13*y*z0^2 - x^13*z0^3 - 2*x^11*y*z0^4 - x^14*y + x^12*y*z0^2 + 2*x^12*z0^3 - 2*x^10*y*z0^4 + x^13*z0 - x^11*y*z0^2 + 2*x^11*z0^3 + 2*x^12*y + x^12*z0 - 2*x^10*y*z0^2 + 2*x^10*z0^3 - 2*x^8*y*z0^4 + 2*x^11*y - 2*x^9*y*z0^2 - x^9*z0^3 - 2*x^10*y - 2*x^10*z0 - 2*x^8*y*z0^2 - 2*x^6*y*z0^4 + 2*x^9*y + 2*x^9*z0 + 2*x^7*z0^3 + x^5*y*z0^4 + x^8*z0 - x^6*y*z0^2 - x^4*y*z0^4 + 2*x^7*y - x^7*z0 - x^5*y*z0^2 + 2*x^3*y*z0^4 + x^6*y + x^4*y*z0^2 - 2*x^4*z0^3 + x^2*y*z0^4 - x^5*y + x^5*z0 - x^3*y*z0^2 - x^4*y + x^4*z0 + 2*x^2*y*z0^2 + 2*x^2*z0^3 + x^3*y - 2*x^3*z0 - 2*x^2*z0)/y) * dx, - ((2*x^61*z0^4 - 2*x^60*z0^4 - 2*x^58*y^2*z0^4 - 2*x^61*z0^2 + 2*x^57*y^2*z0^4 - 2*x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + x^61 + 2*x^57*y^2*z0^2 + 2*x^57*z0^4 - 2*x^60 - x^58*y^2 + 2*x^58*z0^2 + 2*x^57*y^2 + 2*x^57*z0^2 + 2*x^55*z0^4 - x^58 - 2*x^54*z0^4 + 2*x^57 - 2*x^55*z0^2 - 2*x^54*z0^2 - 2*x^52*z0^4 + x^55 + 2*x^51*z0^4 - 2*x^54 + 2*x^52*z0^2 + 2*x^51*z0^2 + 2*x^49*z0^4 - x^52 - 2*x^48*z0^4 + 2*x^51 - 2*x^49*z0^2 - x^47*z0^4 - 2*x^48*z0^2 - 2*x^46*z0^4 + x^44*y^2*z0^4 + x^49 + 2*x^45*z0^4 - 2*x^48 + 2*x^46*z0^2 + x^44*z0^4 + 2*x^45*z0^2 + 2*x^43*z0^4 - x^46 - 2*x^42*z0^4 + 2*x^45 - 2*x^43*z0^2 - x^41*z0^4 - 2*x^42*z0^2 + x^40*y*z0^3 + 2*x^40*z0^4 + x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - 2*x^42 - x^40*y*z0 + x^38*z0^4 - x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 + 2*x^37*z0^4 + x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 - x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 - 2*x^35*z0^4 + x^36*y*z0 + x^36*z0^2 - 2*x^34*y*z0^3 + x^37 - 2*x^36 + 2*x^34*y*z0 + x^34*z0^2 + x^32*y*z0^3 + x^32*z0^4 + 2*x^35 + x^33*y*z0 - x^33*z0^2 - x^31*y*z0^3 + 2*x^31*z0^4 + x^34 + x^32*y*z0 + 2*x^32*z0^2 + 2*x^30*z0^4 - 2*x^33 + 2*x^31*y*z0 - 2*x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^32 + 2*x^30*y*z0 - 2*x^28*y*z0^3 - x^28*z0^4 - x^31 + 2*x^29*z0^2 + 2*x^27*y*z0^3 - x^27*z0^4 - 2*x^28*z0^2 + 2*x^26*y*z0^3 - 2*x^26*z0^4 + x^29 - 2*x^27*y*z0 + x^27*z0^2 + 2*x^25*z0^4 - 2*x^28 + x^26*y*z0 + x^24*y*z0^3 + 2*x^27 + 2*x^23*y*z0^3 - 2*x^23*z0^4 - 2*x^26 - x^24*y*z0 + 2*x^24*z0^2 - 2*x^22*y*z0^3 + x^22*z0^4 - x^25 - 2*x^23*y*z0 - 2*x^23*z0^2 + 2*x^21*y*z0^3 + 2*x^21*z0^4 - 2*x^24 - 2*x^22*y*z0 - 2*x^22*z0^2 + 2*x^20*y*z0^3 + x^20*z0^4 - 2*x^23 - x^21*y*z0 + 2*x^19*y*z0^3 + 2*x^19*z0^4 - x^22 - 2*x^20*y*z0 - 2*x^20*z0^2 + x^18*y*z0^3 - x^18*z0^4 - x^21 + x^19*y*z0 + x^19*z0^2 + 2*x^17*y*z0^3 + x^17*z0^4 + 2*x^20 - 2*x^18*y*z0 - 2*x^18*z0^2 + x^16*z0^4 - x^19 + x^17*y*z0 + x^17*z0^2 + x^15*y*z0^3 - 2*x^15*z0^4 - 2*x^18 - 2*x^16*y*z0 + x^16*z0^2 + x^14*y*z0^3 + x^14*z0^4 - 2*x^15*z0^2 - 2*x^13*y*z0^3 + 2*x^13*z0^4 + 2*x^14*z0^2 + 2*x^12*z0^4 + 2*x^15 - 2*x^13*y*z0 - x^11*y*z0^3 + x^11*z0^4 + x^14 - x^12*y*z0 + x^12*z0^2 + x^10*z0^4 - 2*x^13 - x^11*y*z0 + 2*x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 - 2*x^10*y*z0 + 2*x^10*z0^2 + x^8*y*z0^3 + x^8*z0^4 - 2*x^11 - x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 - 2*x^7*z0^4 + 2*x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 + x^6*y*z0^3 + 2*x^9 - x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 + 2*x^6*y*z0 + x^4*z0^4 + 2*x^7 + x^5*y*z0 - x^5*z0^2 + 2*x^3*z0^4 - 2*x^6 - 2*x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 - 2*x^3*y*z0 + x^3*z0^2 + 2*x^2*z0^2 - x^3 - 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 - x^61*z0^2 + 2*x^60*z0^2 + x^58*y^2*z0^2 - x^58*z0^4 + 2*x^61 - 2*x^57*y^2*z0^2 + 2*x^60 - 2*x^58*y^2 + x^58*z0^2 - 2*x^57*y^2 - 2*x^57*z0^2 + x^55*z0^4 - 2*x^58 - 2*x^57 - x^55*z0^2 + 2*x^54*z0^2 - x^52*z0^4 + 2*x^55 + 2*x^54 + x^52*z0^2 - 2*x^51*z0^2 + x^49*z0^4 - 2*x^52 - 2*x^51 - x^49*z0^2 + 2*x^48*z0^2 - x^46*z0^4 + 2*x^49 + x^48 + x^46*z0^2 + x^45*y^2 - 2*x^45*z0^2 + x^43*z0^4 - 2*x^46 - x^45 - x^43*z0^2 + 2*x^41*z0^4 + 2*x^42*z0^2 - 2*x^40*y*z0^3 + 2*x^40*z0^4 + 2*x^43 - x^41*z0^2 - x^39*y*z0^3 + x^39*z0^4 + x^42 + 2*x^40*y*z0 + x^38*y*z0^3 - x^38*z0^4 + 2*x^41 - x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 + x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^39 + 2*x^37*y*z0 - 2*x^35*y*z0^3 - x^38 + 2*x^36*y*z0 + x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^34*z0^4 - x^37 + 2*x^35*y*z0 + 2*x^35*z0^2 + x^33*y*z0^3 + x^33*z0^4 - x^36 + 2*x^34*y*z0 - x^34*z0^2 - 2*x^32*y*z0^3 - x^32*z0^4 - 2*x^33*y*z0 - 2*x^33*z0^2 + 2*x^31*y*z0^3 + 2*x^31*z0^4 - x^34 + x^32*y*z0 - x^32*z0^2 - 2*x^30*z0^4 - x^31*y*z0 - x^31*z0^2 + 2*x^29*y*z0^3 - x^29*z0^4 - x^32 + x^30*y*z0 + x^30*z0^2 - x^28*y*z0^3 - x^28*z0^4 + x^31 + 2*x^29*y*z0 - x^29*z0^2 + 2*x^27*y*z0^3 - 2*x^27*z0^4 + 2*x^30 + x^28*y*z0 - x^28*z0^2 - 2*x^26*y*z0^3 + x^26*z0^4 - x^29 + x^27*y*z0 + 2*x^27*z0^2 + 2*x^25*y*z0^3 + x^25*z0^4 - 2*x^28 + 2*x^26*y*z0 + x^26*z0^2 - x^24*y*z0^3 - x^24*z0^4 - 2*x^27 + 2*x^25*z0^2 - x^23*y*z0^3 - 2*x^23*z0^4 - x^24*y*z0 + x^24*z0^2 - 2*x^25 - x^23*y*z0 + x^23*z0^2 + x^21*z0^4 - x^22*z0^2 - x^20*y*z0^3 - 2*x^20*z0^4 + 2*x^21*y*z0 + x^21*z0^2 - 2*x^19*y*z0^3 - 2*x^22 + 2*x^20*y*z0 - 2*x^20*z0^2 + x^18*y*z0^3 + x^18*z0^4 - x^21 - 2*x^19*y*z0 - x^19*z0^2 + x^17*y*z0^3 + 2*x^18*y*z0 - 2*x^18*z0^2 + x^16*z0^4 + 2*x^19 + x^17*y*z0 - x^17*z0^2 + x^15*y*z0^3 - 2*x^15*z0^4 - 2*x^16*y*z0 + x^14*y*z0^3 - x^17 + x^15*y*z0 - 2*x^15*z0^2 - x^13*y*z0^3 - x^13*z0^4 + x^16 + x^14*y*z0 - x^14*z0^2 - 2*x^12*y*z0^3 - x^12*z0^4 + x^15 + x^13*y*z0 - 2*x^13*z0^2 - 2*x^11*y*z0^3 - 2*x^11*z0^4 - 2*x^14 + 2*x^12*y*z0 - x^12*z0^2 + x^10*y*z0^3 - x^10*z0^4 + x^13 - x^11*z0^2 + 2*x^9*y*z0^3 + 2*x^12 - x^10*y*z0 - 2*x^10*z0^2 + 2*x^8*y*z0^3 - 2*x^11 + x^9*y*z0 - 2*x^9*z0^2 - 2*x^7*y*z0^3 - 2*x^7*z0^4 - 2*x^10 - x^8*y*z0 - 2*x^8*z0^2 + x^6*y*z0^3 - 2*x^6*z0^4 + x^9 + x^7*y*z0 - 2*x^5*y*z0^3 + 2*x^5*z0^4 + x^6*y*z0 + 2*x^6*z0^2 - 2*x^4*y*z0^3 - x^5*y*z0 - 2*x^3*z0^4 + x^6 - x^4*y*z0 - x^4*z0^2 - x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^3*y*z0 + x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 + 2*x^3 - x^2)/y) * dx, - ((-x^60*z0^3 + x^57*y^2*z0^3 + x^60*z0 - x^58*z0^3 + 2*x^59*z0 - x^57*y^2*z0 + 2*x^57*z0^3 + x^55*y^2*z0^3 - 2*x^56*y^2*z0 - x^54*y^2*z0^3 - x^57*z0 + x^55*z0^3 - 2*x^56*z0 - 2*x^54*z0^3 + x^54*z0 - x^52*z0^3 + 2*x^53*z0 + 2*x^51*z0^3 - x^51*z0 + x^49*z0^3 - 2*x^50*z0 - 2*x^48*z0^3 - x^46*z0^3 + 2*x^47*z0 + x^45*y^2*z0 + 2*x^45*z0^3 + x^43*z0^3 - 2*x^44*z0 - 2*x^42*z0^3 + x^38*y*z0^4 + 2*x^41*z0 - x^39*z0^3 + x^37*y*z0^4 + x^40*z0 + 2*x^38*y*z0^2 + 2*x^39*y - x^39*z0 + x^37*y*z0^2 - x^37*z0^3 + 2*x^35*y*z0^4 + 2*x^38*y - x^36*y*z0^2 + x^36*z0^3 - 2*x^34*y*z0^4 - x^37*z0 + 2*x^35*y*z0^2 - x^35*z0^3 + x^33*y*z0^4 + 2*x^36*z0 - x^34*y*z0^2 + x^34*z0^3 + x^32*y*z0^4 + x^35*z0 + 2*x^33*z0^3 + x^34*y + x^34*z0 - x^32*y*z0^2 - x^32*z0^3 - 2*x^30*y*z0^4 + x^33*y + 2*x^33*z0 + 2*x^31*z0^3 - 2*x^29*y*z0^4 - 2*x^32*y + x^32*z0 + 2*x^30*y*z0^2 + 2*x^30*z0^3 - 2*x^28*y*z0^4 - 2*x^31*y + 2*x^29*y*z0^2 + x^29*z0^3 + 2*x^27*y*z0^4 + x^30*y + 2*x^30*z0 + x^28*y*z0^2 - x^26*y*z0^4 + x^29*y - 2*x^27*y*z0^2 - 2*x^27*z0^3 + 2*x^25*y*z0^4 + x^28*z0 - x^26*y*z0^2 + x^24*y*z0^4 - x^27*y + 2*x^25*y*z0^2 + x^25*z0^3 - x^23*y*z0^4 - 2*x^26*y - 2*x^26*z0 + x^24*y*z0^2 - 2*x^24*z0^3 + 2*x^22*y*z0^4 + 2*x^25*z0 - 2*x^23*y*z0^2 - x^23*z0^3 + x^21*y*z0^4 + x^24*z0 + 2*x^22*z0^3 + x^20*y*z0^4 + x^23*z0 + x^21*y*z0^2 + x^21*z0^3 + 2*x^19*y*z0^4 - 2*x^22*y + 2*x^22*z0 - 2*x^20*z0^3 - x^18*y*z0^4 - 2*x^21*y + 2*x^21*z0 - 2*x^19*z0^3 + 2*x^17*y*z0^4 - 2*x^20*y - 2*x^18*y*z0^2 + 2*x^18*z0^3 + x^16*y*z0^4 + 2*x^19*y - x^19*z0 + x^17*z0^3 - 2*x^15*y*z0^4 + 2*x^18*y + 2*x^18*z0 - x^16*y*z0^2 + x^17*y - x^17*z0 - 2*x^15*y*z0^2 + 2*x^15*z0^3 - x^13*y*z0^4 - 2*x^16*y + 2*x^14*z0^3 + x^12*y*z0^4 - x^15*y + x^15*z0 + x^13*y*z0^2 + 2*x^11*y*z0^4 - x^14*y + 2*x^14*z0 - x^12*y*z0^2 + x^12*z0^3 + 2*x^10*y*z0^4 - x^13*y - 2*x^13*z0 - 2*x^11*y*z0^2 - x^11*z0^3 - x^9*y*z0^4 + 2*x^12*y - 2*x^12*z0 + x^10*y*z0^2 + 2*x^10*z0^3 + 2*x^8*y*z0^4 + x^11*z0 - x^9*y*z0^2 - 2*x^9*z0^3 + 2*x^7*y*z0^4 + x^10*y + x^10*z0 - 2*x^6*y*z0^4 + 2*x^9*y - x^9*z0 + 2*x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 + 2*x^8*y - 2*x^6*z0^3 - x^4*y*z0^4 - 2*x^7*y - x^5*y*z0^2 + 2*x^5*z0^3 + x^6*y + 2*x^6*z0 + x^4*y*z0^2 - 2*x^4*z0^3 + 2*x^2*y*z0^4 + x^5*y - 2*x^3*y*z0^2 + x^3*z0^3 + x^2*y*z0^2 + x^2*z0^3 - x^3*z0 + 2*x^2*y - 2*x^2*z0)/y) * dx, - ((-x^61*z0^4 - 2*x^60*z0^4 + x^58*y^2*z0^4 + 2*x^61*z0^2 + x^59*z0^4 + 2*x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 + x^58*z0^4 - x^56*y^2*z0^4 - 2*x^61 + x^57*y^2*z0^2 + 2*x^57*z0^4 - x^60 + 2*x^58*y^2 - 2*x^58*z0^2 - x^56*z0^4 + x^57*y^2 + x^57*z0^2 - x^55*z0^4 + 2*x^58 - 2*x^54*z0^4 + x^57 + 2*x^55*z0^2 + x^53*z0^4 - x^54*z0^2 + x^52*z0^4 - 2*x^55 + 2*x^51*z0^4 - x^54 - 2*x^52*z0^2 - x^50*z0^4 + x^51*z0^2 - x^49*z0^4 + 2*x^52 - 2*x^48*z0^4 + x^51 + 2*x^49*z0^2 + x^47*z0^4 - 2*x^48*z0^2 + x^46*z0^4 - 2*x^49 + x^45*y^2*z0^2 + 2*x^45*z0^4 - x^48 - 2*x^46*z0^2 - x^44*z0^4 + 2*x^45*z0^2 - x^43*z0^4 + 2*x^46 - 2*x^42*z0^4 + x^45 + 2*x^43*z0^2 - x^41*z0^4 - 2*x^42*z0^2 + 2*x^40*y*z0^3 - 2*x^40*z0^4 - 2*x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^42 + x^40*y*z0 - x^38*y*z0^3 + x^38*z0^4 - 2*x^41 + 2*x^37*y*z0^3 + x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 - x^36*z0^4 - 2*x^39 - x^37*y*z0 - 2*x^35*y*z0^3 - 2*x^38 + x^36*y*z0 - x^34*y*z0^3 - x^35*y*z0 - 2*x^35*z0^2 - x^33*y*z0^3 + x^33*z0^4 - 2*x^36 + 2*x^34*y*z0 - x^32*y*z0^3 - 2*x^33*y*z0 + 2*x^31*y*z0^3 + 2*x^31*z0^4 - 2*x^34 - 2*x^32*z0^2 + 2*x^30*y*z0^3 - x^30*z0^4 - 2*x^33 - x^31*y*z0 - 2*x^31*z0^2 - x^29*y*z0^3 - x^29*z0^4 - 2*x^30*y*z0 + x^30*z0^2 - 2*x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 + 2*x^29*y*z0 - x^27*y*z0^3 + 2*x^27*z0^4 - x^30 + x^28*z0^2 - x^26*z0^4 - 2*x^29 - x^27*y*z0 - x^27*z0^2 + x^25*y*z0^3 + x^26*y*z0 - 2*x^24*y*z0^3 - x^27 - x^25*y*z0 + 2*x^25*z0^2 + x^23*z0^4 - 2*x^26 + x^24*z0^2 + 2*x^22*y*z0^3 - 2*x^22*z0^4 + x^25 + x^23*y*z0 + x^21*y*z0^3 + 2*x^24 - x^22*y*z0 + x^22*z0^2 - 2*x^20*y*z0^3 + 2*x^23 - 2*x^21*y*z0 + 2*x^21*z0^2 + 2*x^19*y*z0^3 - 2*x^19*z0^4 - 2*x^22 - 2*x^20*z0^2 + x^18*y*z0^3 + x^21 - 2*x^19*z0^2 + 2*x^20 - 2*x^18*z0^2 - 2*x^16*z0^4 + 2*x^19 - x^17*y*z0 - x^17*z0^2 + 2*x^15*y*z0^3 + x^16*y*z0 - x^16*z0^2 - x^14*y*z0^3 + 2*x^17 + x^15*y*z0 + x^15*z0^2 + 2*x^13*y*z0^3 - x^13*z0^4 + x^16 + x^14*z0^2 - x^12*y*z0^3 - x^12*z0^4 - 2*x^15 + x^13*y*z0 - 2*x^13*z0^2 - 2*x^11*y*z0^3 - x^11*z0^4 + x^14 + 2*x^12*y*z0 - x^12*z0^2 + 2*x^10*y*z0^3 + 2*x^13 + x^11*y*z0 + 2*x^11*z0^2 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*z0^4 - x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 - x^10 + x^6*y*z0^3 - x^9 - x^7*y*z0 + x^7*z0^2 - x^5*y*z0^3 - x^5*z0^4 + x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 - x^4*y*z0^3 - x^7 + 2*x^5*z0^2 + x^3*y*z0^3 - x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - x^2*z0^4 - 2*x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2)/y) * dx, - ((-x^61*z0^3 + 2*x^60*z0^3 + x^58*y^2*z0^3 + x^61*z0 - 2*x^57*y^2*z0^3 - x^60*z0 - x^58*y^2*z0 + x^58*z0^3 + 2*x^59*z0 + x^57*y^2*z0 - x^58*z0 - 2*x^56*y^2*z0 - 2*x^54*y^2*z0^3 + x^57*z0 - x^55*z0^3 - 2*x^56*z0 + x^55*z0 - x^54*z0 + x^52*z0^3 + 2*x^53*z0 - x^52*z0 + x^51*z0 - x^49*z0^3 - 2*x^50*z0 - x^48*z0^3 + x^49*z0 + x^45*y^2*z0^3 - x^48*z0 + x^46*z0^3 + 2*x^47*z0 + x^45*z0^3 - x^46*z0 + x^45*z0 - x^43*z0^3 - 2*x^44*z0 - x^42*z0^3 + x^43*z0 - x^41*z0^3 - x^39*y*z0^4 - x^42*z0 + 2*x^40*y*z0^2 - 2*x^41*z0 + x^39*y*z0^2 - x^39*z0^3 - x^37*y*z0^4 - 2*x^40*y + 2*x^40*z0 - 2*x^38*z0^3 + 2*x^36*y*z0^4 - x^39*z0 - x^37*y*z0^2 + x^37*z0^3 + 2*x^35*y*z0^4 + 2*x^38*y + 2*x^38*z0 + 2*x^36*y*z0^2 + x^36*z0^3 + x^37*y + 2*x^37*z0 - x^35*y*z0^2 + 2*x^35*z0^3 + 2*x^33*y*z0^4 + 2*x^36*z0 + 2*x^34*y*z0^2 - 2*x^34*z0^3 - x^32*y*z0^4 + 2*x^35*y - 2*x^35*z0 - x^33*y*z0^2 + x^34*z0 - x^32*y*z0^2 - x^32*z0^3 - x^30*y*z0^4 + x^33*y - 2*x^31*z0^3 + 2*x^29*y*z0^4 - 2*x^32*y + 2*x^32*z0 + 2*x^30*y*z0^2 + x^30*z0^3 - 2*x^28*y*z0^4 - x^31*z0 + x^29*y*z0^2 + 2*x^29*z0^3 - 2*x^27*y*z0^4 - 2*x^30*y + 2*x^30*z0 + 2*x^28*y*z0^2 - x^28*z0^3 - x^26*y*z0^4 - x^29*y + 2*x^27*y*z0^2 + x^25*y*z0^4 - x^28*y + x^26*y*z0^2 + 2*x^26*z0^3 + 2*x^27*y - x^27*z0 - x^25*y*z0^2 + 2*x^25*z0^3 + x^23*y*z0^4 - x^26*y + x^26*z0 + 2*x^24*y*z0^2 + 2*x^24*z0^3 + 2*x^22*y*z0^4 - 2*x^25*y - 2*x^23*y*z0^2 - x^23*z0^3 + x^21*y*z0^4 + x^22*y*z0^2 + 2*x^22*z0^3 - x^23*y - x^23*z0 + 2*x^21*y*z0^2 + 2*x^21*z0^3 - x^19*y*z0^4 - x^22*y + x^22*z0 + 2*x^20*z0^3 - x^18*y*z0^4 + 2*x^21*y + 2*x^21*z0 + 2*x^19*z0^3 + x^17*y*z0^4 + 2*x^20*y + x^20*z0 + 2*x^18*y*z0^2 + 2*x^18*z0^3 - x^16*y*z0^4 + 2*x^19*y - x^19*z0 - 2*x^17*y*z0^2 + x^15*y*z0^4 + 2*x^18*y - x^18*z0 + x^16*y*z0^2 - x^16*z0^3 + x^14*y*z0^4 - x^17*y + x^17*z0 + x^15*y*z0^2 + 2*x^15*z0^3 + x^13*y*z0^4 - 2*x^16*y + x^14*y*z0^2 - x^12*y*z0^4 + 2*x^15*y - 2*x^15*z0 + x^13*y*z0^2 - 2*x^13*z0^3 + x^11*y*z0^4 - 2*x^12*y*z0^2 - x^12*z0^3 - 2*x^10*y*z0^4 - x^13*y + 2*x^13*z0 + x^11*z0^3 - x^9*y*z0^4 - x^12*y + x^10*y*z0^2 - 2*x^10*z0^3 + x^8*y*z0^4 + x^11*z0 + x^9*y*z0^2 - 2*x^9*z0^3 - 2*x^7*y*z0^4 + x^10*z0 + 2*x^8*z0^3 - 2*x^6*y*z0^4 - 2*x^9*z0 - 2*x^7*y*z0^2 + 2*x^5*y*z0^4 - 2*x^8*y - 2*x^8*z0 - 2*x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^4*y*z0^4 + 2*x^6*y + x^6*z0 - 2*x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 + 2*x^3*y*z0^2 + 2*x^3*z0^3 - 2*x^4*y + x^4*z0 - x^2*y*z0^2 - x^2*z0^3 + x^3*y + x^2*y + x^2*z0)/y) * dx, - ((2*x^61*z0^4 - x^60*z0^4 - 2*x^58*y^2*z0^4 - 2*x^61*z0^2 - 2*x^59*z0^4 + x^57*y^2*z0^4 - x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^58*z0^4 + 2*x^56*y^2*z0^4 + x^57*y^2*z0^2 + x^57*z0^4 + 2*x^58*z0^2 + 2*x^56*z0^4 + x^57*z0^2 + 2*x^55*z0^4 - x^54*z0^4 - 2*x^55*z0^2 - 2*x^53*z0^4 - x^54*z0^2 - 2*x^52*z0^4 + x^51*z0^4 + 2*x^52*z0^2 + 2*x^50*z0^4 + x^51*z0^2 + 2*x^49*z0^4 - 2*x^48*z0^4 - 2*x^49*z0^2 - 2*x^47*z0^4 + x^45*y^2*z0^4 - x^48*z0^2 - 2*x^46*z0^4 + 2*x^45*z0^4 + 2*x^46*z0^2 + 2*x^44*z0^4 + x^45*z0^2 + 2*x^43*z0^4 - 2*x^42*z0^4 - 2*x^43*z0^2 - x^42*z0^2 + x^40*y*z0^3 + 2*x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - x^40*y*z0 - 2*x^40*z0^2 - x^38*y*z0^3 - x^38*z0^4 + 2*x^41 + x^39*y*z0 - 2*x^39*z0^2 + x^37*y*z0^3 + 2*x^40 + x^38*z0^2 - x^36*y*z0^3 - 2*x^36*z0^4 - 2*x^37*y*z0 + 2*x^35*y*z0^3 - x^35*z0^4 + x^36*y*z0 + 2*x^36*z0^2 - x^34*y*z0^3 - 2*x^34*z0^4 + x^35*z0^2 + x^33*y*z0^3 - x^33*z0^4 + x^36 - x^34*y*z0 + 2*x^34*z0^2 + 2*x^32*y*z0^3 + x^32*z0^4 - 2*x^35 - 2*x^33*y*z0 - 2*x^31*y*z0^3 + 2*x^34 - 2*x^32*z0^2 + 2*x^30*y*z0^3 + 2*x^30*z0^4 - 2*x^33 - x^31*y*z0 - x^31*z0^2 + x^29*y*z0^3 - 2*x^29*z0^4 + x^32 + x^30*y*z0 - 2*x^30*z0^2 - 2*x^28*y*z0^3 + x^28*z0^4 + x^27*y*z0^3 + 2*x^27*z0^4 - x^28*y*z0 - 2*x^28*z0^2 + 2*x^26*y*z0^3 - x^26*z0^4 + 2*x^29 + 2*x^25*y*z0^3 + x^28 - 2*x^26*z0^2 - 2*x^24*y*z0^3 - x^24*z0^4 - x^27 - 2*x^25*y*z0 + x^25*z0^2 - 2*x^23*y*z0^3 + 2*x^23*z0^4 + 2*x^26 + x^24*y*z0 - 2*x^24*z0^2 - x^22*y*z0^3 + x^25 + x^23*y*z0 - 2*x^23*z0^2 - x^21*y*z0^3 - 2*x^24 + x^22*z0^2 + x^20*z0^4 + x^23 - 2*x^21*y*z0 - x^21*z0^2 + x^19*z0^4 - 2*x^22 - 2*x^20*y*z0 + 2*x^20*z0^2 + x^18*y*z0^3 + x^18*z0^4 + x^19*y*z0 + 2*x^17*y*z0^3 - x^20 - 2*x^18*y*z0 + x^18*z0^2 - x^16*y*z0^3 - x^16*z0^4 + 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + x^18 - x^16*z0^2 + x^14*z0^4 - 2*x^17 + x^15*y*z0 + x^15*z0^2 - x^13*y*z0^3 - 2*x^16 + 2*x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 + 2*x^15 - x^13*z0^2 - x^11*y*z0^3 - x^11*z0^4 - 2*x^12*y*z0 - 2*x^12*z0^2 - x^10*z0^4 + x^13 - x^11*z0^2 + x^9*y*z0^3 - x^9*z0^4 + 2*x^12 + x^10*z0^2 + 2*x^8*y*z0^3 - x^8*z0^4 - x^11 - x^9*y*z0 - x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 - x^10 + x^8*y*z0 + x^8*z0^2 + x^6*z0^4 - x^7*z0^2 - x^5*z0^4 - 2*x^8 - x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 + 2*x^4*z0^4 + x^7 - 2*x^5*y*z0 - 2*x^5*z0^2 - x^3*y*z0^3 + x^3*z0^4 + x^6 - 2*x^4*y*z0 - x^4*z0^2 - 2*x^2*z0^4 - x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*z0^2 - 2*x^3 - 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((2*x^61*z0^4 + x^60*z0^4 - 2*x^58*y^2*z0^4 - 2*x^61*z0^2 + x^59*z0^4 - x^57*y^2*z0^4 - 2*x^60*z0^2 + 2*x^58*y^2*z0^2 - 2*x^58*z0^4 - x^56*y^2*z0^4 + x^61 + 2*x^57*y^2*z0^2 - x^57*z0^4 - x^58*y^2 + 2*x^58*z0^2 - x^56*z0^4 + 2*x^57*z0^2 + 2*x^55*z0^4 - x^58 + x^54*z0^4 - 2*x^55*z0^2 + x^53*z0^4 - 2*x^54*z0^2 - 2*x^52*z0^4 + x^55 - x^51*z0^4 + 2*x^52*z0^2 - x^50*z0^4 + 2*x^51*z0^2 + 2*x^49*z0^4 - x^52 + x^48*z0^4 - 2*x^49*z0^2 + x^47*z0^4 - 2*x^48*z0^2 - 2*x^46*z0^4 - x^45*z0^4 + x^46*y^2 + 2*x^46*z0^2 - x^44*z0^4 + 2*x^45*z0^2 + 2*x^43*z0^4 + x^42*z0^4 - 2*x^43*z0^2 + x^41*z0^4 - 2*x^42*z0^2 + x^40*y*z0^3 - 2*x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - 2*x^39*z0^4 - x^40*y*z0 - x^40*z0^2 + x^38*y*z0^3 - 2*x^39*y*z0 - x^39*z0^2 + x^37*y*z0^3 + x^40 + 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + x^37*y*z0 + 2*x^37*z0^2 - 2*x^35*y*z0^3 + 2*x^35*z0^4 + 2*x^38 - x^36*y*z0 + x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 - x^35*y*z0 - x^35*z0^2 - 2*x^33*y*z0^3 + 2*x^33*z0^4 + 2*x^34*y*z0 + x^34*z0^2 - 2*x^32*y*z0^3 - 2*x^32*z0^4 + x^35 + 2*x^33*z0^2 + 2*x^31*y*z0^3 + 2*x^31*z0^4 + x^32*y*z0 - 2*x^30*y*z0^3 + x^30*z0^4 - 2*x^31*y*z0 + 2*x^29*y*z0^3 + 2*x^29*z0^4 + x^32 + x^30*y*z0 + 2*x^30*z0^2 - x^28*y*z0^3 + x^28*z0^4 - 2*x^29*y*z0 - x^29*z0^2 + 2*x^27*z0^4 + 2*x^30 - x^28*y*z0 + 2*x^28*z0^2 - x^26*y*z0^3 - x^29 + 2*x^27*y*z0 + x^27*z0^2 + 2*x^25*y*z0^3 + 2*x^28 + x^26*z0^2 + x^24*y*z0^3 - x^27 + 2*x^25*y*z0 - x^25*z0^2 + 2*x^23*y*z0^3 - x^23*z0^4 - 2*x^24*y*z0 - 2*x^24*z0^2 - x^22*z0^4 + 2*x^25 + x^23*y*z0 + 2*x^23*z0^2 - x^21*z0^4 - 2*x^24 - x^22*y*z0 - x^22*z0^2 + x^20*y*z0^3 + 2*x^23 - 2*x^21*y*z0 + x^21*z0^2 + x^22 + x^20*y*z0 + 2*x^20*z0^2 - 2*x^18*z0^4 + 2*x^21 + x^19*y*z0 + 2*x^19*z0^2 + x^17*y*z0^3 + x^17*z0^4 - 2*x^20 + 2*x^18*z0^2 + 2*x^16*y*z0^3 + x^16*z0^4 + 2*x^19 + 2*x^17*z0^2 - x^15*z0^4 - x^18 - x^16*y*z0 + x^16*z0^2 + x^14*y*z0^3 - x^14*z0^4 + x^15*y*z0 - x^15*z0^2 - 2*x^13*z0^4 - x^16 - x^14*z0^2 - x^12*y*z0^3 + x^15 + 2*x^13*z0^2 + 2*x^11*y*z0^3 - 2*x^11*z0^4 + x^14 - x^12*y*z0 - x^12*z0^2 - x^10*y*z0^3 - x^10*z0^4 - x^13 + 2*x^11*y*z0 - x^11*z0^2 - 2*x^9*y*z0^3 - x^9*z0^4 + 2*x^10*y*z0 + 2*x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^11 - x^7*y*z0^3 + 2*x^7*z0^4 + 2*x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 - x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 - 2*x^7*y*z0 + 2*x^7*z0^2 + 2*x^5*y*z0^3 - x^5*z0^4 + 2*x^6*z0^2 - 2*x^7 - 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + x^6 - 2*x^4*y*z0 - 2*x^4*z0^2 + x^2*y*z0^3 - x^3*y*z0 + x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 + x^2)/y) * dx, - ((2*x^61*z0^3 - 2*x^58*y^2*z0^3 - x^61*z0 + x^58*y^2*z0 - 2*x^58*z0^3 - x^59*z0 + 2*x^57*z0^3 + x^58*z0 + x^56*y^2*z0 - 2*x^54*y^2*z0^3 + 2*x^55*z0^3 + x^56*z0 - 2*x^54*z0^3 - x^55*z0 - 2*x^52*z0^3 - x^53*z0 + 2*x^51*z0^3 + x^52*z0 + 2*x^49*z0^3 + x^50*z0 - 2*x^48*z0^3 - 2*x^49*z0 + x^46*y^2*z0 - 2*x^46*z0^3 - x^47*z0 + 2*x^45*z0^3 + 2*x^46*z0 + 2*x^43*z0^3 + x^44*z0 - 2*x^42*z0^3 - 2*x^43*z0 + 2*x^41*z0^3 + 2*x^39*y*z0^4 + x^40*y*z0^2 - 2*x^40*z0^3 + x^38*y*z0^4 - 2*x^41*z0 - x^39*y*z0^2 - x^39*z0^3 + 2*x^37*y*z0^4 + 2*x^40*y - x^40*z0 + x^38*y*z0^2 - x^38*z0^3 + x^36*y*z0^4 + 2*x^39*y - x^39*z0 + 2*x^37*y*z0^2 + x^37*z0^3 + 2*x^35*y*z0^4 + x^38*y - 2*x^38*z0 + x^36*z0^3 - 2*x^34*y*z0^4 - x^37*y - 2*x^37*z0 - x^35*y*z0^2 - 2*x^35*z0^3 - 2*x^36*z0 + x^34*y*z0^2 - 2*x^34*z0^3 + x^32*y*z0^4 + 2*x^35*z0 - x^33*y*z0^2 - x^33*z0^3 + x^34*y + 2*x^32*y*z0^2 - 2*x^30*y*z0^4 + x^33*y - 2*x^33*z0 + x^31*y*z0^2 + 2*x^29*y*z0^4 + x^32*y + 2*x^30*y*z0^2 - 2*x^30*z0^3 + x^28*y*z0^4 + 2*x^31*y - x^29*y*z0^2 - 2*x^27*y*z0^4 - 2*x^30*y + 2*x^28*y*z0^2 - x^29*y + x^29*z0 + 2*x^27*y*z0^2 + x^27*z0^3 - x^28*y + x^26*y*z0^2 + 2*x^26*z0^3 + x^24*y*z0^4 + x^27*y - x^27*z0 - x^25*y*z0^2 - x^23*y*z0^4 - x^26*y - 2*x^24*y*z0^2 - 2*x^24*z0^3 + x^23*z0^3 + x^21*y*z0^4 - 2*x^24*z0 - 2*x^22*y*z0^2 - x^22*z0^3 + 2*x^20*y*z0^4 - 2*x^23*z0 - 2*x^21*y*z0^2 - x^21*z0^3 - x^19*y*z0^4 + 2*x^22*y + 2*x^22*z0 - x^20*z0^3 - x^18*y*z0^4 - 2*x^21*y - x^19*y*z0^2 + x^19*z0^3 - 2*x^17*y*z0^4 + 2*x^20*z0 + x^16*y*z0^4 - x^19*y + 2*x^17*y*z0^2 + 2*x^15*y*z0^4 - 2*x^18*y - 2*x^16*y*z0^2 + 2*x^14*y*z0^4 + 2*x^17*y + 2*x^17*z0 + x^15*y*z0^2 + 2*x^15*z0^3 - 2*x^16*y + 2*x^16*z0 - x^14*y*z0^2 - 2*x^14*z0^3 + x^12*y*z0^4 - x^15*y - x^15*z0 + 2*x^13*y*z0^2 - 2*x^13*z0^3 + 2*x^11*y*z0^4 + x^14*y + 2*x^14*z0 - x^12*y*z0^2 - x^12*z0^3 + 2*x^10*y*z0^4 + x^13*y - x^13*z0 + x^11*y*z0^2 - 2*x^11*z0^3 + x^9*y*z0^4 - 2*x^12*y + x^12*z0 + x^10*y*z0^2 + x^10*z0^3 - x^8*y*z0^4 + 2*x^11*y + 2*x^11*z0 + 2*x^9*y*z0^2 + 2*x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y - x^10*z0 + 2*x^8*y*z0^2 - 2*x^9*z0 + 2*x^7*y*z0^2 - 2*x^7*z0^3 + x^8*z0 + 2*x^6*z0^3 + 2*x^4*y*z0^4 - x^7*y + x^7*z0 - 2*x^3*y*z0^4 - 2*x^6*y - x^6*z0 - x^4*y*z0^2 + x^4*z0^3 + x^2*y*z0^4 + x^5*y + 2*x^5*z0 - 2*x^3*y*z0^2 + 2*x^3*z0^3 + 2*x^4*y - x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - x^3*y - x^2*y)/y) * dx, - ((-2*x^61*z0^4 + 2*x^60*z0^4 + 2*x^58*y^2*z0^4 - x^61*z0^2 - 2*x^57*y^2*z0^4 + x^58*y^2*z0^2 + 2*x^58*z0^4 + 2*x^61 - 2*x^57*z0^4 + x^60 - 2*x^58*y^2 + x^58*z0^2 - x^57*y^2 - 2*x^55*z0^4 - 2*x^58 + 2*x^54*z0^4 - x^57 - x^55*z0^2 + 2*x^52*z0^4 + 2*x^55 - 2*x^51*z0^4 + x^54 + x^52*z0^2 - 2*x^49*z0^4 - 2*x^52 + 2*x^48*z0^4 - x^51 - 2*x^49*z0^2 + x^46*y^2*z0^2 + 2*x^46*z0^4 + 2*x^49 - 2*x^45*z0^4 + x^48 + 2*x^46*z0^2 - 2*x^43*z0^4 - 2*x^46 + 2*x^42*z0^4 - x^45 - 2*x^43*z0^2 - x^41*z0^4 - x^40*y*z0^3 - x^40*z0^4 + 2*x^43 - x^41*z0^2 - x^39*y*z0^3 + x^42 + 2*x^40*y*z0 + x^40*z0^2 - 2*x^38*z0^4 - x^41 - x^39*y*z0 + x^39*z0^2 + x^40 - 2*x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 - x^36*z0^4 + x^35*y*z0^3 + 2*x^35*z0^4 - 2*x^38 - 2*x^36*y*z0 - x^36*z0^2 + x^34*z0^4 + 2*x^37 + 2*x^35*y*z0 + x^35*z0^2 + 2*x^33*y*z0^3 + x^33*z0^4 - 2*x^36 + 2*x^34*y*z0 + 2*x^34*z0^2 + 2*x^32*y*z0^3 + x^32*z0^4 - 2*x^35 + x^31*y*z0^3 - 2*x^31*z0^4 + x^34 + x^32*y*z0 + 2*x^32*z0^2 - 2*x^30*y*z0^3 - x^30*z0^4 - x^33 + 2*x^31*z0^2 - 2*x^29*y*z0^3 - x^29*z0^4 + x^32 - 2*x^30*y*z0 - 2*x^30*z0^2 - x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^31 + x^29*y*z0 - x^29*z0^2 - 2*x^27*y*z0^3 + 2*x^27*z0^4 - x^30 - 2*x^28*y*z0 - x^28*z0^2 - x^26*y*z0^3 - x^26*z0^4 + 2*x^29 + x^27*y*z0 - x^27*z0^2 + x^25*y*z0^3 + x^25*z0^4 + 2*x^28 - x^26*y*z0 + 2*x^24*z0^4 - x^27 - x^25*z0^2 + 2*x^23*y*z0^3 - 2*x^23*z0^4 - x^26 + x^24*y*z0 - 2*x^24*z0^2 + x^22*y*z0^3 + x^23*y*z0 + x^23*z0^2 + 2*x^21*y*z0^3 + 2*x^21*z0^4 + 2*x^22*y*z0 + 2*x^20*y*z0^3 - x^20*z0^4 - 2*x^23 - 2*x^21*y*z0 - x^21*z0^2 + x^19*y*z0^3 - x^19*z0^4 - 2*x^20*y*z0 + x^18*y*z0^3 - 2*x^18*z0^4 + x^21 + x^19*y*z0 + 2*x^19*z0^2 - x^17*y*z0^3 - x^17*z0^4 + 2*x^20 + x^18*y*z0 + 2*x^18*z0^2 - x^16*z0^4 + x^19 - 2*x^17*y*z0 - 2*x^17*z0^2 - 2*x^15*y*z0^3 - x^15*z0^4 - 2*x^18 + x^16*y*z0 - x^16*z0^2 + x^14*y*z0^3 + x^14*z0^4 - 2*x^17 - x^15*y*z0 + 2*x^15*z0^2 - x^13*y*z0^3 - 2*x^13*z0^4 + 2*x^14*y*z0 - 2*x^12*y*z0^3 + x^12*z0^4 + x^15 + x^13*y*z0 + 2*x^13*z0^2 - x^11*y*z0^3 + x^11*z0^4 - x^14 - x^12*y*z0 + x^12*z0^2 + 2*x^10*y*z0^3 + x^10*z0^4 - x^13 - x^11*z0^2 - 2*x^9*y*z0^3 + 2*x^9*z0^4 + x^12 + 2*x^10*y*z0 + 2*x^10*z0^2 + 2*x^8*y*z0^3 + x^8*z0^4 + x^11 - x^9*z0^2 + x^7*y*z0^3 - 2*x^10 - x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 - 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - x^8 + x^6*y*z0 - x^6*z0^2 + x^4*y*z0^3 - 2*x^4*z0^4 - 2*x^5*y*z0 - x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^4*y*z0 - x^4*z0^2 - 2*x^5 - x^3*y*z0 + x^2*z0^2 - x^3)/y) * dx, - ((x^61*z0^3 + 2*x^60*z0^3 - x^58*y^2*z0^3 - 2*x^57*y^2*z0^3 - x^60*z0 + x^58*z0^3 - x^59*z0 + x^57*y^2*z0 - x^57*z0^3 - 2*x^55*y^2*z0^3 + x^56*y^2*z0 - x^54*y^2*z0^3 + x^57*z0 - x^55*z0^3 + x^56*z0 + x^54*z0^3 - x^54*z0 + x^52*z0^3 - x^53*z0 - x^51*z0^3 + x^51*z0 - 2*x^49*z0^3 + x^50*z0 + x^48*z0^3 + x^46*y^2*z0^3 - x^48*z0 + 2*x^46*z0^3 - x^47*z0 - x^45*z0^3 + x^45*z0 - 2*x^43*z0^3 + x^44*z0 + x^42*z0^3 + x^41*z0^3 + x^39*y*z0^4 - x^42*z0 - 2*x^40*y*z0^2 + x^40*z0^3 + x^38*y*z0^4 - x^41*z0 + 2*x^39*z0^3 - 2*x^37*y*z0^4 + x^38*y*z0^2 + 2*x^38*z0^3 - 2*x^36*y*z0^4 + 2*x^39*y - x^39*z0 + 2*x^37*y*z0^2 + x^35*y*z0^4 - 2*x^38*y - 2*x^36*y*z0^2 - 2*x^36*z0^3 + x^34*y*z0^4 + 2*x^37*z0 + 2*x^35*y*z0^2 - x^35*z0^3 + x^33*y*z0^4 - x^36*y - 2*x^36*z0 + x^34*z0^3 - x^32*y*z0^4 - x^35*y + x^35*z0 - 2*x^33*z0^3 + x^31*y*z0^4 + 2*x^34*y - 2*x^32*y*z0^2 - 2*x^32*z0^3 + x^30*y*z0^4 - 2*x^33*z0 - 2*x^31*z0^3 - x^29*y*z0^4 + 2*x^32*y - x^32*z0 + x^30*y*z0^2 - 2*x^30*z0^3 - 2*x^28*y*z0^4 - 2*x^31*z0 + x^29*y*z0^2 + 2*x^29*z0^3 - 2*x^27*y*z0^4 - 2*x^30*y + x^30*z0 - 2*x^28*z0^3 + 2*x^29*y - 2*x^27*y*z0^2 - x^27*z0^3 - x^25*y*z0^4 + 2*x^28*y + 2*x^28*z0 - 2*x^26*y*z0^2 - 2*x^26*z0^3 + 2*x^24*y*z0^4 - x^27*y + 2*x^25*y*z0^2 - x^25*z0^3 + 2*x^23*y*z0^4 + x^24*y*z0^2 + x^24*z0^3 - 2*x^22*y*z0^4 - 2*x^25*y + 2*x^25*z0 - 2*x^23*y*z0^2 + x^23*z0^3 - x^21*y*z0^4 - x^24*z0 - x^22*z0^3 + x^20*y*z0^4 + 2*x^23*y + 2*x^23*z0 - 2*x^21*y*z0^2 + 2*x^19*y*z0^4 + 2*x^22*y + 2*x^22*z0 - 2*x^20*y*z0^2 + 2*x^20*z0^3 - 2*x^18*y*z0^4 - x^21*y - 2*x^21*z0 - 2*x^19*y*z0^2 - 2*x^19*z0^3 - x^17*y*z0^4 - x^20*z0 + 2*x^18*y*z0^2 - 2*x^18*z0^3 - 2*x^16*y*z0^4 + 2*x^19*y + x^19*z0 - x^17*y*z0^2 - 2*x^17*z0^3 + 2*x^15*y*z0^4 + 2*x^18*y - x^18*z0 + 2*x^16*y*z0^2 + x^16*z0^3 + x^17*y + x^17*z0 + x^15*y*z0^2 + x^15*z0^3 - 2*x^13*y*z0^4 + x^16*y + 2*x^16*z0 - 2*x^14*y*z0^2 - 2*x^14*z0^3 + 2*x^12*y*z0^4 - 2*x^15*y + x^15*z0 - x^13*y*z0^2 - x^13*z0^3 + x^11*y*z0^4 - x^14*y - 2*x^14*z0 + x^12*y*z0^2 + 2*x^12*z0^3 - 2*x^10*y*z0^4 - x^13*y + 2*x^13*z0 + x^11*y*z0^2 - x^11*z0^3 + 2*x^9*y*z0^4 - x^12*y + x^12*z0 - x^10*y*z0^2 + 2*x^10*z0^3 + x^8*y*z0^4 - 2*x^11*y + 2*x^11*z0 - 2*x^9*y*z0^2 + x^9*z0^3 - x^7*y*z0^4 - 2*x^10*z0 + x^8*y*z0^2 + x^8*z0^3 + x^6*y*z0^4 - 2*x^9*y - x^7*y*z0^2 - 2*x^7*z0^3 - 2*x^5*y*z0^4 + x^8*y + x^8*z0 + 2*x^6*y*z0^2 - 2*x^6*z0^3 + x^4*y*z0^4 + x^7*y + x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 + x^6*y - x^6*z0 - 2*x^4*y*z0^2 - x^4*z0^3 - x^2*y*z0^4 + 2*x^3*y*z0^2 - 2*x^3*z0^3 + 2*x^4*y + 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y + x^3*z0 + x^2*y + 2*x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + 2*x^58*y^2*z0^4 - x^59*z0^4 + 2*x^58*z0^4 + x^56*y^2*z0^4 - x^60 + x^56*z0^4 + x^57*y^2 - 2*x^55*z0^4 + x^57 - x^53*z0^4 + 2*x^52*z0^4 - x^54 + x^50*z0^4 + 2*x^49*z0^4 + x^46*y^2*z0^4 + x^51 - x^47*z0^4 - 2*x^46*z0^4 - x^48 + x^44*z0^4 + 2*x^43*z0^4 + x^45 + 2*x^41*z0^4 - x^40*y*z0^3 + 2*x^40*z0^4 - 2*x^39*z0^4 - x^42 + 2*x^40*z0^2 + x^38*y*z0^3 + x^38*z0^4 - 2*x^41 + x^39*y*z0 - x^37*y*z0^3 - 2*x^40 + 2*x^38*y*z0 - 2*x^37*z0^2 + x^35*y*z0^3 + x^35*z0^4 - x^38 + x^36*y*z0 + x^34*z0^4 + x^37 - 2*x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 + 2*x^34*z0^2 - x^32*y*z0^3 - 2*x^32*z0^4 + 2*x^35 - x^33*z0^2 + 2*x^31*y*z0^3 + x^31*z0^4 - 2*x^32*y*z0 + x^30*y*z0^3 + 2*x^30*z0^4 - 2*x^33 + x^31*y*z0 + x^31*z0^2 - 2*x^29*y*z0^3 + 2*x^29*z0^4 + 2*x^32 - x^30*y*z0 + 2*x^30*z0^2 - 2*x^28*y*z0^3 - x^28*z0^4 - x^29*y*z0 - x^29*z0^2 + x^27*y*z0^3 + x^27*z0^4 - x^30 + 2*x^28*y*z0 - x^28*z0^2 - x^26*y*z0^3 + 2*x^29 - 2*x^27*y*z0 - x^27*z0^2 - x^25*y*z0^3 - x^25*z0^4 - x^28 - x^26*z0^2 - 2*x^24*z0^4 - 2*x^27 + x^25*z0^2 - x^23*y*z0^3 - 2*x^23*z0^4 - x^26 + 2*x^24*y*z0 + 2*x^24*z0^2 - 2*x^22*y*z0^3 + x^23*y*z0 - x^23*z0^2 + 2*x^21*z0^4 - 2*x^22*y*z0 - 2*x^22*z0^2 + 2*x^20*y*z0^3 - 2*x^20*z0^4 + 2*x^21*y*z0 - 2*x^21*z0^2 - x^19*y*z0^3 + x^19*z0^4 + 2*x^22 - 2*x^20*y*z0 - 2*x^20*z0^2 + x^18*y*z0^3 - x^18*z0^4 - x^21 - 2*x^19*y*z0 + 2*x^19*z0^2 + x^17*y*z0^3 - 2*x^17*z0^4 - 2*x^20 + x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 - 2*x^19 + x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + x^15*z0^4 - 2*x^18 - x^16*y*z0 + x^14*y*z0^3 + 2*x^14*z0^4 - 2*x^17 + x^15*y*z0 + 2*x^15*z0^2 - x^13*y*z0^3 - 2*x^13*z0^4 + 2*x^14*y*z0 + 2*x^14*z0^2 + 2*x^12*y*z0^3 - 2*x^12*z0^4 - 2*x^15 + x^13*y*z0 - 2*x^13*z0^2 + 2*x^11*y*z0^3 + x^11*z0^4 + 2*x^14 - x^12*z0^2 - x^10*y*z0^3 - x^11*y*z0 + x^11*z0^2 - 2*x^9*y*z0^3 - x^9*z0^4 - x^10*y*z0 + 2*x^8*y*z0^3 - x^8*z0^4 - 2*x^11 + x^9*y*z0 - x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 - x^10 - 2*x^8*y*z0 + x^8*z0^2 + x^6*z0^4 + 2*x^9 + 2*x^7*y*z0 - x^5*y*z0^3 + x^5*z0^4 - 2*x^8 - 2*x^6*y*z0 + x^4*y*z0^3 - 2*x^4*z0^4 + 2*x^7 - 2*x^5*z0^2 - x^3*y*z0^3 - 2*x^3*z0^4 - x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 - x^5 + 2*x^3*y*z0 + x^3*z0^2 + x^2*y*z0 + x^3)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^2 + 2*x^59*z0^4 + 2*x^60*z0^2 - x^58*y^2*z0^2 - 2*x^56*y^2*z0^4 - x^61 - 2*x^57*y^2*z0^2 - 2*x^60 + x^58*y^2 - x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 - 2*x^57*z0^2 + x^58 + 2*x^57 + x^55*z0^2 + 2*x^53*z0^4 + 2*x^54*z0^2 - x^55 - 2*x^54 - x^52*z0^2 - 2*x^50*z0^4 - 2*x^51*z0^2 + x^52 + 2*x^51 + x^49*z0^2 + 2*x^47*z0^4 - x^50 + 2*x^48*z0^2 - x^49 + x^47*y^2 - 2*x^48 - x^46*z0^2 - 2*x^44*z0^4 + x^47 - 2*x^45*z0^2 + x^46 + 2*x^45 + x^43*z0^2 - x^41*z0^4 - x^44 + 2*x^42*z0^2 + 2*x^40*z0^4 - x^43 + x^41*z0^2 + x^39*y*z0^3 + x^39*z0^4 - 2*x^42 - 2*x^40*y*z0 - x^40*z0^2 - x^38*y*z0^3 - x^38*z0^4 - 2*x^41 - x^39*y*z0 + 2*x^39*z0^2 + 2*x^37*z0^4 - x^40 + x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 + 2*x^36*z0^4 - 2*x^37*y*z0 + 2*x^37*z0^2 - 2*x^35*z0^4 + 2*x^38 + x^36*y*z0 - 2*x^36*z0^2 + 2*x^34*y*z0^3 + x^34*z0^4 - x^37 + x^35*y*z0 + x^35*z0^2 + x^33*y*z0^3 - x^33*z0^4 + x^36 + x^34*y*z0 - x^34*z0^2 - 2*x^32*y*z0^3 + 2*x^32*z0^4 + 2*x^35 - 2*x^33*y*z0 - x^31*y*z0^3 - x^31*z0^4 + x^34 + x^32*y*z0 + x^32*z0^2 + x^30*y*z0^3 - 2*x^30*z0^4 + x^33 - 2*x^31*y*z0 - x^31*z0^2 - x^29*y*z0^3 + 2*x^32 + x^30*y*z0 + 2*x^30*z0^2 - 2*x^28*y*z0^3 - x^28*z0^4 + 2*x^31 + 2*x^29*y*z0 + x^29*z0^2 - 2*x^27*y*z0^3 + x^27*z0^4 - x^28*y*z0 - 2*x^28*z0^2 + 2*x^26*y*z0^3 - x^29 + x^27*y*z0 - x^25*y*z0^3 - 2*x^25*z0^4 - 2*x^28 + x^26*z0^2 - x^24*y*z0^3 - x^24*z0^4 - x^27 + 2*x^25*z0^2 - x^26 + x^24*y*z0 - x^24*z0^2 - x^22*y*z0^3 - 2*x^25 - x^23*y*z0 + 2*x^23*z0^2 - x^21*y*z0^3 + x^21*z0^4 + x^24 + 2*x^22*y*z0 + 2*x^22*z0^2 - x^20*y*z0^3 + x^20*z0^4 + x^23 - 2*x^21*y*z0 + 2*x^19*y*z0^3 + 2*x^22 - x^20*y*z0 + 2*x^20*z0^2 - 2*x^18*y*z0^3 + x^21 + x^19*z0^2 + x^17*y*z0^3 - x^20 + 2*x^18*y*z0 + x^18*z0^2 + x^16*y*z0^3 + 2*x^19 + 2*x^17*y*z0 + 2*x^17*z0^2 - 2*x^15*z0^4 + x^18 - x^16*y*z0 + x^16*z0^2 - 2*x^14*y*z0^3 + x^14*z0^4 + 2*x^17 - 2*x^15*y*z0 - x^15*z0^2 + x^13*y*z0^3 + 2*x^13*z0^4 - 2*x^14*y*z0 - 2*x^14*z0^2 - x^12*y*z0^3 + 2*x^12*z0^4 + 2*x^13*y*z0 - x^13*z0^2 + 2*x^11*y*z0^3 - 2*x^14 - 2*x^12*y*z0 - x^12*z0^2 + x^10*y*z0^3 - 2*x^10*z0^4 + 2*x^13 - 2*x^11*z0^2 + 2*x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^12 - 2*x^10*y*z0 - x^8*y*z0^3 - x^9*y*z0 + 2*x^9*z0^2 + 2*x^7*y*z0^3 - x^7*z0^4 - x^8*y*z0 + x^8*z0^2 + x^9 - 2*x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 - x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 - x^4*z0^4 + x^7 + 2*x^5*y*z0 - 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + x^6 + x^4*y*z0 + x^4*z0^2 - 2*x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 - x^3)/y) * dx, - ((-2*x^60*z0^3 + x^61*z0 + x^59*z0^3 + 2*x^57*y^2*z0^3 + 2*x^60*z0 - x^58*y^2*z0 - 2*x^58*z0^3 - x^56*y^2*z0^3 + x^59*z0 - 2*x^57*y^2*z0 + x^57*z0^3 + 2*x^55*y^2*z0^3 - x^58*z0 - x^56*y^2*z0 - x^56*z0^3 + x^54*y^2*z0^3 - 2*x^57*z0 + 2*x^55*z0^3 - x^56*z0 - x^54*z0^3 + x^55*z0 + x^53*z0^3 + 2*x^54*z0 - 2*x^52*z0^3 + x^53*z0 + x^51*z0^3 - x^52*z0 - x^50*z0^3 - 2*x^51*z0 + 2*x^49*z0^3 - 2*x^50*z0 - x^48*z0^3 + x^49*z0 + x^47*y^2*z0 + x^47*z0^3 + 2*x^48*z0 - 2*x^46*z0^3 + 2*x^47*z0 + x^45*z0^3 - x^46*z0 - x^44*z0^3 - 2*x^45*z0 + 2*x^43*z0^3 - 2*x^44*z0 - x^42*z0^3 + x^43*z0 + x^41*z0^3 + 2*x^42*z0 + x^40*z0^3 + x^38*y*z0^4 - 2*x^41*z0 + x^39*y*z0^2 - x^39*z0^3 + 2*x^37*y*z0^4 - 2*x^40*y - x^40*z0 - x^38*y*z0^2 + 2*x^36*y*z0^4 - x^39*y - x^39*z0 - 2*x^37*y*z0^2 + x^37*z0^3 - x^38*y + x^38*z0 - x^36*z0^3 - 2*x^34*y*z0^4 + x^37*y + x^37*z0 + x^35*y*z0^2 + x^35*z0^3 - x^33*y*z0^4 - x^36*y - x^36*z0 + x^34*y*z0^2 - x^34*z0^3 - 2*x^35*y - 2*x^35*z0 + x^33*y*z0^2 + x^33*z0^3 - x^31*y*z0^4 - 2*x^34*y - 2*x^32*y*z0^2 + 2*x^32*z0^3 - 2*x^33*y + 2*x^33*z0 - x^29*y*z0^4 - x^32*y - 2*x^30*y*z0^2 - 2*x^30*z0^3 + 2*x^28*y*z0^4 + 2*x^31*y - 2*x^29*y*z0^2 + 2*x^27*y*z0^4 - x^30*y + 2*x^30*z0 - x^28*y*z0^2 - 2*x^28*z0^3 - x^29*z0 - 2*x^27*y*z0^2 - x^27*z0^3 - x^25*y*z0^4 - x^28*z0 - 2*x^26*y*z0^2 - 2*x^27*z0 - 2*x^25*y*z0^2 + x^25*z0^3 - 2*x^23*y*z0^4 + x^26*y - x^26*z0 - x^24*y*z0^2 + x^24*z0^3 + x^22*y*z0^4 - 2*x^25*y - x^25*z0 + x^23*y*z0^2 + x^23*z0^3 + 2*x^21*y*z0^4 - x^24*y - 2*x^24*z0 + 2*x^22*y*z0^2 + x^22*z0^3 - x^23*z0 + x^21*y*z0^2 - 2*x^19*y*z0^4 + 2*x^22*y + 2*x^22*z0 - 2*x^20*z0^3 + x^18*y*z0^4 - 2*x^21*y + 2*x^21*z0 + 2*x^19*z0^3 - 2*x^17*y*z0^4 + 2*x^20*y + x^18*y*z0^2 + x^18*z0^3 - x^16*y*z0^4 + 2*x^19*y + 2*x^19*z0 + 2*x^17*y*z0^2 - 2*x^17*z0^3 + 2*x^15*y*z0^4 + 2*x^18*y - 2*x^18*z0 + x^16*y*z0^2 + 2*x^14*y*z0^4 - 2*x^17*y - x^17*z0 + x^15*y*z0^2 + x^15*z0^3 - 2*x^16*y - x^16*z0 + x^14*y*z0^2 - x^15*y - x^15*z0 - x^13*y*z0^2 - x^11*y*z0^4 - 2*x^14*y + 2*x^12*y*z0^2 - x^12*z0^3 + x^13*y - 2*x^13*z0 + 2*x^11*z0^3 - 2*x^9*y*z0^4 + 2*x^12*y - x^12*z0 + x^10*y*z0^2 - x^10*z0^3 - x^8*y*z0^4 - x^11*y + 2*x^11*z0 + x^9*y*z0^2 + 2*x^7*y*z0^4 + x^10*z0 + 2*x^8*z0^3 + 2*x^6*y*z0^4 - x^9*y + x^7*y*z0^2 - 2*x^5*y*z0^4 + x^8*y + x^8*z0 - x^6*z0^3 + 2*x^7*y - x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + 2*x^3*y*z0^4 + 2*x^6*y + x^4*z0^3 - 2*x^2*y*z0^4 + 2*x^5*y + x^5*z0 + x^3*y*z0^2 - x^3*z0^3 + 2*x^4*y - 2*x^4*z0 + x^2*y*z0^2 - 2*x^3*y - x^3*z0 - 2*x^2*y - 2*x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + 2*x^58*y^2*z0^4 - x^61*z0^2 + 2*x^59*z0^4 + x^60*z0^2 + x^58*y^2*z0^2 + 2*x^58*z0^4 - 2*x^56*y^2*z0^4 - x^61 - x^57*y^2*z0^2 - x^60 + x^58*y^2 + x^58*z0^2 - 2*x^56*z0^4 + x^57*y^2 - x^57*z0^2 - 2*x^55*z0^4 + x^58 + x^57 - x^55*z0^2 + 2*x^53*z0^4 + x^54*z0^2 + 2*x^52*z0^4 - x^55 - x^54 + x^52*z0^2 - 2*x^50*z0^4 - x^51*z0^2 - 2*x^49*z0^4 + x^52 - x^50*z0^2 + x^51 - x^49*z0^2 + x^47*y^2*z0^2 + 2*x^47*z0^4 + x^48*z0^2 + 2*x^46*z0^4 - x^49 + x^47*z0^2 - x^48 + x^46*z0^2 - 2*x^44*z0^4 - x^45*z0^2 - 2*x^43*z0^4 + x^46 - x^44*z0^2 + x^45 - x^43*z0^2 + 2*x^41*z0^4 + x^42*z0^2 - x^40*y*z0^3 - 2*x^40*z0^4 - x^43 - x^39*y*z0^3 - x^42 + 2*x^40*y*z0 + x^40*z0^2 - x^38*y*z0^3 + 2*x^38*y*z0 + 2*x^38*z0^2 + 2*x^36*y*z0^3 + 2*x^36*z0^4 + x^39 + 2*x^37*y*z0 - x^37*z0^2 + x^35*y*z0^3 - x^35*z0^4 - x^38 - x^36*y*z0 + x^34*y*z0^3 - 2*x^34*z0^4 - x^35*y*z0 - x^33*y*z0^3 + x^33*z0^4 + x^36 + 2*x^34*y*z0 + x^34*z0^2 - x^32*z0^4 - x^35 - 2*x^33*y*z0 + 2*x^33*z0^2 + 2*x^31*y*z0^3 - 2*x^31*z0^4 + x^34 - x^32*y*z0 + 2*x^30*y*z0^3 + 2*x^30*z0^4 - x^33 - x^31*y*z0 - 2*x^31*z0^2 + 2*x^29*z0^4 + x^32 + x^30*y*z0 + 2*x^30*z0^2 + x^28*y*z0^3 + x^28*z0^4 - 2*x^31 + 2*x^29*y*z0 - x^29*z0^2 - 2*x^27*y*z0^3 + 2*x^27*z0^4 + x^30 + x^28*y*z0 + x^28*z0^2 + x^26*z0^4 - 2*x^29 - 2*x^27*y*z0 - x^27*z0^2 - 2*x^25*y*z0^3 + x^25*z0^4 + x^28 - x^27 - x^25*y*z0 - 2*x^25*z0^2 + 2*x^23*y*z0^3 + 2*x^23*z0^4 - x^26 + x^24*z0^2 - 2*x^22*y*z0^3 - x^22*z0^4 - x^25 + 2*x^23*y*z0 - x^23*z0^2 - x^21*y*z0^3 + x^21*z0^4 + x^24 - 2*x^22*y*z0 + 2*x^20*y*z0^3 - x^20*z0^4 + x^23 - 2*x^21*z0^2 + x^19*y*z0^3 + 2*x^19*z0^4 + x^22 - 2*x^20*y*z0 - x^20*z0^2 - x^18*y*z0^3 - x^18*z0^4 + 2*x^21 + x^19*y*z0 - 2*x^19*z0^2 - x^17*y*z0^3 - 2*x^17*z0^4 - 2*x^20 + 2*x^18*y*z0 - x^18*z0^2 + x^16*y*z0^3 - x^16*z0^4 + 2*x^19 - x^17*y*z0 - x^15*z0^4 + 2*x^18 - x^16*y*z0 + x^16*z0^2 - x^14*y*z0^3 - x^14*z0^4 + 2*x^15*y*z0 + 2*x^15*z0^2 + 2*x^13*y*z0^3 - x^13*z0^4 - 2*x^16 + 2*x^14*y*z0 - x^14*z0^2 - x^12*y*z0^3 - 2*x^15 - 2*x^13*y*z0 + 2*x^13*z0^2 + 2*x^11*z0^4 - 2*x^14 + 2*x^12*y*z0 - x^12*z0^2 - x^10*y*z0^3 + 2*x^10*z0^4 + 2*x^13 + 2*x^11*y*z0 + 2*x^11*z0^2 + 2*x^9*y*z0^3 + x^9*z0^4 - 2*x^12 + x^10*y*z0 - x^10*z0^2 - x^8*y*z0^3 - x^8*z0^4 - 2*x^9*y*z0 - 2*x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 - x^10 + x^8*y*z0 - x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + 2*x^5*z0^4 - x^8 - x^6*y*z0 - x^6*z0^2 + 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 - x^5*z0^2 - 2*x^3*y*z0^3 - x^3*z0^4 - x^4*y*z0 + x^4*z0^2 + x^3*y*z0 + 2*x^3*z0^2 + x^2)/y) * dx, - ((x^61*z0^3 - x^58*y^2*z0^3 + x^61*z0 + 2*x^59*z0^3 - 2*x^60*z0 - x^58*y^2*z0 - 2*x^56*y^2*z0^3 - x^59*z0 + 2*x^57*y^2*z0 - 2*x^57*z0^3 - x^55*y^2*z0^3 - x^58*z0 + x^56*y^2*z0 - 2*x^56*z0^3 + 2*x^54*y^2*z0^3 + 2*x^57*z0 + x^56*z0 + 2*x^54*z0^3 + x^55*z0 + 2*x^53*z0^3 - 2*x^54*z0 - x^53*z0 - 2*x^51*z0^3 - x^52*z0 + 2*x^50*z0^3 + 2*x^51*z0 + x^47*y^2*z0^3 + x^50*z0 + 2*x^48*z0^3 + x^49*z0 - 2*x^47*z0^3 - 2*x^48*z0 - x^47*z0 - 2*x^45*z0^3 - x^46*z0 + 2*x^44*z0^3 + 2*x^45*z0 + x^44*z0 + 2*x^42*z0^3 + x^43*z0 - x^41*z0^3 + x^39*y*z0^4 - 2*x^42*z0 - 2*x^40*y*z0^2 - 2*x^40*z0^3 - 2*x^38*y*z0^4 + x^39*y*z0^2 - 2*x^37*y*z0^4 - 2*x^40*y - 2*x^40*z0 - x^38*y*z0^2 + x^38*z0^3 + 2*x^36*y*z0^4 + x^39*y - x^39*z0 + x^37*y*z0^2 - 2*x^37*z0^3 - x^35*y*z0^4 + 2*x^38*y + 2*x^38*z0 + x^36*y*z0^2 + x^36*z0^3 + x^37*y - x^37*z0 - x^35*y*z0^2 - x^36*y - 2*x^36*z0 - x^34*y*z0^2 + 2*x^34*z0^3 + x^35*y - x^33*y*z0^2 + x^33*z0^3 - x^34*y + 2*x^34*z0 - 2*x^32*y*z0^2 - x^32*z0^3 - 2*x^30*y*z0^4 - x^33*y - 2*x^33*z0 + x^31*y*z0^2 - 2*x^29*y*z0^4 - 2*x^32*y + x^32*z0 + 2*x^30*y*z0^2 + 2*x^28*y*z0^4 + 2*x^31*y + x^31*z0 + x^29*y*z0^2 - 2*x^29*z0^3 + x^27*y*z0^4 + 2*x^30*y - 2*x^30*z0 + x^28*y*z0^2 - x^28*z0^3 + 2*x^26*y*z0^4 + x^29*z0 - x^27*z0^3 - x^25*y*z0^4 - 2*x^28*y + x^26*y*z0^2 + x^26*z0^3 + x^24*y*z0^4 - x^27*y + x^27*z0 + x^25*y*z0^2 - x^25*z0^3 - 2*x^23*y*z0^4 + x^26*z0 - x^24*y*z0^2 - 2*x^24*z0^3 - 2*x^22*y*z0^4 + x^25*y + 2*x^25*z0 + 2*x^23*y*z0^2 + x^23*z0^3 - 2*x^24*y + x^22*y*z0^2 + x^22*z0^3 + 2*x^20*y*z0^4 - 2*x^23*z0 + x^21*y*z0^2 - 2*x^21*z0^3 + 2*x^19*y*z0^4 + x^22*y + 2*x^22*z0 - x^18*y*z0^4 + x^19*y*z0^2 - x^19*z0^3 - x^17*y*z0^4 - 2*x^20*y + 2*x^20*z0 + x^18*z0^3 + 2*x^16*y*z0^4 + 2*x^19*y - x^19*z0 + 2*x^17*y*z0^2 + x^17*z0^3 - x^15*y*z0^4 - x^18*y + 2*x^18*z0 + 2*x^16*y*z0^2 + x^16*z0^3 + 2*x^14*y*z0^4 + x^17*y + 2*x^17*z0 + 2*x^15*y*z0^2 - 2*x^15*z0^3 + x^13*y*z0^4 - 2*x^16*z0 - x^14*y*z0^2 + 2*x^14*z0^3 - 2*x^12*y*z0^4 - x^15*z0 + 2*x^13*y*z0^2 + x^13*z0^3 + 2*x^11*y*z0^4 + x^14*y + 2*x^14*z0 + x^12*y*z0^2 - 2*x^12*z0^3 - x^10*y*z0^4 - x^13*y + 2*x^13*z0 + 2*x^11*y*z0^2 + x^9*y*z0^4 + 2*x^12*y + 2*x^12*z0 + x^10*y*z0^2 + 2*x^10*z0^3 - x^8*y*z0^4 + 2*x^11*y - x^9*y*z0^2 + x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y - x^10*z0 - x^8*y*z0^2 + x^8*z0^3 - x^6*y*z0^4 - x^9*y + x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 + x^5*y*z0^4 - 2*x^8*y - x^6*y*z0^2 + x^6*z0^3 + 2*x^4*y*z0^4 + 2*x^7*y + x^7*z0 - 2*x^5*y*z0^2 + x^5*z0^3 + 2*x^6*z0 + x^4*y*z0^2 + x^4*z0^3 - x^2*y*z0^4 - x^5*y - x^5*z0 + 2*x^3*z0^3 - x^4*y + x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + x^3*y - x^3*z0 + x^2*z0)/y) * dx, - ((-x^61*z0^4 + x^58*y^2*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 - 2*x^60*z0^2 + 2*x^58*y^2*z0^2 + x^58*z0^4 - 2*x^56*y^2*z0^4 + x^61 + 2*x^57*y^2*z0^2 - 2*x^60 - x^58*y^2 + 2*x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 + 2*x^57*z0^2 - x^55*z0^4 - x^58 + 2*x^57 - 2*x^55*z0^2 + 2*x^53*z0^4 - 2*x^54*z0^2 + x^52*z0^4 + x^55 - 2*x^54 + 2*x^52*z0^2 + 2*x^50*z0^4 + 2*x^51*z0^2 - x^49*z0^4 + x^47*y^2*z0^4 - x^52 + 2*x^51 - 2*x^49*z0^2 - 2*x^47*z0^4 - 2*x^48*z0^2 + x^46*z0^4 + x^49 - 2*x^48 + 2*x^46*z0^2 + 2*x^44*z0^4 + 2*x^45*z0^2 - x^43*z0^4 - x^46 + 2*x^45 - 2*x^43*z0^2 - 2*x^42*z0^2 + 2*x^40*y*z0^3 + x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - 2*x^42 - x^40*y*z0 + 2*x^40*z0^2 + x^38*y*z0^3 - 2*x^38*z0^4 + 2*x^41 - x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 - x^40 + 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 - 2*x^36*z0^4 + 2*x^39 - 2*x^37*y*z0 - 2*x^37*z0^2 + x^35*y*z0^3 - 2*x^38 + x^36*y*z0 + x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 + x^37 + 2*x^35*y*z0 + x^33*y*z0^3 - 2*x^33*z0^4 - x^36 + x^34*y*z0 - 2*x^34*z0^2 - x^32*y*z0^3 - x^32*z0^4 - 2*x^35 + x^33*y*z0 + x^33*z0^2 - x^31*y*z0^3 + x^31*z0^4 - 2*x^34 + 2*x^32*z0^2 + x^30*y*z0^3 - 2*x^33 - x^31*y*z0 - x^31*z0^2 - x^29*y*z0^3 + 2*x^29*z0^4 + 2*x^32 + 2*x^28*z0^4 - 2*x^31 - x^29*y*z0 + x^29*z0^2 - x^27*y*z0^3 - x^27*z0^4 - x^30 - x^28*y*z0 - x^28*z0^2 - 2*x^26*y*z0^3 + 2*x^29 + 2*x^27*y*z0 - x^25*z0^4 + 2*x^28 + x^26*y*z0 - 2*x^26*z0^2 + x^24*y*z0^3 - x^25*y*z0 - 2*x^25*z0^2 + x^26 + x^24*y*z0 + 2*x^24*z0^2 + x^22*z0^4 + 2*x^23*y*z0 - 2*x^23*z0^2 - 2*x^21*y*z0^3 + x^24 - 2*x^22*y*z0 - 2*x^22*z0^2 - 2*x^20*z0^4 - x^23 - x^21*y*z0 - 2*x^21*z0^2 + 2*x^19*z0^4 - 2*x^22 + x^20*y*z0 - 2*x^20*z0^2 - 2*x^18*y*z0^3 + x^18*z0^4 + x^21 + 2*x^19*y*z0 + x^19*z0^2 - 2*x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^20 + x^18*y*z0 + x^16*y*z0^3 - x^16*z0^4 + x^19 + 2*x^17*y*z0 - x^15*y*z0^3 - 2*x^18 - x^16*y*z0 + x^14*y*z0^3 + 2*x^14*z0^4 + x^15*y*z0 + x^15*z0^2 + 2*x^13*y*z0^3 + x^13*z0^4 + 2*x^16 + x^14*y*z0 + x^14*z0^2 + 2*x^12*y*z0^3 + 2*x^12*z0^4 - 2*x^15 + 2*x^13*y*z0 - 2*x^13*z0^2 + x^11*y*z0^3 - 2*x^11*z0^4 - x^14 - x^12*y*z0 + x^10*y*z0^3 + x^11*y*z0 - 2*x^11*z0^2 + x^9*y*z0^3 + x^9*z0^4 - 2*x^10*z0^2 + 2*x^8*y*z0^3 - x^11 + x^9*y*z0 - 2*x^9*z0^2 - 2*x^7*y*z0^3 - 2*x^7*z0^4 - x^10 + x^6*y*z0^3 + x^6*z0^4 - x^9 + 2*x^7*y*z0 - x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - 2*x^8 - x^6*y*z0 + x^6*z0^2 + x^4*y*z0^3 - 2*x^4*z0^4 + 2*x^7 - 2*x^5*y*z0 + x^5*z0^2 + 2*x^3*y*z0^3 - 2*x^3*z0^4 + x^6 - 2*x^4*y*z0 - 2*x^4*z0^2 - x^2*y*z0^3 + x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + x^2*z0^2 - x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 + 2*x^60*z0^4 + x^58*y^2*z0^4 + x^61*z0^2 - 2*x^57*y^2*z0^4 - x^58*y^2*z0^2 + x^58*z0^4 + 2*x^61 - 2*x^57*z0^4 - 2*x^60 - 2*x^58*y^2 - x^58*z0^2 + 2*x^57*y^2 - x^55*z0^4 - 2*x^58 + 2*x^54*z0^4 + 2*x^57 + x^55*z0^2 + x^52*z0^4 + 2*x^55 - 2*x^51*z0^4 - 2*x^54 - x^52*z0^2 - x^49*z0^4 - 2*x^52 + 2*x^48*z0^4 + x^51 + x^49*z0^2 + x^48*y^2 + x^46*z0^4 + 2*x^49 - 2*x^45*z0^4 - x^48 - x^46*z0^2 - x^43*z0^4 - 2*x^46 + 2*x^42*z0^4 + x^45 + x^43*z0^2 + 2*x^40*y*z0^3 - 2*x^40*z0^4 + 2*x^43 + x^41*z0^2 + x^39*y*z0^3 - 2*x^39*z0^4 - x^42 - 2*x^40*y*z0 - x^38*y*z0^3 + x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 - 2*x^40 - 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - x^36*z0^4 + x^39 - x^37*y*z0 - x^37*z0^2 - 2*x^35*y*z0^3 - 2*x^35*z0^4 - x^36*y*z0 + x^36*z0^2 + 2*x^34*z0^4 + 2*x^37 + x^35*y*z0 + 2*x^35*z0^2 - 2*x^33*y*z0^3 + x^33*z0^4 - x^36 - x^34*y*z0 + x^34*z0^2 - x^32*y*z0^3 - 2*x^32*z0^4 - x^33*y*z0 - x^33*z0^2 + x^31*y*z0^3 - 2*x^31*z0^4 - x^34 - x^32*y*z0 - x^32*z0^2 - x^30*z0^4 - x^33 - 2*x^31*y*z0 + x^31*z0^2 + x^29*y*z0^3 - x^29*z0^4 - 2*x^32 + 2*x^30*y*z0 + x^30*z0^2 - x^28*y*z0^3 - x^28*z0^4 + 2*x^31 + x^29*y*z0 + x^27*y*z0^3 - 2*x^27*z0^4 - 2*x^30 - 2*x^28*y*z0 - x^28*z0^2 + 2*x^26*y*z0^3 + 2*x^29 + 2*x^27*y*z0 - 2*x^27*z0^2 + x^25*y*z0^3 + 2*x^25*z0^4 - x^28 - 2*x^26*y*z0 + x^26*z0^2 + x^24*z0^4 - 2*x^27 - x^25*y*z0 + x^25*z0^2 + 2*x^23*y*z0^3 + x^23*z0^4 - 2*x^26 - x^24*z0^2 + 2*x^22*y*z0^3 - 2*x^22*z0^4 + x^25 - x^23*y*z0 + x^23*z0^2 + 2*x^21*y*z0^3 + 2*x^21*z0^4 + 2*x^24 - 2*x^22*y*z0 - 2*x^20*y*z0^3 + x^20*z0^4 - x^23 + x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 - x^19*z0^4 - x^20*y*z0 + 2*x^20*z0^2 - 2*x^18*y*z0^3 + x^18*z0^4 - 2*x^21 - 2*x^19*y*z0 + 2*x^17*y*z0^3 + x^20 - x^18*y*z0 + 2*x^18*z0^2 + x^16*y*z0^3 + x^16*z0^4 + x^19 + 2*x^17*y*z0 + 2*x^17*z0^2 - x^15*y*z0^3 - x^15*z0^4 - 2*x^18 + x^16*z0^2 - 2*x^14*y*z0^3 - 2*x^14*z0^4 - x^17 + x^15*y*z0 - x^13*y*z0^3 - x^13*z0^4 + 2*x^16 - 2*x^14*y*z0 - 2*x^14*z0^2 + x^12*y*z0^3 - x^12*z0^4 + x^15 + x^13*y*z0 + 2*x^13*z0^2 - x^11*y*z0^3 - x^11*z0^4 + 2*x^14 - 2*x^12*y*z0 - 2*x^12*z0^2 + x^10*y*z0^3 - x^10*z0^4 + x^13 + 2*x^11*y*z0 + 2*x^11*z0^2 + x^9*y*z0^3 - 2*x^10*y*z0 + 2*x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 - x^11 - 2*x^9*y*z0 + x^9*z0^2 - x^7*y*z0^3 - 2*x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^7*z0^2 + 2*x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 - x^6*y*z0 + x^6*z0^2 - 2*x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^7 - x^5*y*z0 - 2*x^5*z0^2 + x^3*y*z0^3 + x^6 + 2*x^4*z0^2 + x^2*y*z0^3 - x^2*z0^4 - x^5 + x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^3 - 2*x^2)/y) * dx, - ((2*x^61*z0^3 + x^60*z0^3 - 2*x^58*y^2*z0^3 - 2*x^59*z0^3 - x^57*y^2*z0^3 + 2*x^60*z0 - 2*x^58*z0^3 + 2*x^56*y^2*z0^3 - 2*x^57*y^2*z0 + 2*x^56*z0^3 - x^54*y^2*z0^3 - 2*x^57*z0 + 2*x^55*z0^3 - 2*x^53*z0^3 + 2*x^54*z0 - 2*x^52*z0^3 + 2*x^50*z0^3 + 2*x^51*z0 + 2*x^49*z0^3 + x^48*y^2*z0 - 2*x^47*z0^3 - 2*x^48*z0 - 2*x^46*z0^3 + 2*x^44*z0^3 + 2*x^45*z0 + 2*x^43*z0^3 + 2*x^39*y*z0^4 - 2*x^42*z0 + x^40*y*z0^2 + 2*x^40*z0^3 - 2*x^38*y*z0^4 - x^39*z0^3 - x^37*y*z0^4 - x^38*z0^3 + 2*x^36*y*z0^4 + 2*x^39*z0 - 2*x^37*y*z0^2 - x^37*z0^3 - 2*x^35*y*z0^4 + 2*x^38*y + 2*x^34*y*z0^4 + 2*x^35*y*z0^2 + 2*x^35*z0^3 + 2*x^33*y*z0^4 - 2*x^36*z0 + 2*x^34*y*z0^2 + x^32*y*z0^4 + x^35*y - x^35*z0 - 2*x^33*y*z0^2 + 2*x^34*z0 - x^32*y*z0^2 - 2*x^32*z0^3 + 2*x^33*y - x^33*z0 - x^31*y*z0^2 - 2*x^31*z0^3 - 2*x^29*y*z0^4 - 2*x^30*y*z0^2 + 2*x^31*y - 2*x^31*z0 + x^29*y*z0^2 - 2*x^29*z0^3 + 2*x^27*y*z0^4 + 2*x^30*y + x^28*z0^3 + x^26*y*z0^4 - x^29*y + x^29*z0 - 2*x^27*z0^3 - 2*x^28*y - x^28*z0 + 2*x^26*y*z0^2 + x^24*y*z0^4 - x^27*y - 2*x^25*y*z0^2 - x^25*z0^3 + 2*x^26*y - x^26*z0 - x^24*y*z0^2 - 2*x^22*y*z0^4 - 2*x^25*y + x^23*y*z0^2 - 2*x^21*y*z0^4 + 2*x^24*y + 2*x^24*z0 + 2*x^22*y*z0^2 - x^22*z0^3 + 2*x^20*y*z0^4 + x^23*y - x^23*z0 - 2*x^22*z0 + 2*x^20*y*z0^2 + x^20*z0^3 - x^18*y*z0^4 - 2*x^21*z0 - x^19*z0^3 + x^20*y - x^20*z0 + x^18*z0^3 - 2*x^16*y*z0^4 - x^19*z0 + x^17*y*z0^2 + 2*x^17*z0^3 + 2*x^15*y*z0^4 - x^18*y - 2*x^18*z0 - 2*x^16*y*z0^2 - x^16*z0^3 - 2*x^14*y*z0^4 - x^17*y + x^17*z0 - 2*x^15*y*z0^2 + 2*x^15*z0^3 + x^13*y*z0^4 + 2*x^16*y - x^16*z0 + x^12*y*z0^4 + x^15*y + 2*x^15*z0 + x^13*y*z0^2 + 2*x^13*z0^3 - 2*x^11*y*z0^4 + x^14*y - 2*x^14*z0 - 2*x^12*y*z0^2 - x^12*z0^3 + x^10*y*z0^4 - x^13*y - x^13*z0 - x^11*y*z0^2 - 2*x^11*z0^3 - 2*x^9*y*z0^4 - 2*x^12*y - x^10*y*z0^2 + x^10*z0^3 - 2*x^8*y*z0^4 - x^11*y - 2*x^11*z0 + x^9*z0^3 + 2*x^10*z0 + 2*x^8*z0^3 + x^6*y*z0^4 + 2*x^9*y - x^9*z0 + x^7*y*z0^2 + x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - x^8*z0 + x^6*y*z0^2 + x^6*z0^3 - 2*x^7*z0 + x^5*y*z0^2 - x^5*z0^3 - 2*x^3*y*z0^4 + 2*x^6*y - 2*x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 - x^2*y*z0^4 + 2*x^5*y - x^5*z0 - x^3*y*z0^2 + x^3*z0^3 + x^4*z0 - 2*x^2*z0^3 + x^3*y + x^3*z0 + 2*x^2*y)/y) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 + 2*x^59*z0^4 - 2*x^60*z0^2 - x^58*z0^4 - 2*x^56*y^2*z0^4 + 2*x^61 + 2*x^57*y^2*z0^2 + 2*x^60 - 2*x^58*y^2 - 2*x^56*z0^4 - 2*x^57*y^2 + 2*x^57*z0^2 + x^55*z0^4 - 2*x^58 - 2*x^57 + 2*x^53*z0^4 - 2*x^54*z0^2 - x^52*z0^4 + 2*x^55 + 2*x^54 - 2*x^50*z0^4 + x^51*z0^2 + x^49*z0^4 - 2*x^52 + x^48*y^2*z0^2 - 2*x^51 + 2*x^47*z0^4 - x^48*z0^2 - x^46*z0^4 + 2*x^49 + 2*x^48 - 2*x^44*z0^4 + x^45*z0^2 + x^43*z0^4 - 2*x^46 - 2*x^45 - x^41*z0^4 - x^42*z0^2 - 2*x^40*y*z0^3 + x^40*z0^4 + 2*x^43 + 2*x^42 - x^40*z0^2 - 2*x^38*y*z0^3 - x^38*z0^4 + 2*x^41 - x^39*y*z0 + x^39*z0^2 - 2*x^37*z0^4 + 2*x^40 + x^38*y*z0 - x^36*z0^4 + x^39 + 2*x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 + x^35*z0^4 - 2*x^38 + x^36*y*z0 - x^36*z0^2 - 2*x^34*y*z0^3 + 2*x^34*z0^4 - x^37 - 2*x^33*y*z0^3 - 2*x^33*z0^4 - x^36 + 2*x^34*z0^2 + 2*x^32*y*z0^3 + x^32*z0^4 - 2*x^35 - x^33*y*z0 - 2*x^31*y*z0^3 - x^31*z0^4 - 2*x^34 - x^32*y*z0 + x^32*z0^2 - x^30*y*z0^3 + x^30*z0^4 - x^33 - x^31*z0^2 - 2*x^29*y*z0^3 + 2*x^29*z0^4 - x^32 + x^30*y*z0 + 2*x^28*y*z0^3 - x^28*z0^4 - 2*x^29*y*z0 - x^29*z0^2 + x^27*y*z0^3 - 2*x^27*z0^4 - 2*x^30 - 2*x^28*y*z0 - 2*x^28*z0^2 + 2*x^26*y*z0^3 + x^26*z0^4 - x^29 + 2*x^27*y*z0 - x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 + x^28 + x^26*z0^2 + x^24*y*z0^3 - x^27 - 2*x^25*y*z0 - 2*x^23*y*z0^3 + 2*x^23*z0^4 - x^26 + x^24*y*z0 - 2*x^22*y*z0^3 - x^22*z0^4 - 2*x^25 - x^23*z0^2 - x^21*y*z0^3 + 2*x^24 - x^22*y*z0 - x^22*z0^2 - x^20*y*z0^3 + 2*x^20*z0^4 - 2*x^23 + 2*x^21*y*z0 + x^21*z0^2 + 2*x^19*y*z0^3 - x^19*z0^4 + x^22 - 2*x^20*y*z0 + 2*x^20*z0^2 + 2*x^18*y*z0^3 - x^18*z0^4 - 2*x^21 - x^19*y*z0 - 2*x^19*z0^2 - x^17*y*z0^3 - 2*x^17*z0^4 + x^20 - 2*x^18*y*z0 - x^18*z0^2 - 2*x^16*y*z0^3 - x^16*z0^4 + 2*x^19 + x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 - x^15*z0^4 - x^18 + 2*x^16*y*z0 + 2*x^16*z0^2 + 2*x^14*y*z0^3 - 2*x^17 - x^15*y*z0 + 2*x^15*z0^2 + 2*x^13*y*z0^3 + 2*x^13*z0^4 + x^16 + x^14*y*z0 - 2*x^12*y*z0^3 + x^15 - 2*x^13*y*z0 + 2*x^13*z0^2 + 2*x^11*y*z0^3 - x^11*z0^4 + x^14 - 2*x^12*y*z0 + 2*x^12*z0^2 - 2*x^10*y*z0^3 + 2*x^10*z0^4 + x^13 + x^11*z0^2 - 2*x^9*y*z0^3 + 2*x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 + x^8*y*z0^3 + x^8*z0^4 - 2*x^9*z0^2 + 2*x^7*y*z0^3 - x^7*z0^4 + x^10 + 2*x^8*y*z0 + 2*x^6*y*z0^3 - 2*x^6*z0^4 + x^9 + x^7*y*z0 + 2*x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + 2*x^8 - 2*x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 - x^7 + x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*z0^4 - x^6 - x^4*y*z0 - 2*x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 - x^5 - x^3*y*z0 - x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((2*x^60*z0^3 + 2*x^61*z0 - x^59*z0^3 - 2*x^57*y^2*z0^3 - 2*x^60*z0 - 2*x^58*y^2*z0 + 2*x^58*z0^3 + x^56*y^2*z0^3 + 2*x^59*z0 + 2*x^57*y^2*z0 + x^57*z0^3 - 2*x^55*y^2*z0^3 - 2*x^58*z0 - 2*x^56*y^2*z0 + x^56*z0^3 + 2*x^54*y^2*z0^3 + 2*x^57*z0 - 2*x^55*z0^3 - 2*x^56*z0 - x^54*z0^3 + 2*x^55*z0 - x^53*z0^3 - 2*x^54*z0 + 2*x^52*z0^3 + 2*x^53*z0 - 2*x^52*z0 + x^50*z0^3 + x^48*y^2*z0^3 + 2*x^51*z0 - 2*x^49*z0^3 - 2*x^50*z0 + 2*x^49*z0 - x^47*z0^3 - 2*x^48*z0 + 2*x^46*z0^3 + 2*x^47*z0 - 2*x^46*z0 + x^44*z0^3 + 2*x^45*z0 - 2*x^43*z0^3 - 2*x^44*z0 + 2*x^43*z0 - x^41*z0^3 - 2*x^42*z0 + 2*x^40*z0^3 + x^38*y*z0^4 - x^41*z0 + 2*x^39*y*z0^2 + x^40*y + 2*x^40*z0 + x^38*y*z0^2 - 2*x^36*y*z0^4 + x^39*y - x^39*z0 + 2*x^37*y*z0^2 - 2*x^37*z0^3 - 2*x^35*y*z0^4 - 2*x^38*y - x^38*z0 + 2*x^36*z0^3 + 2*x^37*y + x^37*z0 + x^33*y*z0^4 + 2*x^36*z0 + x^34*y*z0^2 + 2*x^35*y + 2*x^35*z0 + x^33*y*z0^2 + x^33*z0^3 - x^31*y*z0^4 - 2*x^34*y - x^34*z0 - 2*x^32*y*z0^2 + x^30*y*z0^4 - x^33*y - 2*x^31*y*z0^2 - x^31*z0^3 - x^32*y - 2*x^32*z0 - x^30*y*z0^2 + 2*x^28*y*z0^4 + 2*x^31*z0 + x^29*y*z0^2 - x^29*z0^3 - 2*x^27*y*z0^4 - x^30*y - 2*x^30*z0 + x^29*z0 + 2*x^27*y*z0^2 - 2*x^27*z0^3 + 2*x^25*y*z0^4 + 2*x^28*y + x^28*z0 + 2*x^26*y*z0^2 - 2*x^26*z0^3 + x^24*y*z0^4 - x^27*y + x^27*z0 - 2*x^25*y*z0^2 - 2*x^25*z0^3 + 2*x^23*y*z0^4 + 2*x^24*z0^3 - x^22*y*z0^4 + 2*x^25*y - 2*x^25*z0 + x^23*y*z0^2 - 2*x^23*z0^3 + x^24*y - x^24*z0 + 2*x^22*y*z0^2 + 2*x^20*y*z0^4 + 2*x^23*z0 - x^21*y*z0^2 + 2*x^21*z0^3 + x^19*y*z0^4 + x^22*y - x^22*z0 - 2*x^20*z0^3 - 2*x^18*y*z0^4 - x^21*z0 - 2*x^19*y*z0^2 - 2*x^19*z0^3 - 2*x^17*y*z0^4 - x^20*z0 + 2*x^18*y*z0^2 + x^18*z0^3 + 2*x^16*y*z0^4 + x^19*y - x^19*z0 + x^17*z0^3 + x^18*y - 2*x^18*z0 + 2*x^16*y*z0^2 + 2*x^14*y*z0^4 - 2*x^17*y - x^17*z0 - x^15*z0^3 + x^13*y*z0^4 - 2*x^16*y + 2*x^14*y*z0^2 + 2*x^14*z0^3 - x^12*y*z0^4 + 2*x^15*y + x^15*z0 + 2*x^13*y*z0^2 - x^13*z0^3 - 2*x^11*y*z0^4 - x^14*z0 - 2*x^12*y*z0^2 + 2*x^12*z0^3 + x^10*y*z0^4 + 2*x^13*y - 2*x^13*z0 + 2*x^11*y*z0^2 + x^11*z0^3 + 2*x^9*y*z0^4 - x^12*y - x^10*y*z0^2 - x^10*z0^3 - 2*x^11*z0 + x^9*y*z0^2 - 2*x^9*z0^3 + 2*x^10*y - x^10*z0 + 2*x^8*y*z0^2 - x^8*z0^3 - 2*x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 - x^8*z0 - 2*x^6*y*z0^2 - 2*x^6*z0^3 + x^4*y*z0^4 - 2*x^7*y - x^5*y*z0^2 - 2*x^5*z0^3 - 2*x^3*y*z0^4 - 2*x^6*y - x^6*z0 + 2*x^4*y*z0^2 - 2*x^4*z0^3 + 2*x^2*y*z0^4 + x^5*z0 + x^3*z0^3 + 2*x^4*y - 2*x^4*z0 - 2*x^2*y*z0^2 - 2*x^2*z0^3 - 2*x^3*y + x^3*z0 - x^2*y - 2*x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + 2*x^60*z0^4 + 2*x^58*y^2*z0^4 + 2*x^61*z0^2 - 2*x^57*y^2*z0^4 - x^60*z0^2 - 2*x^58*y^2*z0^2 + 2*x^58*z0^4 + x^61 + x^57*y^2*z0^2 - 2*x^57*z0^4 - x^60 - x^58*y^2 - 2*x^58*z0^2 + x^57*y^2 + x^57*z0^2 - 2*x^55*z0^4 - x^58 + 2*x^54*z0^4 + x^57 + 2*x^55*z0^2 - x^54*z0^2 + 2*x^52*z0^4 + x^55 + 2*x^51*z0^4 - x^54 - 2*x^52*z0^2 + x^48*y^2*z0^4 + x^51*z0^2 - 2*x^49*z0^4 - x^52 - 2*x^48*z0^4 + x^51 + 2*x^49*z0^2 - x^48*z0^2 + 2*x^46*z0^4 + x^49 + 2*x^45*z0^4 - x^48 - 2*x^46*z0^2 + x^45*z0^2 - 2*x^43*z0^4 - x^46 - 2*x^42*z0^4 + x^45 + 2*x^43*z0^2 + x^41*z0^4 - x^42*z0^2 - x^40*y*z0^3 - x^40*z0^4 + x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + x^39*z0^4 - x^42 + x^40*y*z0 + 2*x^40*z0^2 - 2*x^38*y*z0^3 + 2*x^38*z0^4 + x^41 - 2*x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 + 2*x^37*z0^4 - x^40 - 2*x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + x^39 + x^37*y*z0 - x^37*z0^2 + 2*x^35*y*z0^3 + 2*x^38 + x^36*z0^2 - x^34*y*z0^3 + x^34*z0^4 + x^37 - 2*x^35*z0^2 + x^33*y*z0^3 + x^33*z0^4 + x^34*z0^2 + 2*x^32*z0^4 - 2*x^33*y*z0 - 2*x^33*z0^2 + 2*x^31*y*z0^3 + x^31*z0^4 + 2*x^34 + 2*x^32*y*z0 + x^32*z0^2 + 2*x^30*y*z0^3 + 2*x^30*z0^4 + 2*x^31*y*z0 - 2*x^31*z0^2 - 2*x^29*y*z0^3 - 2*x^29*z0^4 + 2*x^30*y*z0 - x^30*z0^2 + 2*x^28*y*z0^3 + x^28*z0^4 + 2*x^31 - 2*x^29*y*z0 + x^29*z0^2 + x^27*y*z0^3 + x^27*z0^4 - 2*x^30 - x^28*y*z0 + x^28*z0^2 - 2*x^26*y*z0^3 + 2*x^29 + 2*x^27*y*z0 - x^27*z0^2 + x^25*y*z0^3 + x^25*z0^4 - 2*x^24*y*z0^3 + 2*x^27 + x^25*y*z0 - 2*x^25*z0^2 + 2*x^24*y*z0 + 2*x^24*z0^2 + x^22*y*z0^3 + 2*x^22*z0^4 + x^25 + x^23*y*z0 + 2*x^23*z0^2 - x^21*y*z0^3 - x^21*z0^4 - 2*x^24 - 2*x^22*y*z0 + x^22*z0^2 + 2*x^20*y*z0^3 - 2*x^20*z0^4 - x^23 - x^21*z0^2 + x^19*y*z0^3 - 2*x^19*z0^4 - 2*x^22 + 2*x^20*y*z0 + x^20*z0^2 + x^18*y*z0^3 + 2*x^18*z0^4 - x^21 - x^19*z0^2 - x^17*y*z0^3 - x^20 + 2*x^18*y*z0 + 2*x^18*z0^2 + x^16*y*z0^3 + x^16*z0^4 + x^19 + 2*x^17*y*z0 - x^17*z0^2 - 2*x^15*y*z0^3 + 2*x^16*y*z0 - x^16*z0^2 - 2*x^14*y*z0^3 - 2*x^14*z0^4 + x^15*y*z0 - x^13*y*z0^3 - 2*x^13*z0^4 + 2*x^16 + x^14*y*z0 - 2*x^14*z0^2 + x^12*y*z0^3 - 2*x^12*z0^4 - x^15 - x^13*y*z0 + x^13*z0^2 + x^11*y*z0^3 - x^14 + x^12*y*z0 - 2*x^10*y*z0^3 - 2*x^13 - x^11*y*z0 + x^11*z0^2 + 2*x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^12 - x^10*y*z0 + 2*x^10*z0^2 + x^8*y*z0^3 - x^11 - 2*x^9*y*z0 + x^7*y*z0^3 - x^7*z0^4 + x^10 - x^8*y*z0 - x^8*z0^2 - x^6*z0^4 - x^7*z0^2 + x^5*y*z0^3 + 2*x^8 - 2*x^6*y*z0 + 2*x^6*z0^2 + 2*x^4*y*z0^3 - 2*x^4*z0^4 + x^7 + 2*x^5*y*z0 + x^3*y*z0^3 - x^3*z0^4 + 2*x^6 + 2*x^4*z0^2 + x^2*y*z0^3 - x^2*z0^4 - x^5 + x^3*y*z0 - 2*x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 + x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-2*x^61*z0^4 + x^60*z0^4 + 2*x^58*y^2*z0^4 + x^61*z0^2 - 2*x^59*z0^4 - x^57*y^2*z0^4 - x^60*z0^2 - x^58*y^2*z0^2 + 2*x^58*z0^4 + 2*x^56*y^2*z0^4 + x^61 + x^57*y^2*z0^2 - x^57*z0^4 + 2*x^60 - x^58*y^2 - x^58*z0^2 + 2*x^56*z0^4 - 2*x^57*y^2 + x^57*z0^2 - 2*x^55*z0^4 - x^58 + x^54*z0^4 - 2*x^57 + x^55*z0^2 - 2*x^53*z0^4 - x^54*z0^2 + 2*x^52*z0^4 + x^55 - x^51*z0^4 + 2*x^54 - x^52*z0^2 + 2*x^50*z0^4 + x^51*z0^2 - 2*x^49*z0^4 - 2*x^52 + x^48*z0^4 - 2*x^51 + x^49*y^2 + x^49*z0^2 - 2*x^47*z0^4 - x^48*z0^2 + 2*x^46*z0^4 + 2*x^49 - x^45*z0^4 + 2*x^48 - x^46*z0^2 + 2*x^44*z0^4 + x^45*z0^2 - 2*x^43*z0^4 - 2*x^46 + x^42*z0^4 - 2*x^45 + x^43*z0^2 - x^41*z0^4 - x^42*z0^2 - x^40*y*z0^3 + x^40*z0^4 + 2*x^43 + x^41*z0^2 + x^39*y*z0^3 + 2*x^42 - 2*x^40*y*z0 - 2*x^40*z0^2 + 2*x^38*y*z0^3 + 2*x^38*z0^4 + x^41 + x^37*y*z0^3 - 2*x^37*z0^4 - 2*x^40 + 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 + 2*x^36*z0^4 + x^39 - 2*x^37*z0^2 - x^35*z0^4 - 2*x^38 - x^36*y*z0 - x^34*y*z0^3 - x^34*z0^4 + 2*x^37 + x^35*y*z0 - 2*x^35*z0^2 + x^33*y*z0^3 - x^33*z0^4 - x^36 + 2*x^34*y*z0 - x^34*z0^2 - x^32*y*z0^3 + 2*x^32*z0^4 + x^35 - x^33*z0^2 - 2*x^31*y*z0^3 + 2*x^31*z0^4 + 2*x^32*y*z0 + 2*x^32*z0^2 - 2*x^30*y*z0^3 + 2*x^30*z0^4 + x^33 + 2*x^31*y*z0 - 2*x^31*z0^2 - 2*x^29*y*z0^3 - 2*x^29*z0^4 + x^32 - x^30*y*z0 + 2*x^30*z0^2 + x^28*y*z0^3 - x^28*z0^4 - 2*x^29*z0^2 - x^27*y*z0^3 + 2*x^30 + x^28*y*z0 - x^28*z0^2 - x^26*z0^4 - 2*x^29 - 2*x^27*y*z0 - 2*x^27*z0^2 - 2*x^25*y*z0^3 - x^25*z0^4 - x^26*z0^2 - 2*x^24*y*z0^3 - x^24*z0^4 - x^27 + x^25*y*z0 - x^25*z0^2 - 2*x^23*y*z0^3 - 2*x^23*z0^4 - x^26 - x^24*y*z0 - 2*x^24*z0^2 + x^22*y*z0^3 - x^22*z0^4 - 2*x^25 + 2*x^23*y*z0 - x^23*z0^2 + x^21*y*z0^3 + 2*x^21*z0^4 - x^24 - 2*x^22*y*z0 + x^22*z0^2 - 2*x^20*y*z0^3 - 2*x^20*z0^4 - x^23 - x^21*y*z0 + x^21*z0^2 + x^19*y*z0^3 + 2*x^19*z0^4 + x^22 + x^20*y*z0 + x^18*y*z0^3 + 2*x^18*z0^4 - 2*x^19*z0^2 - 2*x^17*y*z0^3 - x^17*z0^4 + 2*x^20 - 2*x^18*z0^2 - 2*x^16*y*z0^3 - 2*x^19 + x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + x^15*z0^4 + 2*x^18 + x^16*y*z0 - x^16*z0^2 + 2*x^14*y*z0^3 + x^14*z0^4 - 2*x^17 - x^15*y*z0 + 2*x^15*z0^2 - 2*x^13*z0^4 - 2*x^16 - x^14*z0^2 + 2*x^12*y*z0^3 - x^12*z0^4 - 2*x^15 + 2*x^13*y*z0 + 2*x^13*z0^2 + 2*x^11*y*z0^3 + x^11*z0^4 - 2*x^14 - x^12*y*z0 + 2*x^12*z0^2 + x^10*z0^4 - x^13 + x^11*y*z0 - 2*x^11*z0^2 + x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^9*y*z0 + 2*x^9*z0^2 + 2*x^7*y*z0^3 + 2*x^7*z0^4 - x^10 - 2*x^8*y*z0 - x^8*z0^2 + 2*x^6*y*z0^3 - 2*x^6*z0^4 - 2*x^9 - 2*x^7*z0^2 + x^5*z0^4 - x^6*z0^2 - 2*x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*y*z0 - x^5*z0^2 - 2*x^3*y*z0^3 + x^6 - x^4*y*z0 + x^4*z0^2 + 2*x^2*y*z0^3 + x^2*z0^4 + x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0 + x^2*z0^2 - x^3)/y) * dx, - ((2*x^61*z0^3 + x^60*z0^3 - 2*x^58*y^2*z0^3 - 2*x^61*z0 + x^59*z0^3 - x^57*y^2*z0^3 - x^60*z0 + 2*x^58*y^2*z0 - 2*x^58*z0^3 - x^56*y^2*z0^3 + x^57*y^2*z0 + x^57*z0^3 + 2*x^58*z0 - x^56*z0^3 - 2*x^54*y^2*z0^3 + x^57*z0 + 2*x^55*z0^3 - x^54*z0^3 - 2*x^55*z0 + x^53*z0^3 - x^54*z0 - 2*x^52*z0^3 + x^51*z0^3 + x^52*z0 - x^50*z0^3 + x^51*z0 + x^49*y^2*z0 + 2*x^49*z0^3 - x^48*z0^3 - x^49*z0 + x^47*z0^3 - x^48*z0 - 2*x^46*z0^3 + x^45*z0^3 + x^46*z0 - x^44*z0^3 + x^45*z0 + 2*x^43*z0^3 - x^42*z0^3 - x^43*z0 - 2*x^41*z0^3 + 2*x^39*y*z0^4 - x^42*z0 + x^40*y*z0^2 + x^40*z0^3 + x^38*y*z0^4 - 2*x^41*z0 - 2*x^39*y*z0^2 + x^39*z0^3 - x^40*y - x^40*z0 - x^38*y*z0^2 - x^38*z0^3 - 2*x^36*y*z0^4 - 2*x^39*z0 - 2*x^37*y*z0^2 + 2*x^37*z0^3 - 2*x^35*y*z0^4 + x^38*y + x^38*z0 - x^36*y*z0^2 + 2*x^36*z0^3 - 2*x^34*y*z0^4 - 2*x^37*y + 2*x^37*z0 - x^35*y*z0^2 - x^33*y*z0^4 + 2*x^36*y + 2*x^36*z0 - x^34*y*z0^2 - x^34*z0^3 + x^32*y*z0^4 + x^35*z0 - x^33*y*z0^2 - x^33*z0^3 + x^31*y*z0^4 - 2*x^34*y + x^32*y*z0^2 - x^32*z0^3 + 2*x^33*y - x^33*z0 - 2*x^31*y*z0^2 - x^31*z0^3 + 2*x^29*y*z0^4 + 2*x^32*y - x^32*z0 + 2*x^30*y*z0^2 + 2*x^30*z0^3 + 2*x^28*y*z0^4 - 2*x^31*y + x^31*z0 - 2*x^29*y*z0^2 + 2*x^29*z0^3 - 2*x^27*y*z0^4 - x^30*z0 - 2*x^28*y*z0^2 + 2*x^28*z0^3 - x^26*y*z0^4 - x^29*y + x^27*y*z0^2 + x^28*y - x^28*z0 + x^26*z0^3 + x^27*z0 + 2*x^25*y*z0^2 + 2*x^25*z0^3 + 2*x^23*y*z0^4 + 2*x^26*y - x^26*z0 - 2*x^24*y*z0^2 - x^24*z0^3 - x^22*y*z0^4 - 2*x^25*z0 - x^23*y*z0^2 - 2*x^23*z0^3 + x^21*y*z0^4 - x^24*y - x^24*z0 + x^22*y*z0^2 - x^22*z0^3 + x^23*y + 2*x^23*z0 + 2*x^21*y*z0^2 + 2*x^21*z0^3 + x^19*y*z0^4 + 2*x^22*y + 2*x^20*y*z0^2 - 2*x^20*z0^3 - 2*x^18*y*z0^4 + 2*x^21*y + x^21*z0 + x^19*y*z0^2 + 2*x^19*z0^3 - x^17*y*z0^4 - 2*x^20*y + 2*x^20*z0 - x^18*z0^3 - x^16*y*z0^4 - x^19*y - 2*x^19*z0 + 2*x^17*y*z0^2 + 2*x^17*z0^3 - x^15*y*z0^4 + x^18*y + 2*x^18*z0 - x^16*y*z0^2 + 2*x^16*z0^3 - x^14*y*z0^4 - 2*x^15*z0^3 + x^13*y*z0^4 + 2*x^16*y + x^12*y*z0^4 - x^15*y + x^15*z0 + 2*x^13*y*z0^2 + 2*x^13*z0^3 - 2*x^11*y*z0^4 - x^14*y + 2*x^14*z0 + x^12*y*z0^2 + x^12*z0^3 + x^10*y*z0^4 + 2*x^13*y + 2*x^13*z0 - 2*x^9*y*z0^4 + 2*x^12*z0 + 2*x^10*y*z0^2 - x^10*z0^3 + x^8*y*z0^4 + x^11*y - x^9*y*z0^2 - 2*x^7*y*z0^4 - x^10*y + 2*x^10*z0 + 2*x^8*z0^3 - x^6*y*z0^4 + 2*x^9*z0 + 2*x^7*y*z0^2 + 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y + 2*x^8*z0 + 2*x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^4*y*z0^4 - x^7*y - x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^3*y*z0^4 - 2*x^6*y - 2*x^4*y*z0^2 + 2*x^4*z0^3 + x^2*y*z0^4 - 2*x^5*y - x^5*z0 - x^3*y*z0^2 - 2*x^3*z0^3 - 2*x^4*y - x^4*z0 + 2*x^2*y*z0^2 + 2*x^2*z0^3 - x^3*y + 2*x^2*z0)/y) * dx, - ((-x^61*z0^4 + x^58*y^2*z0^4 - x^61*z0^2 - 2*x^59*z0^4 - 2*x^60*z0^2 + x^58*y^2*z0^2 + x^58*z0^4 + 2*x^56*y^2*z0^4 - 2*x^61 + 2*x^57*y^2*z0^2 + 2*x^58*y^2 + x^58*z0^2 + 2*x^56*z0^4 + 2*x^57*z0^2 - x^55*z0^4 + 2*x^58 - x^55*z0^2 - 2*x^53*z0^4 - 2*x^54*z0^2 + x^52*z0^4 - 2*x^55 + 2*x^50*z0^4 + 2*x^51*z0^2 + x^49*y^2*z0^2 - x^49*z0^4 + 2*x^52 - 2*x^47*z0^4 - 2*x^48*z0^2 + x^46*z0^4 - 2*x^49 + 2*x^44*z0^4 + 2*x^45*z0^2 - x^43*z0^4 + 2*x^46 + x^41*z0^4 - 2*x^42*z0^2 + 2*x^40*y*z0^3 + x^40*z0^4 - 2*x^43 - x^41*z0^2 - x^39*y*z0^3 - x^39*z0^4 + 2*x^40*y*z0 + x^40*z0^2 + x^38*z0^4 - 2*x^41 + x^39*y*z0 - 2*x^39*z0^2 - x^37*y*z0^3 + x^37*z0^4 + x^40 - 2*x^38*z0^2 + 2*x^36*y*z0^3 - 2*x^39 + x^37*y*z0 + x^37*z0^2 - 2*x^35*y*z0^3 + x^35*z0^4 + 2*x^38 - x^36*y*z0 + 2*x^36*z0^2 - 2*x^34*y*z0^3 + x^34*z0^4 - x^37 + 2*x^35*y*z0 - 2*x^33*y*z0^3 + x^33*z0^4 - x^36 + 2*x^34*y*z0 - 2*x^34*z0^2 + x^32*y*z0^3 - x^32*z0^4 - x^35 - 2*x^33*y*z0 - x^33*z0^2 + 2*x^31*y*z0^3 - x^31*z0^4 + 2*x^34 + 2*x^32*y*z0 - 2*x^32*z0^2 + x^30*z0^4 + x^33 - 2*x^31*y*z0 - 2*x^31*z0^2 - 2*x^29*y*z0^3 + x^29*z0^4 - 2*x^32 + x^30*z0^2 - x^28*y*z0^3 - x^28*z0^4 - 2*x^29*y*z0 + 2*x^29*z0^2 - 2*x^27*y*z0^3 + x^27*z0^4 + 2*x^30 + 2*x^28*y*z0 - x^26*y*z0^3 - x^26*z0^4 - 2*x^29 + 2*x^27*y*z0 - x^27*z0^2 - x^25*y*z0^3 + x^25*z0^4 - x^28 - x^26*z0^2 + x^24*y*z0^3 + 2*x^24*z0^4 + 2*x^27 + 2*x^25*y*z0 - 2*x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 - 2*x^26 - 2*x^24*y*z0 - 2*x^22*z0^4 - 2*x^23*y*z0 + x^21*y*z0^3 - 2*x^21*z0^4 - 2*x^24 + x^22*y*z0 - x^22*z0^2 - 2*x^20*z0^4 + 2*x^23 - 2*x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 + 2*x^19*z0^4 + x^22 + 2*x^18*z0^4 + 2*x^21 - x^19*y*z0 - 2*x^19*z0^2 + x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^20 + 2*x^18*y*z0 + x^18*z0^2 + 2*x^16*y*z0^3 + 2*x^19 - 2*x^15*y*z0^3 + x^15*z0^4 - x^18 - x^16*y*z0 + x^14*z0^4 - x^17 - 2*x^15*y*z0 - x^15*z0^2 - x^13*y*z0^3 + x^13*z0^4 + x^16 + x^14*y*z0 - x^14*z0^2 - x^12*y*z0^3 + x^12*z0^4 + x^15 - x^13*y*z0 + x^13*z0^2 + x^11*y*z0^3 + 2*x^11*z0^4 - x^14 - 2*x^12*y*z0 - 2*x^12*z0^2 + x^10*y*z0^3 - 2*x^10*z0^4 + x^13 - 2*x^11*z0^2 - 2*x^12 - x^10*y*z0 + 2*x^10*z0^2 + x^8*z0^4 + 2*x^11 + x^9*z0^2 + x^7*y*z0^3 - x^7*z0^4 - 2*x^10 - 2*x^8*y*z0 - x^8*z0^2 + 2*x^6*y*z0^3 - x^7*y*z0 - x^5*z0^4 + 2*x^8 + x^6*y*z0 - 2*x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 - 2*x^5*z0^2 - 2*x^3*y*z0^3 - x^3*z0^4 - x^6 + 2*x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 + 2*x^3*z0^2 - 2*x^2*y*z0 + 2*x^2*z0^2 - 2*x^3)/y) * dx, - ((-x^61*z0^3 + 2*x^60*z0^3 + x^58*y^2*z0^3 + x^61*z0 + 2*x^59*z0^3 - 2*x^57*y^2*z0^3 + 2*x^60*z0 - x^58*y^2*z0 - 2*x^58*z0^3 - 2*x^56*y^2*z0^3 - 2*x^59*z0 - 2*x^57*y^2*z0 + 2*x^57*z0^3 - 2*x^55*y^2*z0^3 - x^58*z0 + 2*x^56*y^2*z0 - 2*x^56*z0^3 + x^54*y^2*z0^3 - 2*x^57*z0 + 2*x^55*z0^3 + 2*x^56*z0 - 2*x^54*z0^3 + x^55*z0 + 2*x^53*z0^3 + 2*x^54*z0 + 2*x^52*z0^3 - 2*x^53*z0 + 2*x^51*z0^3 + x^49*y^2*z0^3 - x^52*z0 - 2*x^50*z0^3 - 2*x^51*z0 - 2*x^49*z0^3 + 2*x^50*z0 - 2*x^48*z0^3 + x^49*z0 + 2*x^47*z0^3 + 2*x^48*z0 + 2*x^46*z0^3 - 2*x^47*z0 + 2*x^45*z0^3 - x^46*z0 - 2*x^44*z0^3 - 2*x^45*z0 - 2*x^43*z0^3 + 2*x^44*z0 - 2*x^42*z0^3 + x^43*z0 + x^41*z0^3 - x^39*y*z0^4 + 2*x^42*z0 + 2*x^40*y*z0^2 - x^38*y*z0^4 - x^41*z0 + x^39*y*z0^2 + 2*x^37*y*z0^4 - 2*x^40*y - 2*x^40*z0 + x^38*y*z0^2 - 2*x^38*z0^3 + x^36*y*z0^4 - 2*x^39*z0 + 2*x^37*z0^3 + 2*x^35*y*z0^4 + 2*x^38*z0 - x^36*y*z0^2 + x^36*z0^3 + x^34*y*z0^4 + x^37*y + x^37*z0 + x^35*z0^3 - x^33*y*z0^4 - x^36*y + x^36*z0 - x^34*y*z0^2 - 2*x^32*y*z0^4 + x^35*z0 - x^33*y*z0^2 + x^33*z0^3 - 2*x^31*y*z0^4 + x^34*y - 2*x^34*z0 + x^32*y*z0^2 + 2*x^32*z0^3 - x^33*y + x^33*z0 - x^31*y*z0^2 + x^31*z0^3 - x^29*y*z0^4 - x^32*z0 - x^30*y*z0^2 + 2*x^30*z0^3 + x^28*y*z0^4 - 2*x^31*y - 2*x^31*z0 + 2*x^29*y*z0^2 - x^29*z0^3 - x^27*y*z0^4 - 2*x^28*z0^3 - 2*x^26*y*z0^4 - x^27*y*z0^2 - x^27*z0^3 + x^25*y*z0^4 + 2*x^28*y + 2*x^28*z0 + x^26*y*z0^2 + x^26*z0^3 - 2*x^27*y - x^27*z0 + 2*x^25*y*z0^2 - x^25*z0^3 + x^26*z0 - x^24*z0^3 + x^25*y - x^25*z0 - 2*x^23*y*z0^2 - 2*x^21*y*z0^4 - 2*x^24*y + 2*x^24*z0 - x^22*y*z0^2 - 2*x^22*z0^3 + 2*x^20*y*z0^4 - 2*x^23*z0 - x^21*y*z0^2 + 2*x^19*y*z0^4 - x^22*y - x^22*z0 - 2*x^20*y*z0^2 - x^20*z0^3 + 2*x^18*y*z0^4 + x^21*y - x^21*z0 + 2*x^19*y*z0^2 - x^19*z0^3 + 2*x^17*y*z0^4 - 2*x^20*y + 2*x^20*z0 + 2*x^18*y*z0^2 + 2*x^16*y*z0^4 + 2*x^19*y - 2*x^19*z0 + 2*x^17*y*z0^2 - x^17*z0^3 - x^15*y*z0^4 + 2*x^18*z0 + 2*x^16*y*z0^2 + 2*x^16*z0^3 + x^17*y + x^17*z0 - 2*x^15*y*z0^2 + 2*x^15*z0^3 + 2*x^13*y*z0^4 - x^16*y - 2*x^16*z0 - 2*x^14*y*z0^2 - 2*x^12*y*z0^4 + 2*x^15*y - x^15*z0 + 2*x^13*y*z0^2 - 2*x^13*z0^3 - 2*x^11*y*z0^4 + x^14*y + x^14*z0 - 2*x^12*y*z0^2 + x^12*z0^3 + 2*x^10*y*z0^4 + 2*x^13*y - 2*x^13*z0 - 2*x^11*y*z0^2 - 2*x^11*z0^3 + x^12*y + 2*x^12*z0 + 2*x^10*y*z0^2 + 2*x^10*z0^3 - x^8*y*z0^4 + x^11*y - 2*x^11*z0 + x^9*y*z0^2 + 2*x^9*z0^3 - x^7*y*z0^4 - x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 - 2*x^9*y - 2*x^9*z0 + x^7*y*z0^2 + x^7*z0^3 - 2*x^5*y*z0^4 + 2*x^8*z0 + x^6*y*z0^2 - x^6*z0^3 + 2*x^4*y*z0^4 - 2*x^7*y + x^7*z0 + 2*x^5*y*z0^2 + x^3*y*z0^4 + x^6*y + 2*x^6*z0 - 2*x^4*y*z0^2 - x^2*y*z0^4 + x^5*y - x^3*z0^3 - 2*x^4*z0 - 2*x^2*y*z0^2 - 2*x^3*y + x^2*y + x^2*z0)/y) * dx, - ((-2*x^61*z0^4 + 2*x^58*y^2*z0^4 + x^61*z0^2 + 2*x^59*z0^4 - 2*x^60*z0^2 - x^58*y^2*z0^2 + 2*x^58*z0^4 - 2*x^56*y^2*z0^4 + 2*x^57*y^2*z0^2 - x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*z0^2 - 2*x^55*z0^4 + x^55*z0^2 + 2*x^53*z0^4 - 2*x^54*z0^2 + x^52*z0^4 + x^49*y^2*z0^4 - x^52*z0^2 - 2*x^50*z0^4 + 2*x^51*z0^2 - x^49*z0^4 + x^49*z0^2 + 2*x^47*z0^4 - 2*x^48*z0^2 + x^46*z0^4 - x^46*z0^2 - 2*x^44*z0^4 + 2*x^45*z0^2 - x^43*z0^4 + x^43*z0^2 - 2*x^42*z0^2 - x^40*y*z0^3 + x^41*z0^2 + x^39*y*z0^3 + x^39*z0^4 - 2*x^40*y*z0 - 2*x^40*z0^2 + x^38*z0^4 - 2*x^41 + x^39*y*z0 + x^39*z0^2 + x^37*z0^4 - 2*x^40 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - 2*x^39 - x^37*y*z0 + 2*x^35*y*z0^3 - 2*x^35*z0^4 + 2*x^36*y*z0 - x^36*z0^2 - 2*x^34*y*z0^3 + 2*x^34*z0^4 - 2*x^37 + x^35*y*z0 + 2*x^35*z0^2 + 2*x^33*y*z0^3 - 2*x^34*y*z0 - x^32*y*z0^3 + x^32*z0^4 - 2*x^35 + 2*x^33*y*z0 - x^33*z0^2 - x^31*y*z0^3 + x^31*z0^4 + x^34 - x^32*y*z0 + 2*x^30*y*z0^3 - 2*x^30*z0^4 - 2*x^33 - 2*x^31*y*z0 + x^31*z0^2 + 2*x^29*y*z0^3 - 2*x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 + x^28*y*z0^3 - 2*x^28*z0^4 + 2*x^31 + 2*x^29*y*z0 - x^29*z0^2 + x^27*y*z0^3 - 2*x^27*z0^4 + x^30 - x^28*z0^2 + x^26*y*z0^3 + 2*x^29 - 2*x^27*y*z0 + x^27*z0^2 + 2*x^25*y*z0^3 + x^25*z0^4 + x^28 - 2*x^26*y*z0 + x^24*y*z0^3 + 2*x^24*z0^4 - x^27 + 2*x^25*y*z0 + x^25*z0^2 + x^23*y*z0^3 + x^23*z0^4 + 2*x^26 + 2*x^24*y*z0 + x^22*z0^4 - x^25 + x^23*y*z0 + 2*x^23*z0^2 + 2*x^21*z0^4 + 2*x^22*z0^2 - 2*x^20*y*z0^3 - 2*x^20*z0^4 - x^23 - 2*x^21*y*z0 - 2*x^19*y*z0^3 - 2*x^20*y*z0 - 2*x^18*y*z0^3 + x^18*z0^4 + 2*x^21 + x^19*y*z0 - 2*x^19*z0^2 - 2*x^17*y*z0^3 + x^20 + x^18*y*z0 - 2*x^18*z0^2 - 2*x^16*y*z0^3 + x^16*z0^4 + x^19 - 2*x^17*y*z0 + 2*x^15*y*z0^3 + 2*x^15*z0^4 + 2*x^18 - x^16*z0^2 + 2*x^14*y*z0^3 + x^17 - 2*x^15*y*z0 + x^13*y*z0^3 + 2*x^13*z0^4 - 2*x^16 - 2*x^14*y*z0 - 2*x^14*z0^2 + 2*x^12*y*z0^3 + 2*x^12*z0^4 - x^13*y*z0 - x^11*y*z0^3 - 2*x^11*z0^4 - x^14 - 2*x^12*y*z0 + x^10*y*z0^3 - 2*x^10*z0^4 - 2*x^13 + x^11*y*z0 + x^11*z0^2 - x^12 + 2*x^10*y*z0 - 2*x^10*z0^2 + 2*x^8*y*z0^3 - x^8*z0^4 - x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 - x^8*y*z0 + x^8*z0^2 - 2*x^6*y*z0^3 + x^6*z0^4 - x^9 - 2*x^7*y*z0 - x^5*y*z0^3 + x^5*z0^4 + x^8 + 2*x^6*y*z0 - x^6*z0^2 + x^4*y*z0^3 - x^4*z0^4 - x^7 - 2*x^5*y*z0 - 2*x^5*z0^2 + x^3*z0^4 - 2*x^6 + 2*x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 - 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 + 2*x^2*z0^2 - x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-2*x^61*z0^4 - 2*x^60*z0^4 + 2*x^58*y^2*z0^4 + x^61*z0^2 - x^59*z0^4 + 2*x^57*y^2*z0^4 - 2*x^60*z0^2 - x^58*y^2*z0^2 + 2*x^58*z0^4 + x^56*y^2*z0^4 + 2*x^57*y^2*z0^2 + 2*x^57*z0^4 + x^60 - x^58*z0^2 + x^56*z0^4 - x^57*y^2 + 2*x^57*z0^2 - 2*x^55*z0^4 - 2*x^54*z0^4 - x^57 + x^55*z0^2 - x^53*z0^4 - 2*x^54*z0^2 + 2*x^52*z0^4 + 2*x^51*z0^4 + x^54 - x^52*z0^2 + x^50*z0^4 - x^53 + 2*x^51*z0^2 - 2*x^49*z0^4 + x^50*y^2 - 2*x^48*z0^4 - x^51 + x^49*z0^2 - x^47*z0^4 + x^50 - 2*x^48*z0^2 + 2*x^46*z0^4 + 2*x^45*z0^4 + x^48 - x^46*z0^2 + x^44*z0^4 - x^47 + 2*x^45*z0^2 - 2*x^43*z0^4 - 2*x^42*z0^4 - x^45 + x^43*z0^2 + 2*x^41*z0^4 + x^44 - 2*x^42*z0^2 - x^40*y*z0^3 + 2*x^40*z0^4 + x^41*z0^2 + x^39*y*z0^3 - x^39*z0^4 + x^42 - 2*x^40*y*z0 - x^40*z0^2 - 2*x^38*y*z0^3 + x^38*z0^4 + 2*x^41 + x^39*z0^2 - 2*x^37*y*z0^3 - 2*x^37*z0^4 + x^40 + 2*x^38*z0^2 - 2*x^36*y*z0^3 + 2*x^36*z0^4 + x^37*y*z0 + 2*x^37*z0^2 - 2*x^35*z0^4 + 2*x^36*y*z0 - x^36*z0^2 - 2*x^34*y*z0^3 - 2*x^34*z0^4 + 2*x^37 + x^35*y*z0 - x^35*z0^2 - 2*x^33*y*z0^3 + x^33*z0^4 + x^34*y*z0 + x^34*z0^2 + x^32*y*z0^3 - x^35 - 2*x^33*y*z0 + x^33*z0^2 + 2*x^31*z0^4 - 2*x^34 - x^30*y*z0^3 + x^30*z0^4 + 2*x^33 + 2*x^31*y*z0 - x^31*z0^2 + 2*x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 + x^28*y*z0^3 - x^28*z0^4 - 2*x^31 - 2*x^29*y*z0 + x^27*y*z0^3 + x^30 + x^28*z0^2 - 2*x^26*y*z0^3 - 2*x^26*z0^4 - 2*x^29 + x^25*z0^4 + 2*x^26*y*z0 + x^24*y*z0^3 + x^24*z0^4 - 2*x^27 + x^25*y*z0 - x^25*z0^2 - x^23*y*z0^3 + 2*x^23*z0^4 - x^24*y*z0 + x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^22*z0^4 + x^25 - x^23*z0^2 + 2*x^21*y*z0^3 + x^21*z0^4 - x^24 - 2*x^22*y*z0 + 2*x^22*z0^2 - x^20*y*z0^3 - 2*x^20*z0^4 + 2*x^23 + x^21*y*z0 - x^21*z0^2 + 2*x^19*y*z0^3 - 2*x^19*z0^4 - 2*x^22 - 2*x^20*y*z0 + 2*x^20*z0^2 - x^18*y*z0^3 + 2*x^19*y*z0 + 2*x^19*z0^2 + 2*x^17*y*z0^3 - x^17*z0^4 - 2*x^18*y*z0 + x^18*z0^2 + x^16*y*z0^3 - 2*x^16*z0^4 + x^19 - x^17*y*z0 + x^17*z0^2 - 2*x^15*y*z0^3 + x^15*z0^4 - x^18 - 2*x^16*y*z0 - 2*x^16*z0^2 + 2*x^14*y*z0^3 - 2*x^14*z0^4 - x^17 + 2*x^15*y*z0 + 2*x^15*z0^2 + 2*x^13*y*z0^3 - x^13*z0^4 + x^14*y*z0 + 2*x^14*z0^2 + x^12*y*z0^3 + 2*x^12*z0^4 + x^13*y*z0 - x^13*z0^2 + 2*x^11*y*z0^3 + 2*x^12*y*z0 - x^10*y*z0^3 + x^10*z0^4 + 2*x^13 + x^11*z0^2 - x^9*y*z0^3 + x^9*z0^4 - x^10*y*z0 - 2*x^10*z0^2 + 2*x^8*y*z0^3 - x^8*z0^4 - 2*x^11 + 2*x^9*y*z0 + x^9*z0^2 - 2*x^7*y*z0^3 - x^7*z0^4 - x^10 + x^8*y*z0 + x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 - 2*x^9 + x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + 2*x^5*z0^4 + x^8 + 2*x^6*y*z0 + 2*x^6*z0^2 + x^4*y*z0^3 - x^7 - 2*x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^6 + x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 - 2*x^3*y*z0 - x^3*z0^2 + 2*x^2*y*z0 - x^2*z0^2 + x^3 - x^2)/y) * dx, - ((x^61*z0^3 + x^60*z0^3 - x^58*y^2*z0^3 - 2*x^59*z0^3 - x^57*y^2*z0^3 + 2*x^60*z0 - 2*x^58*z0^3 + 2*x^56*y^2*z0^3 + 2*x^59*z0 - 2*x^57*y^2*z0 + x^55*y^2*z0^3 - 2*x^56*y^2*z0 + 2*x^56*z0^3 - x^54*y^2*z0^3 - 2*x^57*z0 + 2*x^55*z0^3 - 2*x^56*z0 - 2*x^53*z0^3 + 2*x^54*z0 - 2*x^52*z0^3 + x^53*z0 + x^50*y^2*z0 + 2*x^50*z0^3 - 2*x^51*z0 + 2*x^49*z0^3 - x^50*z0 - 2*x^47*z0^3 + 2*x^48*z0 - 2*x^46*z0^3 + x^47*z0 + 2*x^44*z0^3 - 2*x^45*z0 + 2*x^43*z0^3 - x^44*z0 - x^41*z0^3 + x^39*y*z0^4 + 2*x^42*z0 - 2*x^40*y*z0^2 - x^40*z0^3 - 2*x^38*y*z0^4 + x^41*z0 + 2*x^39*z0^3 - x^37*y*z0^4 + 2*x^38*y*z0^2 + 2*x^38*z0^3 - x^36*y*z0^4 - x^39*y + 2*x^39*z0 + x^37*y*z0^2 - 2*x^35*y*z0^4 + 2*x^38*y + x^38*z0 - x^36*y*z0^2 + 2*x^36*z0^3 + 2*x^34*y*z0^4 + 2*x^35*z0^3 + 2*x^36*y - x^36*z0 - x^34*z0^3 + x^32*y*z0^4 - x^35*y + 2*x^35*z0 + 2*x^33*y*z0^2 - 2*x^31*y*z0^4 - x^34*z0 + x^32*z0^3 + 2*x^30*y*z0^4 + 2*x^33*y + x^33*z0 - x^29*y*z0^4 + x^32*y + 2*x^32*z0 - x^30*y*z0^2 - 2*x^30*z0^3 + 2*x^28*y*z0^4 + x^31*z0 + x^29*y*z0^2 + 2*x^29*z0^3 + x^27*y*z0^4 - 2*x^30*y - x^28*y*z0^2 - x^28*z0^3 + 2*x^26*y*z0^4 + 2*x^29*y - x^29*z0 - x^27*y*z0^2 - 2*x^27*z0^3 + 2*x^25*y*z0^4 - 2*x^28*y + x^28*z0 + 2*x^26*y*z0^2 - 2*x^26*z0^3 + x^24*y*z0^4 - 2*x^27*y + x^27*z0 + 2*x^25*z0^3 - x^26*y - 2*x^24*z0^3 - 2*x^22*y*z0^4 - x^25*y + x^25*z0 + x^23*y*z0^2 - 2*x^23*z0^3 + 2*x^24*y - x^22*z0^3 - 2*x^20*y*z0^4 - x^23*y - 2*x^23*z0 - x^21*y*z0^2 - x^21*z0^3 + 2*x^19*y*z0^4 - x^22*y - 2*x^20*y*z0^2 - 2*x^20*z0^3 + x^21*z0 + 2*x^19*z0^3 + x^17*y*z0^4 + 2*x^20*y - x^20*z0 + 2*x^18*y*z0^2 + x^18*z0^3 + 2*x^16*y*z0^4 + 2*x^19*y + 2*x^19*z0 - 2*x^17*y*z0^2 - 2*x^17*z0^3 + x^15*y*z0^4 - 2*x^18*y + 2*x^16*y*z0^2 + 2*x^16*z0^3 + 2*x^14*y*z0^4 - 2*x^17*y + 2*x^17*z0 + x^15*y*z0^2 + x^16*z0 - x^14*y*z0^2 + 2*x^14*z0^3 + x^15*z0 - 2*x^13*y*z0^2 + 2*x^13*z0^3 + 2*x^11*y*z0^4 + x^14*z0 - 2*x^12*y*z0^2 - x^12*z0^3 + 2*x^10*y*z0^4 - x^13*y - x^13*z0 + x^11*z0^3 + 2*x^9*y*z0^4 - 2*x^12*z0 - 2*x^10*y*z0^2 + 2*x^10*z0^3 + x^8*y*z0^4 + x^11*y + x^11*z0 - x^9*z0^3 + 2*x^7*y*z0^4 - 2*x^10*y - 2*x^10*z0 + x^8*y*z0^2 - x^8*z0^3 - x^6*y*z0^4 - 2*x^9*y + 2*x^9*z0 + x^7*y*z0^2 + 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y + x^8*z0 - x^6*y*z0^2 + 2*x^6*z0^3 - x^4*y*z0^4 + x^7*y + 2*x^5*y*z0^2 - x^3*y*z0^4 - x^6*y - 2*x^6*z0 - x^4*y*z0^2 + x^2*y*z0^4 + 2*x^5*y + x^5*z0 - x^3*y*z0^2 + x^3*z0^3 + 2*x^2*y*z0^2 - x^2*z0^3 - x^3*z0 + 2*x^2*y + 2*x^2*z0)/y) * dx, - ((2*x^60*z0^4 - x^61*z0^2 + x^59*z0^4 - 2*x^57*y^2*z0^4 + 2*x^60*z0^2 + x^58*y^2*z0^2 - x^56*y^2*z0^4 - x^61 - 2*x^57*y^2*z0^2 - 2*x^57*z0^4 + x^60 + x^58*y^2 + x^58*z0^2 - x^56*z0^4 - x^57*y^2 - 2*x^57*z0^2 + x^58 + 2*x^54*z0^4 - x^57 - x^55*z0^2 + x^53*z0^4 + 2*x^54*z0^2 - x^55 - x^53*z0^2 - 2*x^51*z0^4 + x^54 + x^52*z0^2 + x^50*y^2*z0^2 - x^50*z0^4 - 2*x^51*z0^2 + x^52 + x^50*z0^2 + 2*x^48*z0^4 - x^51 - x^49*z0^2 + x^47*z0^4 + 2*x^48*z0^2 - x^49 - x^47*z0^2 - 2*x^45*z0^4 + x^48 + x^46*z0^2 - x^44*z0^4 - 2*x^45*z0^2 + x^46 + x^44*z0^2 + 2*x^42*z0^4 - x^45 - x^43*z0^2 - 2*x^41*z0^4 + 2*x^42*z0^2 - x^40*z0^4 - x^43 - 2*x^41*z0^2 - x^39*y*z0^3 - 2*x^39*z0^4 + x^42 + 2*x^40*y*z0 + x^40*z0^2 - 2*x^38*y*z0^3 - x^38*z0^4 + 2*x^41 - x^39*z0^2 - 2*x^37*z0^4 + x^40 - x^38*y*z0 - x^38*z0^2 + 2*x^36*y*z0^3 - x^36*z0^4 - 2*x^39 - x^37*y*z0 - x^37*z0^2 + 2*x^35*y*z0^3 + x^38 - 2*x^36*y*z0 + x^36*z0^2 + 2*x^34*y*z0^3 - 2*x^35*y*z0 - x^35*z0^2 - 2*x^33*y*z0^3 + x^33*z0^4 - x^36 + x^34*y*z0 - x^34*z0^2 + x^32*z0^4 + 2*x^35 - x^33*y*z0 + x^33*z0^2 + x^31*y*z0^3 - x^31*z0^4 + 2*x^34 + x^32*y*z0 - x^32*z0^2 + x^30*y*z0^3 + x^30*z0^4 + 2*x^33 + 2*x^31*y*z0 + x^31*z0^2 + 2*x^29*y*z0^3 - x^32 - x^30*y*z0 - 2*x^30*z0^2 + 2*x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^31 - x^29*y*z0 + x^29*z0^2 + x^27*y*z0^3 + x^27*z0^4 - x^30 + 2*x^28*z0^2 - x^26*y*z0^3 + x^26*z0^4 + x^29 + x^27*y*z0 + x^27*z0^2 - 2*x^25*y*z0^3 + 2*x^25*z0^4 - x^28 - x^26*y*z0 + x^24*y*z0^3 + 2*x^24*z0^4 + x^27 + 2*x^25*y*z0 - x^25*z0^2 - x^23*y*z0^3 + 2*x^26 + 2*x^24*y*z0 - 2*x^22*z0^4 - 2*x^25 + x^23*y*z0 - 2*x^21*y*z0^3 - x^21*z0^4 + x^24 - 2*x^20*y*z0^3 - x^20*z0^4 - 2*x^23 + x^21*y*z0 - 2*x^21*z0^2 + x^19*y*z0^3 + 2*x^19*z0^4 + x^22 - 2*x^20*y*z0 + 2*x^20*z0^2 + 2*x^18*z0^4 + 2*x^19*y*z0 + 2*x^19*z0^2 - 2*x^17*y*z0^3 - x^17*z0^4 + 2*x^20 - 2*x^18*y*z0 + 2*x^18*z0^2 - 2*x^16*y*z0^3 - x^16*z0^4 - x^19 + 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + x^15*z0^4 + x^18 + x^16*y*z0 - x^16*z0^2 + x^14*y*z0^3 - 2*x^14*z0^4 - 2*x^17 - x^15*y*z0 - x^15*z0^2 - x^13*y*z0^3 - 2*x^13*z0^4 - 2*x^16 - 2*x^12*y*z0^3 - x^12*z0^4 - 2*x^15 + x^13*y*z0 + x^11*y*z0^3 - 2*x^11*z0^4 - 2*x^14 + x^12*z0^2 + x^10*y*z0^3 + x^10*z0^4 - x^13 + x^11*z0^2 + x^9*y*z0^3 - 2*x^10*y*z0 + x^10*z0^2 + x^8*y*z0^3 - 2*x^11 - 2*x^9*y*z0 + x^9*z0^2 + 2*x^7*y*z0^3 + 2*x^7*z0^4 - x^10 - x^8*y*z0 + x^8*z0^2 - x^6*y*z0^3 - 2*x^6*z0^4 - x^9 - 2*x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 + 2*x^6*z0^2 - x^4*y*z0^3 + 2*x^7 + 2*x^5*y*z0 - x^3*y*z0^3 - x^6 - x^4*y*z0 + 2*x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 + x^5 - 2*x^3*y*z0 + x^3*z0^2 - 2*x^2*y*z0 + x^2)/y) * dx, - ((x^60*z0^3 + x^61*z0 + 2*x^59*z0^3 - x^57*y^2*z0^3 + x^60*z0 - x^58*y^2*z0 + x^58*z0^3 - 2*x^56*y^2*z0^3 + x^59*z0 - x^57*y^2*z0 + x^57*z0^3 - x^55*y^2*z0^3 - x^58*z0 - x^56*y^2*z0 - 2*x^56*z0^3 - 2*x^54*y^2*z0^3 - x^57*z0 - x^55*z0^3 - x^56*z0 - x^54*z0^3 + x^55*z0 + x^53*z0^3 + x^54*z0 + x^52*z0^3 + x^50*y^2*z0^3 + x^53*z0 + x^51*z0^3 - x^52*z0 - x^50*z0^3 - x^51*z0 - x^49*z0^3 - x^50*z0 - x^48*z0^3 + x^49*z0 + x^47*z0^3 + x^48*z0 + x^46*z0^3 + x^47*z0 + x^45*z0^3 - x^46*z0 - x^44*z0^3 - x^45*z0 - x^43*z0^3 - x^44*z0 - x^42*z0^3 + x^43*z0 + x^41*z0^3 + x^42*z0 + 2*x^40*z0^3 - x^38*y*z0^4 + 2*x^41*z0 + x^39*y*z0^2 + x^39*z0^3 - 2*x^40*y + 2*x^38*y*z0^2 + x^38*z0^3 - x^36*y*z0^4 - 2*x^39*y - 2*x^37*z0^3 + x^35*y*z0^4 - 2*x^38*y + 2*x^38*z0 + 2*x^34*y*z0^4 + x^37*y - x^37*z0 + 2*x^35*y*z0^2 + 2*x^35*z0^3 - x^33*y*z0^4 + x^36*y - 2*x^36*z0 + x^34*z0^3 + x^32*y*z0^4 + 2*x^33*y*z0^2 - 2*x^31*y*z0^4 - 2*x^34*y + 2*x^34*z0 + x^32*y*z0^2 - 2*x^32*z0^3 + 2*x^30*y*z0^4 + x^33*y - x^33*z0 + x^31*z0^3 + 2*x^29*y*z0^4 - 2*x^32*y + 2*x^32*z0 - 2*x^30*y*z0^2 - 2*x^28*y*z0^4 - 2*x^31*y - 2*x^29*y*z0^2 - x^29*z0^3 - 2*x^27*y*z0^4 - 2*x^30*y + 2*x^28*z0^3 + x^26*y*z0^4 - 2*x^29*y + x^29*z0 - 2*x^27*y*z0^2 + x^27*z0^3 - 2*x^25*y*z0^4 + x^28*z0 + x^26*y*z0^2 - x^24*y*z0^4 + 2*x^27*y - 2*x^27*z0 - x^25*y*z0^2 + x^26*y - x^24*y*z0^2 - 2*x^24*z0^3 + x^25*y + 2*x^25*z0 - x^23*y*z0^2 - 2*x^24*y + 2*x^24*z0 - 2*x^22*y*z0^2 + x^22*z0^3 - x^20*y*z0^4 + 2*x^23*y + 2*x^21*y*z0^2 + 2*x^21*z0^3 - 2*x^19*y*z0^4 - x^22*y - 2*x^22*z0 - 2*x^20*y*z0^2 - 2*x^20*z0^3 - 2*x^18*y*z0^4 - 2*x^21*y + x^17*y*z0^4 - x^20*y - 2*x^20*z0 - x^18*y*z0^2 + 2*x^18*z0^3 + 2*x^19*y - x^19*z0 + x^17*y*z0^2 + 2*x^17*z0^3 + x^15*y*z0^4 - x^18*y + x^18*z0 + 2*x^16*z0^3 - 2*x^14*y*z0^4 + 2*x^15*y*z0^2 + x^13*y*z0^4 - x^16*y - 2*x^16*z0 - x^14*y*z0^2 + 2*x^14*z0^3 - x^12*y*z0^4 - x^15*y + 2*x^13*y*z0^2 + 2*x^13*z0^3 - x^14*y - x^14*z0 - 2*x^12*y*z0^2 + 2*x^13*y - 2*x^13*z0 - 2*x^11*y*z0^2 + 2*x^11*z0^3 + 2*x^9*y*z0^4 - 2*x^12*y - 2*x^12*z0 - x^10*y*z0^2 + 2*x^10*z0^3 - 2*x^8*y*z0^4 + x^11*y + x^11*z0 - 2*x^9*z0^3 + 2*x^7*y*z0^4 + x^10*y + 2*x^10*z0 + 2*x^8*y*z0^2 + x^8*z0^3 - x^9*y + 2*x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 + x^5*y*z0^4 - 2*x^8*y - 2*x^8*z0 + x^6*y*z0^2 - x^6*z0^3 - x^4*y*z0^4 - 2*x^7*y + 2*x^7*z0 - x^5*z0^3 - 2*x^3*y*z0^4 - 2*x^6*y - 2*x^6*z0 - 2*x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^2*y*z0^4 - x^5*z0 - x^3*y*z0^2 + 2*x^3*z0^3 + x^4*y + x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + x^3*y + 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((-x^61*z0^4 - 2*x^60*z0^4 + x^58*y^2*z0^4 - x^59*z0^4 + 2*x^57*y^2*z0^4 + x^60*z0^2 + x^58*z0^4 + x^56*y^2*z0^4 + x^61 - x^57*y^2*z0^2 + 2*x^57*z0^4 - x^58*y^2 + x^56*z0^4 - x^57*z0^2 - x^55*z0^4 - x^58 - 2*x^54*z0^4 - 2*x^53*z0^4 + x^54*z0^2 + x^52*z0^4 + x^50*y^2*z0^4 + x^55 + 2*x^51*z0^4 + 2*x^50*z0^4 - x^51*z0^2 - x^49*z0^4 - x^52 - 2*x^48*z0^4 - 2*x^47*z0^4 + x^48*z0^2 + x^46*z0^4 + x^49 + 2*x^45*z0^4 + 2*x^44*z0^4 - x^45*z0^2 - x^43*z0^4 - x^46 - 2*x^42*z0^4 + x^42*z0^2 + 2*x^40*y*z0^3 + 2*x^40*z0^4 + x^43 + x^40*z0^2 - 2*x^38*y*z0^3 + 2*x^41 - 2*x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 + x^40 + 2*x^36*z0^4 + x^39 - x^37*y*z0 - x^37*z0^2 + 2*x^35*y*z0^3 - x^35*z0^4 + 2*x^38 + x^36*y*z0 + x^36*z0^2 + x^34*y*z0^3 + 2*x^34*z0^4 - x^37 - 2*x^35*y*z0 + 2*x^35*z0^2 - 2*x^33*z0^4 - 2*x^36 + 2*x^34*z0^2 + x^35 - 2*x^33*y*z0 + x^33*z0^2 - 2*x^31*z0^4 - 2*x^32*y*z0 + 2*x^32*z0^2 - x^30*y*z0^3 - 2*x^30*z0^4 + x^33 - x^31*y*z0 + x^29*y*z0^3 + 2*x^29*z0^4 - x^32 + 2*x^30*y*z0 + 2*x^30*z0^2 + x^28*y*z0^3 - x^29*y*z0 - x^27*y*z0^3 - 2*x^27*z0^4 + 2*x^28*y*z0 - 2*x^28*z0^2 + 2*x^26*y*z0^3 - 2*x^26*z0^4 - 2*x^29 - x^27*y*z0 - x^27*z0^2 - 2*x^25*y*z0^3 - x^28 + 2*x^26*y*z0 + x^26*z0^2 + 2*x^24*y*z0^3 - 2*x^27 + 2*x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + 2*x^24*y*z0 - x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^22*z0^4 - 2*x^25 + x^23*z0^2 + x^21*y*z0^3 + x^21*z0^4 + 2*x^22*y*z0 - 2*x^20*y*z0^3 + x^20*z0^4 - x^23 + x^21*y*z0 - x^21*z0^2 + x^19*y*z0^3 - 2*x^19*z0^4 + 2*x^22 - x^20*y*z0 + 2*x^20*z0^2 - x^18*y*z0^3 - 2*x^18*z0^4 + 2*x^19*y*z0 - 2*x^19*z0^2 + x^17*y*z0^3 + 2*x^17*z0^4 - 2*x^20 - 2*x^18*y*z0 + 2*x^16*y*z0^3 + 2*x^16*z0^4 + x^19 + x^15*y*z0^3 - 2*x^18 - 2*x^14*y*z0^3 - 2*x^14*z0^4 - 2*x^17 - 2*x^15*y*z0 + 2*x^15*z0^2 - 2*x^13*z0^4 - x^14*y*z0 - x^13*y*z0 - 2*x^13*z0^2 - 2*x^11*z0^4 + x^12*y*z0 - 2*x^12*z0^2 + x^13 + x^11*y*z0 + x^9*y*z0^3 - x^12 - x^10*y*z0 + 2*x^10*z0^2 - x^8*y*z0^3 - x^8*z0^4 + x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 - x^10 - 2*x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 - x^9 - 2*x^7*y*z0 + 2*x^7*z0^2 + x^5*y*z0^3 + x^5*z0^4 - 2*x^8 - 2*x^6*y*z0 - x^6*z0^2 - x^4*z0^4 + 2*x^7 + x^5*y*z0 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + x^6 + x^4*z0^2 + x^2*y*z0^3 - x^2*z0^4 - x^5 - x^3*y*z0 + x^3*z0^2 - x^2*z0^2 - 2*x^3 + 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 - 2*x^60*z0^4 + x^58*y^2*z0^4 + 2*x^61*z0^2 - x^59*z0^4 + 2*x^57*y^2*z0^4 + 2*x^60*z0^2 - 2*x^58*y^2*z0^2 + x^58*z0^4 + x^56*y^2*z0^4 + 2*x^61 - 2*x^57*y^2*z0^2 + 2*x^57*z0^4 - x^60 - 2*x^58*y^2 - 2*x^58*z0^2 + x^56*z0^4 + x^57*y^2 - 2*x^57*z0^2 - x^55*z0^4 - 2*x^58 - 2*x^54*z0^4 + x^57 + 2*x^55*z0^2 - x^53*z0^4 + 2*x^54*z0^2 + x^52*z0^4 + 2*x^55 + 2*x^51*z0^4 - 2*x^54 - 2*x^52*z0^2 + x^50*z0^4 + x^51*y^2 - 2*x^51*z0^2 - x^49*z0^4 - 2*x^52 - 2*x^48*z0^4 + 2*x^51 + 2*x^49*z0^2 - x^47*z0^4 + 2*x^48*z0^2 + x^46*z0^4 + 2*x^49 + 2*x^45*z0^4 - 2*x^48 - 2*x^46*z0^2 + x^44*z0^4 - 2*x^45*z0^2 - x^43*z0^4 - 2*x^46 - 2*x^42*z0^4 + 2*x^45 + 2*x^43*z0^2 - x^41*z0^4 + 2*x^42*z0^2 + 2*x^40*y*z0^3 + 2*x^40*z0^4 + 2*x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^39*z0^4 - 2*x^42 + x^40*y*z0 + x^38*y*z0^3 - x^39*y*z0 + x^39*z0^2 + x^37*z0^4 + 2*x^40 - x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 + x^36*z0^4 + 2*x^37*y*z0 - 2*x^35*y*z0^3 + 2*x^35*z0^4 - 2*x^38 - x^36*y*z0 - x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^34*z0^4 + 2*x^37 + x^35*y*z0 - x^35*z0^2 + 2*x^33*y*z0^3 + x^33*z0^4 - 2*x^36 - x^34*y*z0 - x^34*z0^2 - x^32*y*z0^3 - 2*x^35 + x^31*y*z0^3 - x^32*y*z0 - 2*x^32*z0^2 - 2*x^30*y*z0^3 + 2*x^33 + 2*x^31*y*z0 + x^31*z0^2 - x^29*y*z0^3 - x^32 + x^30*y*z0 + x^30*z0^2 + 2*x^28*y*z0^3 + x^31 - x^27*y*z0^3 - 2*x^27*z0^4 - x^30 - x^28*z0^2 + 2*x^26*y*z0^3 + 2*x^29 + 2*x^27*y*z0 - 2*x^27*z0^2 + 2*x^25*y*z0^3 + 2*x^25*z0^4 - 2*x^28 + x^26*y*z0 - x^24*y*z0^3 + x^24*z0^4 + x^27 + x^25*z0^2 + 2*x^23*y*z0^3 - 2*x^23*z0^4 - 2*x^24*y*z0 + x^24*z0^2 - x^22*y*z0^3 - 2*x^22*z0^4 + 2*x^23*y*z0 + 2*x^23*z0^2 - x^21*z0^4 - 2*x^24 + 2*x^22*y*z0 + x^22*z0^2 + x^20*y*z0^3 + x^20*z0^4 + x^23 + 2*x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 - 2*x^20*z0^2 + 2*x^18*y*z0^3 - 2*x^18*z0^4 - 2*x^21 + 2*x^19*y*z0 - 2*x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 + 2*x^20 + 2*x^18*y*z0 + x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 - 2*x^19 - x^17*y*z0 + 2*x^17*z0^2 + 2*x^15*y*z0^3 - x^15*z0^4 - x^16*y*z0 - 2*x^16*z0^2 + x^14*y*z0^3 - x^14*z0^4 + 2*x^17 - 2*x^15*z0^2 + x^13*y*z0^3 - x^13*z0^4 - 2*x^16 - 2*x^14*z0^2 + x^12*y*z0^3 - x^12*z0^4 - 2*x^15 - 2*x^13*y*z0 + x^13*z0^2 + x^11*y*z0^3 - x^11*z0^4 + 2*x^12*y*z0 + x^12*z0^2 + 2*x^10*y*z0^3 + 2*x^10*z0^4 + x^13 - x^11*z0^2 + x^9*y*z0^3 + 2*x^9*z0^4 + x^12 - 2*x^10*y*z0 - 2*x^10*z0^2 + x^8*y*z0^3 + x^8*z0^4 - x^11 + x^9*y*z0 + x^9*z0^2 + x^7*y*z0^3 + x^7*z0^4 - x^10 - 2*x^8*y*z0 - 2*x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 - 2*x^9 + x^7*z0^2 - x^5*z0^4 - x^8 + x^6*y*z0 + x^6*z0^2 - x^4*y*z0^3 + x^4*z0^4 + x^5*z0^2 + x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 - x^2*y*z0^3 - 2*x^2*z0^4 + 2*x^5 - x^3*y*z0 + x^3*z0^2 - 2*x^2*y*z0 + x^2*z0^2 + 2*x^3 - x^2)/y) * dx, - ((-2*x^61*z0^3 + 2*x^58*y^2*z0^3 + 2*x^61*z0 + x^59*z0^3 - 2*x^60*z0 - 2*x^58*y^2*z0 - 2*x^58*z0^3 - x^56*y^2*z0^3 + x^59*z0 + 2*x^57*y^2*z0 - x^55*y^2*z0^3 - 2*x^58*z0 - x^56*y^2*z0 - x^56*z0^3 + 2*x^57*z0 + 2*x^55*z0^3 - x^56*z0 + 2*x^55*z0 + x^53*z0^3 + 2*x^54*z0 - 2*x^52*z0^3 + x^53*z0 + x^51*y^2*z0 - 2*x^52*z0 - x^50*z0^3 - 2*x^51*z0 + 2*x^49*z0^3 - x^50*z0 + 2*x^49*z0 + x^47*z0^3 + 2*x^48*z0 - 2*x^46*z0^3 + x^47*z0 - 2*x^46*z0 - x^44*z0^3 - 2*x^45*z0 + 2*x^43*z0^3 - x^44*z0 + 2*x^43*z0 - x^41*z0^3 - 2*x^39*y*z0^4 + 2*x^42*z0 - x^40*y*z0^2 - 2*x^40*z0^3 + 2*x^38*y*z0^4 - 2*x^41*z0 + 2*x^39*y*z0^2 + x^40*y + x^38*z0^3 + x^36*y*z0^4 - 2*x^39*y - 2*x^39*z0 + x^37*y*z0^2 - 2*x^35*y*z0^4 - x^38*z0 - 2*x^36*y*z0^2 - 2*x^36*z0^3 - x^34*y*z0^4 + 2*x^37*y + 2*x^37*z0 + 2*x^35*y*z0^2 - 2*x^33*y*z0^4 - x^36*y + 2*x^34*y*z0^2 + x^34*z0^3 - x^32*y*z0^4 + x^35*y - 2*x^33*y*z0^2 + x^31*y*z0^4 - x^34*z0 - 2*x^32*y*z0^2 + 2*x^32*z0^3 - 2*x^30*y*z0^4 - 2*x^31*y*z0^2 + 2*x^31*z0^3 - x^29*y*z0^4 + x^32*z0 - 2*x^30*y*z0^2 + 2*x^30*z0^3 - x^28*y*z0^4 - x^31*y - x^31*z0 - x^29*y*z0^2 + 2*x^27*y*z0^4 + x^30*y - 2*x^30*z0 + x^28*y*z0^2 - 2*x^28*z0^3 - x^29*y - 2*x^29*z0 + 2*x^27*y*z0^2 - 2*x^25*y*z0^4 + 2*x^28*y + x^28*z0 - x^26*y*z0^2 - 2*x^26*z0^3 + 2*x^24*y*z0^4 + x^27*y - 2*x^27*z0 - x^25*y*z0^2 - x^26*y - x^26*z0 - 2*x^24*y*z0^2 + 2*x^24*z0^3 - 2*x^22*y*z0^4 + x^25*y + 2*x^25*z0 - 2*x^23*y*z0^2 + x^23*z0^3 + x^21*y*z0^4 - x^24*y + 2*x^24*z0 + x^22*y*z0^2 - 2*x^22*z0^3 - x^20*y*z0^4 - 2*x^23*z0 + 2*x^21*z0^3 - 2*x^19*y*z0^4 + 2*x^22*y + 2*x^22*z0 - x^20*y*z0^2 + x^20*z0^3 + 2*x^18*y*z0^4 + x^21*y - x^21*z0 + 2*x^19*y*z0^2 + x^19*z0^3 - x^17*y*z0^4 - x^20*z0 + 2*x^18*z0^3 - x^16*y*z0^4 - 2*x^19*y + x^19*z0 - x^17*y*z0^2 + x^17*z0^3 - x^15*y*z0^4 + 2*x^16*y*z0^2 - x^16*z0^3 + x^14*y*z0^4 + 2*x^17*y + 2*x^17*z0 + x^15*y*z0^2 - 2*x^15*z0^3 - x^13*y*z0^4 + 2*x^16*y + 2*x^14*y*z0^2 - x^14*z0^3 - 2*x^15*y + x^15*z0 + 2*x^13*y*z0^2 - x^13*z0^3 - x^11*y*z0^4 + x^14*y + 2*x^12*y*z0^2 + x^12*z0^3 + x^10*y*z0^4 - x^13*y + 2*x^13*z0 + x^11*y*z0^2 + x^11*z0^3 - 2*x^9*y*z0^4 - 2*x^12*y - 2*x^10*y*z0^2 - x^8*y*z0^4 - x^11*y - 2*x^9*y*z0^2 - x^9*z0^3 + 2*x^7*y*z0^4 + x^10*y - x^6*y*z0^4 - x^9*y + x^9*z0 + x^7*y*z0^2 - x^7*z0^3 + 2*x^5*y*z0^4 - x^8*y - 2*x^8*z0 - 2*x^6*y*z0^2 + 2*x^7*y + 2*x^7*z0 - x^5*y*z0^2 - 2*x^3*y*z0^4 + 2*x^6*z0 - x^4*y*z0^2 - 2*x^4*z0^3 + 2*x^5*y + 2*x^5*z0 - x^3*y*z0^2 - 2*x^3*z0^3 - 2*x^4*y + x^4*z0 - 2*x^2*y*z0^2 + x^3*y + 2*x^3*z0 - 2*x^2*y + 2*x^2*z0)/y) * dx, - ((-x^61*z0^4 + 2*x^60*z0^4 + x^58*y^2*z0^4 - 2*x^61*z0^2 + x^59*z0^4 - 2*x^57*y^2*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 + x^58*z0^4 - x^56*y^2*z0^4 + x^61 - x^57*y^2*z0^2 - 2*x^57*z0^4 - 2*x^60 - x^58*y^2 + 2*x^58*z0^2 - x^56*z0^4 + 2*x^57*y^2 - x^57*z0^2 - x^55*z0^4 - x^58 + 2*x^54*z0^4 + 2*x^57 - 2*x^55*z0^2 + x^53*z0^4 + x^52*z0^4 + x^55 + x^51*y^2*z0^2 - 2*x^51*z0^4 - 2*x^54 + 2*x^52*z0^2 - x^50*z0^4 - x^49*z0^4 - x^52 + 2*x^48*z0^4 + 2*x^51 - 2*x^49*z0^2 + x^47*z0^4 + x^46*z0^4 + x^49 - 2*x^45*z0^4 - 2*x^48 + 2*x^46*z0^2 - x^44*z0^4 - x^43*z0^4 - x^46 + 2*x^42*z0^4 + 2*x^45 - 2*x^43*z0^2 - 2*x^41*z0^4 + 2*x^40*y*z0^3 - 2*x^40*z0^4 + x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 + x^39*z0^4 - 2*x^42 - x^40*y*z0 + 2*x^38*y*z0^3 - x^38*z0^4 + 2*x^41 + 2*x^39*z0^2 - x^37*y*z0^3 + x^37*z0^4 + 2*x^40 + x^38*z0^2 - x^36*y*z0^3 - x^36*z0^4 - x^39 + x^37*z0^2 + 2*x^35*y*z0^3 + 2*x^35*z0^4 + x^38 - 2*x^36*y*z0 - 2*x^36*z0^2 + x^34*y*z0^3 - x^34*z0^4 + 2*x^37 - 2*x^35*y*z0 + x^35*z0^2 - x^33*y*z0^3 - x^33*z0^4 - 2*x^34*y*z0 - x^32*y*z0^3 - x^32*z0^4 + 2*x^35 + x^33*z0^2 - x^31*y*z0^3 - 2*x^31*z0^4 - x^34 - x^32*y*z0 + 2*x^32*z0^2 + x^30*y*z0^3 + 2*x^30*z0^4 + x^33 - 2*x^31*y*z0 + 2*x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 - 2*x^32 - 2*x^30*y*z0 - 2*x^30*z0^2 + 2*x^28*y*z0^3 + x^28*z0^4 + x^31 + x^29*y*z0 + 2*x^29*z0^2 + x^27*z0^4 - 2*x^30 - 2*x^28*y*z0 + 2*x^28*z0^2 - 2*x^26*y*z0^3 + x^29 - x^27*z0^2 - 2*x^25*y*z0^3 + x^25*z0^4 - x^28 - x^26*y*z0 - x^26*z0^2 + 2*x^24*y*z0^3 - 2*x^24*z0^4 - x^27 + x^25*y*z0 + x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 + x^26 + x^24*y*z0 - x^24*z0^2 + x^22*z0^4 + x^21*y*z0^3 - x^21*z0^4 + x^22*y*z0 - 2*x^22*z0^2 - x^20*y*z0^3 - x^21*y*z0 + 2*x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 + x^20*y*z0 + x^20*z0^2 - x^18*y*z0^3 - 2*x^18*z0^4 + x^19*y*z0 - x^19*z0^2 - 2*x^17*y*z0^3 - x^17*z0^4 + x^20 + x^16*y*z0^3 + x^16*z0^4 + x^19 + x^17*y*z0 + x^17*z0^2 - x^15*y*z0^3 - 2*x^16*z0^2 + 2*x^14*y*z0^3 + 2*x^15*z0^2 + x^13*y*z0^3 + x^13*z0^4 - x^16 + x^14*y*z0 + 2*x^14*z0^2 + 2*x^12*y*z0^3 + x^15 - 2*x^13*y*z0 + 2*x^13*z0^2 + x^11*y*z0^3 + x^11*z0^4 + 2*x^14 + 2*x^12*y*z0 - x^12*z0^2 + 2*x^10*z0^4 - x^13 - x^11*z0^2 + 2*x^9*y*z0^3 + x^12 + x^10*y*z0 + x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 - x^9*y*z0 + x^9*z0^2 + x^7*y*z0^3 - x^7*z0^4 + x^10 + x^8*y*z0 + x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 - x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + x^8 - 2*x^6*z0^2 - x^4*y*z0^3 + x^4*z0^4 - x^7 + x^3*z0^4 + 2*x^6 - 2*x^4*y*z0 - 2*x^4*z0^2 - 2*x^2*z0^4 + x^5 + x^3*z0^2 + x^2*y*z0 - 2*x^2*z0^2 + x^3 - x^2)/y) * dx, - ((-2*x^61*z0^3 - 2*x^60*z0^3 + 2*x^58*y^2*z0^3 + 2*x^61*z0 + 2*x^59*z0^3 + 2*x^57*y^2*z0^3 + x^60*z0 - 2*x^58*y^2*z0 - 2*x^56*y^2*z0^3 - x^59*z0 - x^57*y^2*z0 + 2*x^55*y^2*z0^3 - 2*x^58*z0 + x^56*y^2*z0 - 2*x^56*z0^3 + 2*x^54*y^2*z0^3 - x^57*z0 + x^56*z0 - x^54*z0^3 + 2*x^55*z0 + 2*x^53*z0^3 + x^51*y^2*z0^3 + x^54*z0 - x^53*z0 + x^51*z0^3 - 2*x^52*z0 - 2*x^50*z0^3 - x^51*z0 + x^50*z0 - x^48*z0^3 + 2*x^49*z0 + 2*x^47*z0^3 + x^48*z0 - x^47*z0 + x^45*z0^3 - 2*x^46*z0 - 2*x^44*z0^3 - x^45*z0 + x^44*z0 - x^42*z0^3 + 2*x^43*z0 - 2*x^39*y*z0^4 + x^42*z0 - x^40*y*z0^2 + 2*x^38*y*z0^4 + x^41*z0 + 2*x^39*y*z0^2 + x^39*z0^3 + x^40*y - x^40*z0 + x^38*y*z0^2 + x^38*z0^3 - 2*x^36*y*z0^4 + 2*x^39*y + 2*x^37*y*z0^2 - 2*x^37*z0^3 + 2*x^35*y*z0^4 + 2*x^38*y - x^38*z0 - x^36*y*z0^2 - 2*x^34*y*z0^4 + 2*x^37*y - x^37*z0 + x^35*z0^3 - 2*x^33*y*z0^4 + x^36*y + 2*x^36*z0 + 2*x^34*y*z0^2 - x^34*z0^3 - 2*x^35*y + 2*x^35*z0 + 2*x^33*y*z0^2 + 2*x^33*z0^3 + 2*x^31*y*z0^4 - 2*x^34*z0 + x^32*z0^3 + 2*x^30*y*z0^4 + x^33*y - 2*x^33*z0 - x^31*z0^3 + x^29*y*z0^4 - x^32*y + 2*x^32*z0 - 2*x^30*y*z0^2 + x^30*z0^3 - 2*x^28*y*z0^4 - x^31*y + x^31*z0 + 2*x^29*y*z0^2 - 2*x^29*z0^3 - x^27*y*z0^4 - x^30*y + x^30*z0 + x^28*y*z0^2 - x^28*z0^3 + 2*x^26*y*z0^4 + x^29*y + x^29*z0 + 2*x^27*z0^3 + 2*x^25*y*z0^4 + 2*x^28*y + 2*x^28*z0 - x^26*y*z0^2 - x^26*z0^3 - x^24*y*z0^4 + x^27*y - 2*x^25*y*z0^2 - x^25*z0^3 + x^23*y*z0^4 - x^26*y + x^26*z0 + 2*x^24*z0^3 + x^22*y*z0^4 + x^25*y + 2*x^23*z0^3 + x^21*y*z0^4 - 2*x^24*y - 2*x^22*y*z0^2 + x^22*z0^3 + 2*x^23*y + 2*x^23*z0 - x^21*y*z0^2 + 2*x^21*z0^3 + x^19*y*z0^4 - 2*x^22*y - 2*x^22*z0 - x^20*y*z0^2 + 2*x^20*z0^3 + x^18*y*z0^4 - 2*x^21*y + x^21*z0 + x^19*y*z0^2 + 2*x^19*z0^3 + x^17*y*z0^4 - x^20*z0 + x^18*y*z0^2 - x^18*z0^3 - x^19*y + x^19*z0 - x^17*y*z0^2 - 2*x^17*z0^3 + x^15*y*z0^4 + 2*x^18*y + 2*x^18*z0 - 2*x^16*z0^3 + 2*x^14*y*z0^4 - x^17*y + x^17*z0 + x^15*y*z0^2 - 2*x^15*z0^3 - x^13*y*z0^4 + 2*x^16*y - x^16*z0 + x^14*y*z0^2 - 2*x^14*z0^3 + x^12*y*z0^4 + x^15*y - x^13*y*z0^2 - x^11*y*z0^4 + 2*x^14*y - 2*x^14*z0 + x^12*y*z0^2 + 2*x^12*z0^3 - 2*x^10*y*z0^4 - x^13*y - x^13*z0 - x^11*z0^3 + x^10*y*z0^2 - 2*x^8*y*z0^4 - 2*x^11*y - x^11*z0 - 2*x^9*y*z0^2 + x^9*z0^3 + 2*x^7*y*z0^4 - 2*x^10*z0 + x^8*y*z0^2 + 2*x^8*z0^3 - 2*x^6*y*z0^4 + 2*x^9*y - 2*x^9*z0 - x^7*y*z0^2 - x^7*z0^3 - 2*x^5*y*z0^4 + x^8*y + x^8*z0 + 2*x^6*z0^3 + 2*x^4*y*z0^4 + x^7*y - 2*x^7*z0 - 2*x^5*y*z0^2 + x^5*z0^3 + x^3*y*z0^4 + x^6*y - 2*x^6*z0 - 2*x^4*y*z0^2 + x^4*z0^3 + 2*x^2*y*z0^4 + x^5*y - 2*x^5*z0 + x^4*y - 2*x^4*z0 + x^2*y*z0^2 - x^2*z0^3 - 2*x^3*y + 2*x^3*z0 + x^2*y)/y) * dx, - ((-2*x^61*z0^4 + x^60*z0^4 + 2*x^58*y^2*z0^4 - x^61*z0^2 + 2*x^59*z0^4 - x^57*y^2*z0^4 + 2*x^60*z0^2 + x^58*y^2*z0^2 + 2*x^58*z0^4 - 2*x^56*y^2*z0^4 + 2*x^61 - 2*x^57*y^2*z0^2 - x^57*z0^4 + 2*x^60 - 2*x^58*y^2 + x^58*z0^2 - 2*x^56*z0^4 - 2*x^57*y^2 - 2*x^57*z0^2 - 2*x^55*z0^4 - 2*x^58 - 2*x^57 - x^55*z0^2 + 2*x^53*z0^4 + x^51*y^2*z0^4 + 2*x^54*z0^2 + 2*x^52*z0^4 + 2*x^55 + 2*x^54 + x^52*z0^2 - 2*x^50*z0^4 - 2*x^51*z0^2 - 2*x^49*z0^4 - 2*x^52 - 2*x^51 - x^49*z0^2 + 2*x^47*z0^4 + 2*x^48*z0^2 + 2*x^46*z0^4 + 2*x^49 + 2*x^48 + x^46*z0^2 - 2*x^44*z0^4 - 2*x^45*z0^2 - 2*x^43*z0^4 - 2*x^46 - 2*x^45 - x^43*z0^2 + x^41*z0^4 + 2*x^42*z0^2 - x^40*y*z0^3 - 2*x^40*z0^4 + 2*x^43 - x^41*z0^2 - x^39*y*z0^3 - 2*x^39*z0^4 + 2*x^42 + 2*x^40*y*z0 + x^40*z0^2 + 2*x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + x^39*y*z0 - x^39*z0^2 + 2*x^37*y*z0^3 - 2*x^37*z0^4 + 2*x^40 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + x^36*z0^4 - x^39 - x^37*y*z0 - 2*x^35*y*z0^3 - 2*x^35*z0^4 + 2*x^38 + x^36*z0^2 + 2*x^34*y*z0^3 + 2*x^34*z0^4 - 2*x^37 + x^35*y*z0 + 2*x^35*z0^2 + 2*x^33*y*z0^3 - x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 + 2*x^34*z0^2 + x^32*y*z0^3 + 2*x^32*z0^4 + x^35 - 2*x^33*y*z0 + 2*x^31*y*z0^3 + 2*x^31*z0^4 - 2*x^34 + x^32*y*z0 + x^32*z0^2 - x^30*z0^4 - x^33 - 2*x^31*y*z0 + 2*x^31*z0^2 + x^29*y*z0^3 + x^32 - x^30*y*z0 - 2*x^30*z0^2 + x^28*y*z0^3 - 2*x^28*z0^4 - 2*x^31 + 2*x^29*y*z0 - x^29*z0^2 - x^30 - x^28*y*z0 - 2*x^28*z0^2 - 2*x^26*y*z0^3 - x^26*z0^4 + 2*x^29 - 2*x^27*y*z0 - 2*x^27*z0^2 - 2*x^25*y*z0^3 + x^26*y*z0 + 2*x^26*z0^2 - x^24*y*z0^3 - x^24*z0^4 - x^27 + 2*x^25*y*z0 - x^23*y*z0^3 - 2*x^23*z0^4 - 2*x^26 - 2*x^24*y*z0 + x^24*z0^2 + x^22*y*z0^3 + x^22*z0^4 - x^25 + x^23*y*z0 - x^23*z0^2 + 2*x^21*y*z0^3 - x^21*z0^4 + x^22*y*z0 + x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^23 - x^21*y*z0 + 2*x^19*z0^4 - x^20*y*z0 + x^20*z0^2 - x^18*y*z0^3 - 2*x^18*z0^4 + x^21 - x^19*y*z0 - 2*x^19*z0^2 - 2*x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^20 - 2*x^18*y*z0 + x^18*z0^2 - 2*x^16*z0^4 + x^19 - 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^15*z0^4 - x^18 + 2*x^16*y*z0 + x^16*z0^2 - x^14*y*z0^3 - x^14*z0^4 - x^17 - 2*x^15*y*z0 - 2*x^15*z0^2 - x^13*y*z0^3 + 2*x^13*z0^4 - x^16 + x^14*y*z0 - x^12*y*z0^3 - 2*x^15 + 2*x^13*y*z0 + x^13*z0^2 + x^11*y*z0^3 - 2*x^14 + 2*x^12*z0^2 - x^10*y*z0^3 + 2*x^10*z0^4 + 2*x^11*y*z0 - 2*x^9*y*z0^3 + 2*x^9*z0^4 - x^12 - x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 - x^9*y*z0 + 2*x^9*z0^2 + 2*x^7*y*z0^3 - x^7*z0^4 - x^10 + 2*x^8*y*z0 + x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^7*y*z0 - x^7*z0^2 - x^5*z0^4 + 2*x^8 - x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 - x^7 - 2*x^5*y*z0 - x^5*z0^2 + x^3*y*z0^3 - x^3*z0^4 + 2*x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 + x^2*z0^4 - x^5 - x^3*y*z0 + 2*x^3*z0^2 - x^2*y*z0 + 2*x^2*z0^2 - x^3)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-2*x^61*z0^4 + 2*x^58*y^2*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 + x^60*z0^2 + 2*x^58*y^2*z0^2 + 2*x^58*z0^4 - 2*x^56*y^2*z0^4 + x^61 - x^57*y^2*z0^2 - x^58*y^2 + 2*x^58*z0^2 - 2*x^56*z0^4 - x^57*z0^2 - 2*x^55*z0^4 - x^58 - 2*x^55*z0^2 + 2*x^53*z0^4 + x^54*z0^2 + 2*x^52*z0^4 + x^52*y^2 + 2*x^52*z0^2 - 2*x^50*z0^4 - x^51*z0^2 - 2*x^49*z0^4 - 2*x^49*z0^2 + 2*x^47*z0^4 + x^48*z0^2 + 2*x^46*z0^4 + 2*x^46*z0^2 - 2*x^44*z0^4 - x^45*z0^2 - 2*x^43*z0^4 - 2*x^43*z0^2 - 2*x^41*z0^4 + x^42*z0^2 - x^40*y*z0^3 + 2*x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - x^40*y*z0 - x^40*z0^2 + 2*x^38*z0^4 + x^41 + 2*x^39*y*z0 + x^39*z0^2 + 2*x^37*y*z0^3 + 2*x^37*z0^4 - 2*x^40 + x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + x^36*z0^4 - 2*x^39 - x^37*y*z0 - x^35*z0^4 + x^38 - x^36*z0^2 + x^34*y*z0^3 - 2*x^34*z0^4 + 2*x^37 - 2*x^35*y*z0 + 2*x^33*y*z0^3 - x^33*z0^4 - 2*x^34*y*z0 + 2*x^34*z0^2 + 2*x^32*z0^4 - x^33*y*z0 + x^33*z0^2 - x^31*y*z0^3 - x^30*y*z0^3 + x^31*y*z0 - x^31*z0^2 - x^29*y*z0^3 + x^32 + 2*x^30*y*z0 + 2*x^30*z0^2 + x^28*z0^4 - x^31 - 2*x^29*y*z0 + 2*x^29*z0^2 - 2*x^27*y*z0^3 - x^27*z0^4 - 2*x^28*z0^2 - 2*x^26*y*z0^3 - x^26*z0^4 - x^29 + 2*x^27*y*z0 + 2*x^27*z0^2 + 2*x^25*y*z0^3 + x^25*z0^4 - 2*x^26*y*z0 - 2*x^26*z0^2 + 2*x^24*y*z0^3 - x^27 + x^25*y*z0 + 2*x^24*y*z0 + x^24*z0^2 + x^22*y*z0^3 - x^25 + 2*x^23*y*z0 + x^23*z0^2 + 2*x^21*y*z0^3 + 2*x^21*z0^4 - 2*x^24 - 2*x^22*y*z0 + 2*x^22*z0^2 - 2*x^20*z0^4 + 2*x^21*y*z0 + 2*x^21*z0^2 + x^20*y*z0 + 2*x^20*z0^2 - 2*x^18*z0^4 + x^19*y*z0 + x^19*z0^2 - x^17*y*z0^3 - x^18*y*z0 + 2*x^18*z0^2 - x^16*y*z0^3 - x^16*z0^4 + x^19 - 2*x^17*y*z0 - 2*x^17*z0^2 + x^18 + x^16*z0^2 - 2*x^14*y*z0^3 + 2*x^14*z0^4 - 2*x^17 - 2*x^15*y*z0 - 2*x^15*z0^2 + 2*x^13*y*z0^3 - 2*x^13*z0^4 + x^16 - x^14*y*z0 - 2*x^14*z0^2 + x^12*y*z0^3 - x^12*z0^4 - x^13*y*z0 - 2*x^11*y*z0^3 - x^11*z0^4 + x^14 - x^12*z0^2 + 2*x^10*y*z0^3 + x^10*z0^4 - 2*x^13 - x^11*y*z0 + 2*x^9*y*z0^3 + 2*x^9*z0^4 - x^12 + 2*x^10*y*z0 - 2*x^10*z0^2 - x^8*y*z0^3 - x^8*z0^4 - x^11 + x^9*y*z0 - x^9*z0^2 + 2*x^7*y*z0^3 + 2*x^7*z0^4 - x^10 - x^8*y*z0 - x^8*z0^2 - 2*x^9 + 2*x^7*y*z0 - 2*x^7*z0^2 - x^5*y*z0^3 + x^8 - x^6*y*z0 + x^6*z0^2 - x^4*y*z0^3 - x^4*z0^4 + 2*x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*y*z0^3 - x^3*z0^4 - x^6 + 2*x^2*z0^4 + x^5 - x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 - 2*x^3 + 2*x^2)/y) * dx, - ((-2*x^61*z0^3 + 2*x^58*y^2*z0^3 - 2*x^61*z0 - x^59*z0^3 - 2*x^60*z0 + 2*x^58*y^2*z0 + 2*x^58*z0^3 + x^56*y^2*z0^3 + 2*x^59*z0 + 2*x^57*y^2*z0 - x^57*z0^3 + 2*x^58*z0 - 2*x^56*y^2*z0 + x^56*z0^3 + x^54*y^2*z0^3 + 2*x^57*z0 - 2*x^55*z0^3 - 2*x^56*z0 + x^54*z0^3 + 2*x^55*z0 - x^53*z0^3 - 2*x^54*z0 + x^52*y^2*z0 + 2*x^52*z0^3 + 2*x^53*z0 - x^51*z0^3 - 2*x^52*z0 + x^50*z0^3 + 2*x^51*z0 - 2*x^49*z0^3 - 2*x^50*z0 + x^48*z0^3 + 2*x^49*z0 - x^47*z0^3 - 2*x^48*z0 + 2*x^46*z0^3 + 2*x^47*z0 - x^45*z0^3 - 2*x^46*z0 + x^44*z0^3 + 2*x^45*z0 - 2*x^43*z0^3 - 2*x^44*z0 + x^42*z0^3 + 2*x^43*z0 + 2*x^41*z0^3 - 2*x^39*y*z0^4 - 2*x^42*z0 - x^40*y*z0^2 - 2*x^40*z0^3 + x^38*y*z0^4 - 2*x^39*y*z0^2 + x^39*z0^3 - x^40*y - 2*x^40*z0 + x^38*z0^3 + 2*x^36*y*z0^4 - 2*x^39*y - 2*x^39*z0 - 2*x^37*y*z0^2 + x^37*z0^3 - 2*x^35*y*z0^4 + 2*x^38*y + x^38*z0 - 2*x^36*y*z0^2 + x^36*z0^3 + 2*x^34*y*z0^4 - 2*x^37*y + x^35*y*z0^2 - x^35*z0^3 + 2*x^33*y*z0^4 + 2*x^36*y - 2*x^36*z0 + x^34*y*z0^2 + x^34*z0^3 - 2*x^35*y + x^33*y*z0^2 - 2*x^33*z0^3 - x^31*y*z0^4 + 2*x^34*y + 2*x^34*z0 - 2*x^32*y*z0^2 - 2*x^32*z0^3 + 2*x^30*y*z0^4 - x^33*y - 2*x^33*z0 + 2*x^31*y*z0^2 + x^30*y*z0^2 - 2*x^30*z0^3 - x^28*y*z0^4 + x^31*y - 2*x^31*z0 + x^29*y*z0^2 - x^29*z0^3 + x^30*y - x^30*z0 + x^28*z0^3 + 2*x^26*y*z0^4 - x^29*y - 2*x^29*z0 + x^27*y*z0^2 + x^25*y*z0^4 + x^28*y + x^28*z0 + 2*x^26*z0^3 + x^27*y - 2*x^27*z0 - 2*x^25*y*z0^2 + x^25*z0^3 - x^23*y*z0^4 + 2*x^26*y + x^26*z0 + 2*x^24*z0^3 + x^25*y - 2*x^25*z0 + 2*x^23*z0^3 + x^21*y*z0^4 + x^24*y + x^24*z0 + x^22*y*z0^2 + 2*x^22*z0^3 - 2*x^20*y*z0^4 + 2*x^23*y + 2*x^21*y*z0^2 + 2*x^22*z0 + 2*x^20*y*z0^2 + x^20*z0^3 + x^18*y*z0^4 + 2*x^21*y - 2*x^21*z0 - 2*x^19*y*z0^2 + 2*x^19*z0^3 - 2*x^17*y*z0^4 - x^20*y - x^20*z0 - 2*x^18*y*z0^2 - x^19*y - x^19*z0 - x^17*y*z0^2 + 2*x^17*z0^3 - 2*x^15*y*z0^4 + x^18*y - x^18*z0 + 2*x^16*y*z0^2 + 2*x^14*y*z0^4 - x^17*y + 2*x^17*z0 - 2*x^15*y*z0^2 + 2*x^15*z0^3 - x^13*y*z0^4 - 2*x^16*y + 2*x^16*z0 - 2*x^14*y*z0^2 + x^14*z0^3 + 2*x^12*y*z0^4 + x^15*y - 2*x^15*z0 + x^13*y*z0^2 - x^13*z0^3 - 2*x^11*y*z0^4 - x^14*y - x^14*z0 - x^12*y*z0^2 - 2*x^10*y*z0^4 + x^13*y + x^13*z0 - 2*x^11*y*z0^2 + 2*x^11*z0^3 - 2*x^9*y*z0^4 + 2*x^12*y - 2*x^12*z0 - x^10*y*z0^2 - 2*x^10*z0^3 + 2*x^8*y*z0^4 + x^11*y + x^11*z0 - x^9*y*z0^2 + 2*x^7*y*z0^4 - 2*x^10*z0 - 2*x^8*y*z0^2 + 2*x^6*y*z0^4 - 2*x^9*y - 2*x^9*z0 - x^7*z0^3 + x^5*y*z0^4 - 2*x^8*y + x^8*z0 - 2*x^6*y*z0^2 - x^6*z0^3 - 2*x^4*y*z0^4 + x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y + 2*x^6*z0 + 2*x^4*y*z0^2 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - 2*x^5*z0 + x^3*z0^3 + 2*x^4*z0 - 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y - 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((x^61*z0^4 - x^60*z0^4 - x^58*y^2*z0^4 - x^61*z0^2 + x^59*z0^4 + x^57*y^2*z0^4 + x^60*z0^2 + x^58*y^2*z0^2 - x^58*z0^4 - x^56*y^2*z0^4 - x^57*y^2*z0^2 + x^57*z0^4 + x^58*z0^2 - x^56*z0^4 - x^57*z0^2 + x^55*z0^4 - x^54*z0^4 - 2*x^55*z0^2 + x^53*z0^4 + x^54*z0^2 + x^52*y^2*z0^2 - x^52*z0^4 + x^51*z0^4 + 2*x^52*z0^2 - x^50*z0^4 - x^51*z0^2 + x^49*z0^4 - x^48*z0^4 - 2*x^49*z0^2 + x^47*z0^4 + x^48*z0^2 - x^46*z0^4 + x^45*z0^4 + 2*x^46*z0^2 - x^44*z0^4 - x^45*z0^2 + x^43*z0^4 - x^42*z0^4 - 2*x^43*z0^2 + 2*x^41*z0^4 + x^42*z0^2 - 2*x^40*y*z0^3 + 2*x^40*z0^4 - x^41*z0^2 - x^39*y*z0^3 + 2*x^39*z0^4 + 2*x^40*y*z0 + 2*x^38*z0^4 + x^41 - x^39*y*z0 - x^37*y*z0^3 + 2*x^40 + x^38*y*z0 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + x^36*z0^4 - 2*x^39 + 2*x^37*y*z0 - 2*x^37*z0^2 + 2*x^35*y*z0^3 - 2*x^35*z0^4 - x^38 + x^36*y*z0 + x^34*y*z0^3 + 2*x^34*z0^4 - x^37 + x^35*y*z0 - 2*x^35*z0^2 + x^33*z0^4 + x^34*y*z0 - x^34*z0^2 - x^32*y*z0^3 + x^35 - x^33*y*z0 + 2*x^33*z0^2 - 2*x^31*z0^4 + 2*x^32*y*z0 - 2*x^32*z0^2 + 2*x^30*y*z0^3 + x^30*z0^4 + 2*x^33 - x^29*y*z0^3 + x^32 - x^30*y*z0 - x^30*z0^2 - 2*x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^31 - 2*x^29*z0^2 + x^27*z0^4 - 2*x^30 + x^28*y*z0 - x^28*z0^2 - x^26*y*z0^3 + 2*x^26*z0^4 - x^29 + x^27*z0^2 + 2*x^25*y*z0^3 + x^25*z0^4 - 2*x^28 - x^26*y*z0 + x^26*z0^2 + 2*x^24*y*z0^3 + 2*x^24*z0^4 - x^25*y*z0 + x^25*z0^2 - 2*x^23*y*z0^3 + x^23*z0^4 + x^26 - x^24*y*z0 - 2*x^24*z0^2 + 2*x^22*z0^4 - 2*x^25 - x^23*z0^2 - x^21*z0^4 - 2*x^24 + 2*x^22*y*z0 - x^20*y*z0^3 - x^20*z0^4 + 2*x^23 + 2*x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 + x^22 + 2*x^20*y*z0 - x^20*z0^2 + x^18*y*z0^3 + x^18*z0^4 + x^21 - x^19*y*z0 + 2*x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 + x^20 - 2*x^18*y*z0 + x^16*z0^4 + x^19 - 2*x^17*y*z0 - x^17*z0^2 - x^15*y*z0^3 + x^15*z0^4 + x^16*y*z0 - 2*x^16*z0^2 - 2*x^14*y*z0^3 + x^14*z0^4 + 2*x^17 + 2*x^15*y*z0 + 2*x^13*y*z0^3 - 2*x^13*z0^4 + 2*x^16 - x^14*y*z0 - 2*x^12*y*z0^3 - x^12*z0^4 + 2*x^15 + 2*x^13*y*z0 + x^13*z0^2 - x^11*y*z0^3 - 2*x^11*z0^4 + 2*x^14 + 2*x^12*y*z0 - x^12*z0^2 + x^10*y*z0^3 + x^10*z0^4 - x^13 + x^11*y*z0 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 - x^8*y*z0^3 - x^8*z0^4 - x^9*y*z0 + x^9*z0^2 - x^7*y*z0^3 + x^7*z0^4 - x^8*y*z0 - x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^9 - x^7*y*z0 + x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - 2*x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 - x^4*y*z0^3 + x^4*z0^4 + x^7 - x^5*y*z0 - 2*x^3*y*z0^3 - 2*x^3*z0^4 - x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 - 2*x^2*y*z0^3 - x^2*z0^4 + x^5 - x^3*y*z0 + x^2*y*z0 + 2*x^2)/y) * dx, - ((-2*x^61*z0^3 - x^60*z0^3 + 2*x^58*y^2*z0^3 + x^59*z0^3 + x^57*y^2*z0^3 + 2*x^60*z0 + 2*x^58*z0^3 - x^56*y^2*z0^3 + x^59*z0 - 2*x^57*y^2*z0 + 2*x^57*z0^3 - x^56*y^2*z0 - x^56*z0^3 - x^54*y^2*z0^3 - 2*x^57*z0 + 2*x^55*z0^3 - x^56*z0 - 2*x^54*z0^3 + x^52*y^2*z0^3 + x^53*z0^3 + 2*x^54*z0 - 2*x^52*z0^3 + x^53*z0 + 2*x^51*z0^3 - x^50*z0^3 - 2*x^51*z0 + 2*x^49*z0^3 - x^50*z0 - 2*x^48*z0^3 + x^47*z0^3 + 2*x^48*z0 - 2*x^46*z0^3 + x^47*z0 + 2*x^45*z0^3 - x^44*z0^3 - 2*x^45*z0 + 2*x^43*z0^3 - x^44*z0 - 2*x^42*z0^3 - x^41*z0^3 - 2*x^39*y*z0^4 + 2*x^42*z0 - x^40*y*z0^2 + x^40*z0^3 - x^38*y*z0^4 + x^41*z0 + 2*x^39*z0^3 - 2*x^37*y*z0^4 - 2*x^40*z0 - 2*x^38*y*z0^2 + x^38*z0^3 + x^36*y*z0^4 - 2*x^37*y*z0^2 - 2*x^37*z0^3 + x^35*y*z0^4 + 2*x^36*y*z0^2 + x^36*z0^3 + 2*x^34*y*z0^4 + 2*x^35*z0^3 - x^33*y*z0^4 - x^36*y - 2*x^36*z0 + x^34*y*z0^2 - 2*x^32*y*z0^4 + 2*x^35*y + x^35*z0 - x^33*y*z0^2 + x^31*y*z0^4 + x^34*y + x^34*z0 - x^32*y*z0^2 + 2*x^32*z0^3 - 2*x^30*y*z0^4 - 2*x^33*y - 2*x^31*y*z0^2 - 2*x^31*z0^3 + 2*x^29*y*z0^4 + x^32*y + 2*x^32*z0 + 2*x^30*y*z0^2 + 2*x^30*z0^3 - 2*x^28*y*z0^4 + 2*x^31*y - x^29*y*z0^2 + 2*x^29*z0^3 + 2*x^27*y*z0^4 - 2*x^30*y - x^30*z0 + x^28*y*z0^2 + 2*x^28*z0^3 - 2*x^26*y*z0^4 + x^29*z0 - x^27*y*z0^2 + 2*x^27*z0^3 - x^28*y - x^28*z0 - x^26*y*z0^2 - 2*x^24*y*z0^4 - x^27*y - 2*x^25*y*z0^2 + 2*x^25*z0^3 - 2*x^23*y*z0^4 + x^26*y + 2*x^26*z0 + x^24*y*z0^2 + 2*x^22*y*z0^4 + 2*x^25*y + x^25*z0 + 2*x^23*z0^3 - 2*x^21*y*z0^4 - x^24*y + 2*x^24*z0 + 2*x^22*y*z0^2 + 2*x^22*z0^3 + 2*x^20*y*z0^4 - 2*x^23*y - 2*x^23*z0 + 2*x^21*y*z0^2 - x^21*z0^3 - x^19*y*z0^4 + x^22*y + x^22*z0 - 2*x^20*z0^3 - 2*x^18*y*z0^4 - x^21*y - 2*x^21*z0 + 2*x^19*y*z0^2 + x^19*z0^3 - x^17*y*z0^4 - 2*x^20*y - x^20*z0 + 2*x^18*y*z0^2 + x^18*z0^3 + x^16*y*z0^4 - 2*x^19*y - x^17*z0^3 - x^15*y*z0^4 + x^18*y + x^16*z0^3 + 2*x^14*y*z0^4 - 2*x^17*y + 2*x^15*y*z0^2 - 2*x^15*z0^3 + x^13*y*z0^4 + 2*x^16*y + x^16*z0 + x^14*y*z0^2 - x^14*z0^3 - x^12*y*z0^4 - x^15*z0 - 2*x^13*y*z0^2 - 2*x^13*z0^3 - 2*x^11*y*z0^4 - 2*x^14*y - 2*x^14*z0 + 2*x^12*z0^3 - 2*x^10*y*z0^4 - 2*x^13*y - 2*x^11*y*z0^2 + x^11*z0^3 - x^9*y*z0^4 + x^10*z0^3 + 2*x^8*y*z0^4 + 2*x^11*y + x^9*z0^3 + x^7*y*z0^4 + 2*x^8*z0^3 + 2*x^6*y*z0^4 - 2*x^9*y + 2*x^9*z0 + x^7*z0^3 + 2*x^5*y*z0^4 - 2*x^8*y - x^8*z0 - 2*x^6*y*z0^2 + 2*x^6*z0^3 + x^7*z0 + x^5*z0^3 - 2*x^3*y*z0^4 - x^6*y - x^6*z0 + x^4*y*z0^2 - 2*x^2*y*z0^4 + x^5*z0 - 2*x^3*y*z0^2 + 2*x^3*z0^3 + x^4*y - 2*x^4*z0 - x^2*y*z0^2 + 2*x^2*z0^3 - 2*x^3*y + x^3*z0 + 2*x^2*y - x^2*z0)/y) * dx, - ((2*x^61*z0^4 + x^60*z0^4 - 2*x^58*y^2*z0^4 + x^61*z0^2 - x^59*z0^4 - x^57*y^2*z0^4 - x^60*z0^2 - x^58*y^2*z0^2 - 2*x^58*z0^4 + x^56*y^2*z0^4 + 2*x^61 + x^57*y^2*z0^2 - x^57*z0^4 - x^60 - 2*x^58*y^2 - x^58*z0^2 + x^56*z0^4 + x^57*y^2 + x^57*z0^2 + x^55*z0^4 - 2*x^58 + x^54*z0^4 + x^52*y^2*z0^4 + x^57 + x^55*z0^2 - x^53*z0^4 - x^54*z0^2 - x^52*z0^4 + 2*x^55 - x^51*z0^4 - x^54 - x^52*z0^2 + x^50*z0^4 + x^51*z0^2 + x^49*z0^4 - 2*x^52 + x^48*z0^4 + x^51 + x^49*z0^2 - x^47*z0^4 - x^48*z0^2 - x^46*z0^4 + 2*x^49 - x^45*z0^4 - x^48 - x^46*z0^2 + x^44*z0^4 + x^45*z0^2 + x^43*z0^4 - 2*x^46 + x^42*z0^4 + x^45 + x^43*z0^2 + 2*x^41*z0^4 - x^42*z0^2 + x^40*y*z0^3 + 2*x^43 + x^41*z0^2 + x^39*y*z0^3 + x^39*z0^4 - x^42 - 2*x^40*y*z0 - x^38*y*z0^3 + x^38*z0^4 - 2*x^41 - x^39*y*z0 - x^37*y*z0^3 + 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 + 2*x^36*z0^4 - x^39 + x^37*y*z0 + 2*x^35*z0^4 - x^38 - 2*x^36*y*z0 - x^34*y*z0^3 + x^34*z0^4 + x^37 + x^35*y*z0 + 2*x^35*z0^2 - 2*x^33*y*z0^3 + x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 - 2*x^34*z0^2 - 2*x^32*y*z0^3 - x^32*z0^4 - x^35 - 2*x^33*y*z0 - 2*x^33*z0^2 - x^31*y*z0^3 + x^31*z0^4 - 2*x^34 - 2*x^32*y*z0 - x^32*z0^2 - 2*x^30*z0^4 + x^33 + x^31*y*z0 + x^31*z0^2 + x^29*y*z0^3 - x^29*z0^4 + 2*x^30*y*z0 + x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^29*z0^2 - x^27*z0^4 + x^30 - 2*x^28*y*z0 + x^28*z0^2 - 2*x^26*z0^4 - x^29 + x^27*y*z0 + x^27*z0^2 - x^25*y*z0^3 + x^25*z0^4 + 2*x^28 + x^26*y*z0 - 2*x^26*z0^2 - 2*x^24*y*z0^3 + x^24*z0^4 - 2*x^27 - 2*x^25*y*z0 - 2*x^25*z0^2 + 2*x^23*y*z0^3 - x^23*z0^4 - x^26 - x^24*y*z0 + x^22*y*z0^3 + x^25 + 2*x^23*y*z0 + 2*x^23*z0^2 - x^21*y*z0^3 - 2*x^21*z0^4 + x^24 + x^22*z0^2 - x^23 + 2*x^21*y*z0 + x^18*z0^4 + x^21 - 2*x^19*y*z0 + 2*x^19*z0^2 + x^17*y*z0^3 - x^18*z0^2 - x^16*y*z0^3 - x^19 + 2*x^17*y*z0 + 2*x^17*z0^2 - 2*x^15*y*z0^3 - x^15*z0^4 + 2*x^16*y*z0 + x^16*z0^2 - x^14*y*z0^3 - x^14*z0^4 + x^17 + x^15*y*z0 - x^15*z0^2 - 2*x^13*y*z0^3 - 2*x^13*z0^4 + x^14*y*z0 - x^14*z0^2 - x^12*z0^4 - x^15 + 2*x^13*y*z0 - 2*x^11*y*z0^3 - 2*x^11*z0^4 - 2*x^12*y*z0 - 2*x^12*z0^2 + x^10*y*z0^3 + 2*x^10*z0^4 - x^13 - x^11*y*z0 + 2*x^11*z0^2 + x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 - 2*x^10*z0^2 + x^8*y*z0^3 + x^8*z0^4 + x^11 + 2*x^9*z0^2 + x^7*z0^4 - 2*x^8*y*z0 - 2*x^8*z0^2 - 2*x^9 + 2*x^7*y*z0 - 2*x^7*z0^2 - 2*x^5*y*z0^3 + x^5*z0^4 + 2*x^8 + x^6*y*z0 + x^4*y*z0^3 - x^4*z0^4 + x^7 + x^5*y*z0 - x^5*z0^2 + 2*x^3*y*z0^3 - x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 + x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 - x^3)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 + 2*x^60*z0^4 + x^58*y^2*z0^4 - 2*x^61*z0^2 + 2*x^59*z0^4 - 2*x^57*y^2*z0^4 - x^60*z0^2 + 2*x^58*y^2*z0^2 + x^58*z0^4 - 2*x^56*y^2*z0^4 - x^61 + x^57*y^2*z0^2 - 2*x^57*z0^4 - 2*x^60 + x^58*y^2 + 2*x^58*z0^2 - 2*x^56*z0^4 + 2*x^57*y^2 + x^57*z0^2 - x^55*z0^4 + x^58 + 2*x^54*z0^4 + 2*x^57 - 2*x^55*z0^2 + 2*x^53*z0^4 - x^56 - x^54*z0^2 + x^52*z0^4 - x^55 + x^53*y^2 - 2*x^51*z0^4 - 2*x^54 + 2*x^52*z0^2 - 2*x^50*z0^4 + x^53 + x^51*z0^2 - x^49*z0^4 + x^52 + 2*x^48*z0^4 + 2*x^51 - 2*x^49*z0^2 + 2*x^47*z0^4 - x^50 - x^48*z0^2 + x^46*z0^4 - x^49 - 2*x^45*z0^4 - 2*x^48 + 2*x^46*z0^2 - 2*x^44*z0^4 + x^47 + x^45*z0^2 - x^43*z0^4 + x^46 + 2*x^42*z0^4 + 2*x^45 - 2*x^43*z0^2 - 2*x^41*z0^4 - x^44 - x^42*z0^2 + 2*x^40*y*z0^3 + 2*x^40*z0^4 - x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - 2*x^42 - x^40*y*z0 - x^40*z0^2 + 2*x^38*z0^4 + 2*x^41 - 2*x^39*y*z0 - 2*x^39*z0^2 - x^37*y*z0^3 + 2*x^37*z0^4 + 2*x^40 + x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 + x^36*z0^4 + x^39 + x^37*y*z0 - 2*x^37*z0^2 - 2*x^35*y*z0^3 - x^36*y*z0 + 2*x^36*z0^2 - x^34*y*z0^3 + 2*x^37 - 2*x^35*y*z0 - x^35*z0^2 - 2*x^33*z0^4 + 2*x^36 - x^34*y*z0 + x^34*z0^2 + x^32*y*z0^3 + x^35 + x^33*y*z0 - 2*x^33*z0^2 + 2*x^31*y*z0^3 - 2*x^31*z0^4 + x^34 + x^32*y*z0 - x^32*z0^2 - x^30*y*z0^3 + x^30*z0^4 - x^33 + x^31*z0^2 + x^29*y*z0^3 + x^29*z0^4 + 2*x^32 - x^30*y*z0 - x^30*z0^2 + x^28*y*z0^3 - 2*x^28*z0^4 - x^31 - x^29*y*z0 + 2*x^29*z0^2 - x^27*y*z0^3 + 2*x^27*z0^4 + x^30 + 2*x^28*z0^2 + 2*x^29 + 2*x^27*y*z0 - 2*x^27*z0^2 + x^25*y*z0^3 - x^28 - 2*x^24*y*z0^3 - 2*x^24*z0^4 - 2*x^27 - x^25*y*z0 + x^25*z0^2 + x^23*y*z0^3 - x^23*z0^4 - x^24*y*z0 + 2*x^22*z0^4 + 2*x^25 - 2*x^23*y*z0 + 2*x^23*z0^2 - x^21*z0^4 + 2*x^24 - x^22*y*z0 - x^22*z0^2 + 2*x^20*y*z0^3 - 2*x^20*z0^4 - 2*x^23 + x^21*y*z0 + x^21*z0^2 + 2*x^19*y*z0^3 - 2*x^19*z0^4 + 2*x^20*y*z0 - x^20*z0^2 - x^18*y*z0^3 - 2*x^18*z0^4 + 2*x^21 - x^19*y*z0 + 2*x^19*z0^2 - 2*x^18*y*z0 - x^18*z0^2 + x^16*y*z0^3 + x^16*z0^4 - 2*x^19 - x^17*y*z0 + x^17*z0^2 + x^15*y*z0^3 - x^15*z0^4 + x^18 + 2*x^16*y*z0 - 2*x^16*z0^2 - 2*x^14*y*z0^3 + 2*x^14*z0^4 + x^17 - 2*x^15*y*z0 + x^15*z0^2 + x^13*y*z0^3 + 2*x^13*z0^4 + x^16 + x^14*z0^2 + 2*x^12*y*z0^3 + x^12*z0^4 - x^15 + 2*x^13*y*z0 - 2*x^13*z0^2 - 2*x^11*y*z0^3 - 2*x^12*y*z0 + x^12*z0^2 + 2*x^10*y*z0^3 + 2*x^10*z0^4 - x^13 + x^11*z0^2 - x^9*y*z0^3 - 2*x^9*z0^4 - x^12 - 2*x^10*z0^2 - 2*x^8*y*z0^3 + x^11 + x^9*z0^2 - x^7*y*z0^3 + x^7*z0^4 - x^10 - x^8*z0^2 + 2*x^6*y*z0^3 + x^6*z0^4 + x^9 + x^7*z0^2 + 2*x^5*z0^4 + x^8 - 2*x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 + 2*x^5*y*z0 - x^5*z0^2 - 2*x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 + 2*x^2*y*z0^3 - x^2*z0^4 + 2*x^3*y*z0 - 2*x^3*z0^2 + x^2*y*z0 - x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((2*x^61*z0^3 + 2*x^60*z0^3 - 2*x^58*y^2*z0^3 + x^59*z0^3 - 2*x^57*y^2*z0^3 - x^60*z0 - x^56*y^2*z0^3 + x^59*z0 + x^57*y^2*z0 - 2*x^55*y^2*z0^3 - x^56*y^2*z0 - x^56*z0^3 - 2*x^54*y^2*z0^3 + x^57*z0 - 2*x^56*z0 + x^53*y^2*z0 + x^53*z0^3 - x^54*z0 + 2*x^53*z0 - x^50*z0^3 + x^51*z0 - 2*x^50*z0 + x^47*z0^3 - x^48*z0 + 2*x^47*z0 - x^44*z0^3 + x^45*z0 - 2*x^44*z0 - 2*x^41*z0^3 + 2*x^39*y*z0^4 - x^42*z0 + x^40*y*z0^2 + 2*x^40*z0^3 + x^38*y*z0^4 + 2*x^41*z0 + x^39*z0^3 + x^37*y*z0^4 - x^38*y*z0^2 - x^38*z0^3 - 2*x^36*y*z0^4 - 2*x^39*y - 2*x^39*z0 + x^37*y*z0^2 - 2*x^37*z0^3 - x^38*y - x^38*z0 + 2*x^36*y*z0^2 + 2*x^36*z0^3 - x^34*y*z0^4 + 2*x^35*z0^3 - 2*x^33*y*z0^4 - x^36*y - 2*x^36*z0 + 2*x^34*z0^3 - x^35*y + 2*x^35*z0 - 2*x^33*y*z0^2 + x^31*y*z0^4 - x^34*z0 + x^32*y*z0^2 - 2*x^32*z0^3 - 2*x^30*y*z0^4 - x^33*z0 + x^31*z0^3 + 2*x^29*y*z0^4 - x^32*y - 2*x^32*z0 - x^30*z0^3 + x^28*y*z0^4 + 2*x^31*y - 2*x^27*y*z0^4 + x^30*z0 - 2*x^28*y*z0^2 - x^28*z0^3 + 2*x^26*y*z0^4 - x^29*y - 2*x^29*z0 + 2*x^27*y*z0^2 - x^27*z0^3 + 2*x^25*y*z0^4 + 2*x^26*y*z0^2 + 2*x^26*z0^3 + 2*x^24*y*z0^4 - x^27*y + 2*x^27*z0 + 2*x^25*y*z0^2 + 2*x^25*z0^3 + x^23*y*z0^4 - 2*x^26*z0 + 2*x^24*y*z0^2 - 2*x^24*z0^3 - x^22*y*z0^4 + 2*x^25*y - 2*x^25*z0 - 2*x^23*y*z0^2 - 2*x^23*z0^3 - 2*x^21*y*z0^4 - x^24*y - 2*x^22*y*z0^2 - 2*x^22*z0^3 - 2*x^23*y - x^23*z0 - 2*x^21*y*z0^2 - x^19*y*z0^4 + 2*x^22*y + 2*x^22*z0 + x^20*y*z0^2 - x^18*y*z0^4 + 2*x^21*y + 2*x^21*z0 + 2*x^19*y*z0^2 + x^19*z0^3 + x^17*y*z0^4 + x^20*z0 + 2*x^18*y*z0^2 - x^18*z0^3 - x^16*y*z0^4 - x^19*y + 2*x^19*z0 - 2*x^17*y*z0^2 - 2*x^17*z0^3 + x^15*y*z0^4 - x^18*y - x^18*z0 - x^16*z0^3 + x^14*y*z0^4 + 2*x^17*y + 2*x^17*z0 + x^15*y*z0^2 - x^13*y*z0^4 + x^16*y - x^16*z0 - 2*x^14*z0^3 + x^15*y + 2*x^15*z0 - x^13*y*z0^2 - x^13*z0^3 - 2*x^11*y*z0^4 - 2*x^14*y + 2*x^14*z0 - x^12*y*z0^2 - x^12*z0^3 - 2*x^10*y*z0^4 - 2*x^13*y - x^13*z0 + x^11*y*z0^2 - 2*x^11*z0^3 - 2*x^9*y*z0^4 + x^12*y + 2*x^12*z0 + x^10*z0^3 - x^11*z0 + x^9*y*z0^2 + x^9*z0^3 - 2*x^7*y*z0^4 - 2*x^10*y + x^8*z0^3 - 2*x^6*y*z0^4 - x^9*y - 2*x^9*z0 + 2*x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 - x^8*y - 2*x^8*z0 + 2*x^6*y*z0^2 + 2*x^4*y*z0^4 + 2*x^7*y + 2*x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y + 2*x^6*z0 + 2*x^4*y*z0^2 - x^4*z0^3 - 2*x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - x^3*y*z0^2 + x^3*z0^3 + 2*x^4*y - 2*x^4*z0 - 2*x^2*y*z0^2 - 2*x^3*y - 2*x^3*z0 - x^2*z0)/y) * dx, - ((2*x^61*z0^4 + x^60*z0^4 - 2*x^58*y^2*z0^4 + 2*x^59*z0^4 - x^57*y^2*z0^4 + 2*x^60*z0^2 - 2*x^58*z0^4 - 2*x^56*y^2*z0^4 + x^61 - 2*x^57*y^2*z0^2 - x^57*z0^4 + x^60 - x^58*y^2 - 2*x^56*z0^4 - x^57*y^2 - 2*x^57*z0^2 + 2*x^55*z0^4 - x^58 - x^56*z0^2 + x^54*z0^4 - x^57 + x^53*y^2*z0^2 + 2*x^53*z0^4 + 2*x^54*z0^2 - 2*x^52*z0^4 + x^55 + x^53*z0^2 - x^51*z0^4 + x^54 - 2*x^50*z0^4 - 2*x^51*z0^2 + 2*x^49*z0^4 - x^52 - x^50*z0^2 + x^48*z0^4 - x^51 + 2*x^47*z0^4 + 2*x^48*z0^2 - 2*x^46*z0^4 + x^49 + x^47*z0^2 - x^45*z0^4 + x^48 - 2*x^44*z0^4 - 2*x^45*z0^2 + 2*x^43*z0^4 - x^46 - x^44*z0^2 + x^42*z0^4 - x^45 + 2*x^41*z0^4 + 2*x^42*z0^2 + x^40*y*z0^3 + 2*x^40*z0^4 + x^43 + x^41*z0^2 + 2*x^39*z0^4 + x^42 - x^40*z0^2 + 2*x^38*y*z0^3 - 2*x^39*y*z0 - 2*x^39*z0^2 - x^37*y*z0^3 - x^37*z0^4 + 2*x^40 + x^38*y*z0 - x^38*z0^2 - 2*x^36*z0^4 - x^39 + 2*x^37*y*z0 + 2*x^37*z0^2 - 2*x^35*y*z0^3 - x^35*z0^4 - x^38 + x^36*y*z0 - x^34*y*z0^3 + 2*x^34*z0^4 - 2*x^37 - 2*x^35*z0^2 + 2*x^33*y*z0^3 + 2*x^33*z0^4 + x^36 + 2*x^34*y*z0 - x^34*z0^2 + 2*x^32*z0^4 + 2*x^33*y*z0 - 2*x^31*y*z0^3 + 2*x^34 + 2*x^32*y*z0 + 2*x^30*y*z0^3 - 2*x^33 + 2*x^31*y*z0 + 2*x^31*z0^2 + 2*x^29*y*z0^3 - 2*x^32 + 2*x^30*y*z0 + x^30*z0^2 - x^28*y*z0^3 - 2*x^28*z0^4 - x^29*y*z0 - x^29*z0^2 + 2*x^27*y*z0^3 - x^27*z0^4 - x^30 - x^28*y*z0 + 2*x^28*z0^2 - 2*x^26*y*z0^3 - x^26*z0^4 + x^27*y*z0 - x^27*z0^2 - 2*x^25*z0^4 - 2*x^28 - x^26*y*z0 + x^24*y*z0^3 + x^24*z0^4 + 2*x^27 + x^23*y*z0^3 + x^23*z0^4 - 2*x^26 + x^24*y*z0 + 2*x^24*z0^2 - x^22*y*z0^3 + x^22*z0^4 + x^25 - x^23*z0^2 - x^21*y*z0^3 - x^21*z0^4 - x^24 - 2*x^20*y*z0^3 - x^20*z0^4 - 2*x^23 + 2*x^21*y*z0 - 2*x^21*z0^2 - x^19*y*z0^3 + 2*x^19*z0^4 + 2*x^22 + 2*x^20*z0^2 - x^18*y*z0^3 - x^18*z0^4 + 2*x^21 + x^19*y*z0 - x^19*z0^2 + 2*x^17*y*z0^3 + x^17*z0^4 - x^20 - x^18*z0^2 + x^16*y*z0^3 + x^16*z0^4 + 2*x^19 - x^17*z0^2 - x^15*y*z0^3 + 2*x^15*z0^4 + x^18 + 2*x^16*y*z0 + x^16*z0^2 + 2*x^14*y*z0^3 + 2*x^14*z0^4 + x^17 - 2*x^15*y*z0 + 2*x^15*z0^2 - x^13*y*z0^3 - 2*x^13*z0^4 + 2*x^16 + x^14*y*z0 + x^14*z0^2 - x^12*y*z0^3 + x^12*z0^4 + x^15 + x^13*z0^2 - 2*x^11*y*z0^3 + 2*x^11*z0^4 + 2*x^14 + x^12*y*z0 + x^10*y*z0^3 - x^13 + x^11*y*z0 - 2*x^11*z0^2 - x^9*y*z0^3 - 2*x^9*z0^4 + 2*x^12 - x^10*y*z0 - 2*x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^11 - 2*x^9*y*z0 + x^9*z0^2 - x^7*y*z0^3 - 2*x^7*z0^4 - x^10 - 2*x^8*z0^2 - x^6*y*z0^3 - x^6*z0^4 - x^9 - 2*x^7*y*z0 - x^5*y*z0^3 - x^5*z0^4 - x^6*y*z0 + x^4*y*z0^3 - x^4*z0^4 - 2*x^7 - x^5*z0^2 - 2*x^3*z0^4 + 2*x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0 + 2*x^2*z0^2 + x^3 - x^2)/y) * dx, - ((-2*x^61*z0^3 - x^60*z0^3 + 2*x^58*y^2*z0^3 + 2*x^61*z0 + 2*x^59*z0^3 + x^57*y^2*z0^3 + 2*x^60*z0 - 2*x^58*y^2*z0 + x^58*z0^3 - 2*x^56*y^2*z0^3 + 2*x^59*z0 - 2*x^57*y^2*z0 + x^55*y^2*z0^3 - 2*x^58*z0 - 2*x^56*y^2*z0 + 2*x^56*z0^3 + x^54*y^2*z0^3 - 2*x^57*z0 - x^55*z0^3 + x^53*y^2*z0^3 - 2*x^56*z0 + 2*x^55*z0 - 2*x^53*z0^3 + 2*x^54*z0 + x^52*z0^3 + 2*x^53*z0 - 2*x^52*z0 + 2*x^50*z0^3 - 2*x^51*z0 - x^49*z0^3 - 2*x^50*z0 + 2*x^49*z0 - 2*x^47*z0^3 + 2*x^48*z0 + x^46*z0^3 + 2*x^47*z0 - 2*x^46*z0 + 2*x^44*z0^3 - 2*x^45*z0 - x^43*z0^3 - 2*x^44*z0 + 2*x^43*z0 + x^41*z0^3 - 2*x^39*y*z0^4 + 2*x^42*z0 - x^40*y*z0^2 + x^40*z0^3 + 2*x^38*y*z0^4 - x^41*z0 + 2*x^39*y*z0^2 - 2*x^39*z0^3 - x^37*y*z0^4 + x^40*y + 2*x^40*z0 - 2*x^38*y*z0^2 - 2*x^36*y*z0^4 - 2*x^37*z0^3 + 2*x^35*y*z0^4 - x^38*y - x^38*z0 + x^36*z0^3 + 2*x^37*y - 2*x^37*z0 + x^35*y*z0^2 - x^35*z0^3 - 2*x^33*y*z0^4 + x^36*z0 - x^32*y*z0^4 + 2*x^35*y + 2*x^35*z0 - 2*x^33*y*z0^2 - x^33*z0^3 + x^31*y*z0^4 + 2*x^34*y - x^34*z0 - x^32*y*z0^2 - x^32*z0^3 + x^30*y*z0^4 - 2*x^33*y - x^31*y*z0^2 - 2*x^31*z0^3 + 2*x^29*y*z0^4 + x^32*y - 2*x^30*y*z0^2 + x^28*y*z0^4 + x^31*y - x^31*z0 - x^29*y*z0^2 + x^27*y*z0^4 + 2*x^30*y + 2*x^30*z0 - 2*x^28*y*z0^2 + 2*x^28*z0^3 - 2*x^29*z0 - 2*x^27*y*z0^2 - 2*x^27*z0^3 + x^25*y*z0^4 + x^28*z0 - x^26*y*z0^2 + x^24*y*z0^4 - x^27*y - x^25*y*z0^2 - x^25*z0^3 - x^23*y*z0^4 - 2*x^26*z0 - 2*x^24*y*z0^2 + 2*x^24*z0^3 + x^22*y*z0^4 + x^25*y - 2*x^23*z0^3 - x^21*y*z0^4 + 2*x^24*y + 2*x^22*y*z0^2 - 2*x^22*z0^3 - x^20*y*z0^4 + x^23*y + x^21*y*z0^2 + 2*x^21*z0^3 - x^19*y*z0^4 + x^22*y - 2*x^20*y*z0^2 + x^20*z0^3 + 2*x^18*y*z0^4 - 2*x^21*y - 2*x^19*y*z0^2 + 2*x^19*z0^3 - x^17*y*z0^4 + x^18*y*z0^2 - x^18*z0^3 - 2*x^16*y*z0^4 + 2*x^19*y - x^19*z0 + x^17*y*z0^2 - x^17*z0^3 + 2*x^18*y + 2*x^16*y*z0^2 - x^16*z0^3 + 2*x^15*y*z0^2 + 2*x^15*z0^3 + x^13*y*z0^4 - 2*x^16*y - 2*x^14*y*z0^2 + 2*x^14*z0^3 - 2*x^12*y*z0^4 - x^15*z0 + 2*x^13*y*z0^2 + x^13*z0^3 + x^14*z0 - 2*x^12*z0^3 - x^10*y*z0^4 - 2*x^13*y - 2*x^13*z0 - x^11*y*z0^2 - 2*x^11*z0^3 + 2*x^9*y*z0^4 - x^12*y - 2*x^12*z0 + x^10*y*z0^2 - x^10*z0^3 - x^11*y - x^11*z0 + x^9*y*z0^2 - x^9*z0^3 + x^10*y + 2*x^10*z0 - 2*x^8*y*z0^2 - 2*x^8*z0^3 - x^9*y + x^9*z0 - 2*x^8*y - x^8*z0 + 2*x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^7*y - x^5*y*z0^2 + x^5*z0^3 + 2*x^3*y*z0^4 + x^6*y + 2*x^6*z0 - 2*x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^5*y + 2*x^3*z0^3 - 2*x^4*y + x^4*z0 + x^2*y*z0^2 + x^3*y - 2*x^2*y - 2*x^2*z0)/y) * dx, - ((2*x^60*z0^4 - 2*x^61*z0^2 - 2*x^57*y^2*z0^4 + 2*x^58*y^2*z0^2 - 2*x^57*z0^4 + 2*x^58*z0^2 - x^56*z0^4 + x^53*y^2*z0^4 + 2*x^54*z0^4 - 2*x^55*z0^2 + x^53*z0^4 - 2*x^51*z0^4 + 2*x^52*z0^2 - x^50*z0^4 + 2*x^48*z0^4 - 2*x^49*z0^2 + x^47*z0^4 - 2*x^45*z0^4 + 2*x^46*z0^2 - x^44*z0^4 + 2*x^42*z0^4 - 2*x^43*z0^2 + x^41*z0^4 + 2*x^40*z0^4 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - 2*x^39*z0^4 - x^40*y*z0 - 2*x^40*z0^2 - x^38*z0^4 + x^39*y*z0 + 2*x^39*z0^2 - x^37*y*z0^3 + x^37*z0^4 + x^40 - 2*x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 - x^39 + 2*x^37*y*z0 + x^37*z0^2 + x^35*y*z0^3 + x^35*z0^4 - x^36*y*z0 - 2*x^36*z0^2 - 2*x^37 + 2*x^35*y*z0 + x^33*y*z0^3 - 2*x^33*z0^4 - 2*x^34*z0^2 + 2*x^32*y*z0^3 + x^32*z0^4 - 2*x^33*y*z0 - x^33*z0^2 + 2*x^31*y*z0^3 + x^31*z0^4 + 2*x^34 - x^32*y*z0 + x^32*z0^2 - x^30*y*z0^3 - x^33 + x^29*y*z0^3 + x^28*z0^4 + x^29*y*z0 - 2*x^29*z0^2 + x^27*y*z0^3 + x^28*y*z0 - 2*x^28*z0^2 + 2*x^26*y*z0^3 + x^26*z0^4 + x^29 - 2*x^25*y*z0^3 + 2*x^25*z0^4 + 2*x^28 + 2*x^26*y*z0 + x^26*z0^2 + 2*x^24*z0^4 - 2*x^27 + 2*x^25*z0^2 - 2*x^23*z0^4 + 2*x^24*z0^2 - 2*x^22*y*z0^3 - 2*x^22*z0^4 + x^23*y*z0 - 2*x^21*y*z0^3 - 2*x^24 + 2*x^22*y*z0 - x^22*z0^2 - x^20*z0^4 + x^23 - 2*x^21*y*z0 - x^19*y*z0^3 - 2*x^19*z0^4 + x^22 - 2*x^20*z0^2 - x^18*y*z0^3 - 2*x^21 + 2*x^19*y*z0 - 2*x^19*z0^2 - x^17*y*z0^3 + x^17*z0^4 + 2*x^18*z0^2 + x^16*y*z0^3 - x^16*z0^4 + 2*x^19 - x^17*y*z0 + x^15*y*z0^3 - x^15*z0^4 + x^16*y*z0 + x^16*z0^2 + x^14*y*z0^3 - x^14*z0^4 - 2*x^17 - x^15*y*z0 + x^15*z0^2 + 2*x^13*z0^4 + 2*x^16 - 2*x^14*y*z0 + x^14*z0^2 - 2*x^12*y*z0^3 + 2*x^13*y*z0 - 2*x^13*z0^2 + x^11*y*z0^3 + 2*x^11*z0^4 - x^14 + x^12*y*z0 - 2*x^10*y*z0^3 - x^13 + x^11*y*z0 + x^11*z0^2 + 2*x^9*y*z0^3 - 2*x^9*z0^4 + x^12 - 2*x^10*y*z0 - x^8*z0^4 - x^9*y*z0 - x^9*z0^2 + 2*x^7*z0^4 - x^10 + 2*x^8*y*z0 + x^8*z0^2 + 2*x^6*z0^4 - x^7*z0^2 + 2*x^5*y*z0^3 - x^5*z0^4 + 2*x^8 + 2*x^6*y*z0 + 2*x^6*z0^2 + x^4*z0^4 - x^7 - 2*x^5*z0^2 - x^3*y*z0^3 - x^3*z0^4 - 2*x^4*y*z0 + 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + x^3*y*z0 - 2*x^3*z0^2 - x^2*y*z0 + x^2*z0^2 + 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^4 - 2*x^60*z0^4 - x^58*y^2*z0^4 - x^61*z0^2 + 2*x^59*z0^4 + 2*x^57*y^2*z0^4 + 2*x^60*z0^2 + x^58*y^2*z0^2 - x^58*z0^4 - 2*x^56*y^2*z0^4 + x^61 - 2*x^57*y^2*z0^2 + 2*x^57*z0^4 - x^58*y^2 + x^58*z0^2 - 2*x^56*z0^4 - 2*x^57*z0^2 + x^55*z0^4 - x^58 - 2*x^54*z0^4 - x^57 - x^55*z0^2 + 2*x^53*z0^4 + x^54*y^2 + 2*x^54*z0^2 - x^52*z0^4 + x^55 + 2*x^51*z0^4 + x^54 + x^52*z0^2 - 2*x^50*z0^4 - 2*x^51*z0^2 + x^49*z0^4 - x^52 - 2*x^48*z0^4 - x^51 - x^49*z0^2 + 2*x^47*z0^4 + 2*x^48*z0^2 - x^46*z0^4 + x^49 + 2*x^45*z0^4 + x^48 + x^46*z0^2 - 2*x^44*z0^4 - 2*x^45*z0^2 + x^43*z0^4 - x^46 - 2*x^42*z0^4 - x^45 - x^43*z0^2 + x^41*z0^4 + 2*x^42*z0^2 - 2*x^40*y*z0^3 - 2*x^40*z0^4 + x^43 - x^41*z0^2 - x^39*y*z0^3 - x^39*z0^4 + x^42 + 2*x^40*y*z0 + x^40*z0^2 + x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + 2*x^39*y*z0 - x^39*z0^2 + x^37*z0^4 - 2*x^38*z0^2 + 2*x^36*y*z0^3 + x^36*z0^4 + 2*x^39 + x^37*z0^2 + x^35*y*z0^3 + 2*x^38 - x^36*y*z0 + x^36*z0^2 + 2*x^34*y*z0^3 - x^34*z0^4 - 2*x^37 - x^35*y*z0 + x^33*y*z0^3 + x^33*z0^4 - 2*x^34*y*z0 + 2*x^34*z0^2 - x^32*y*z0^3 + 2*x^35 - x^33*y*z0 + x^31*z0^4 - x^34 - x^32*y*z0 - x^32*z0^2 - 2*x^30*y*z0^3 + 2*x^33 - 2*x^31*y*z0 - 2*x^31*z0^2 - x^29*y*z0^3 + x^29*z0^4 - x^32 + 2*x^30*y*z0 + 2*x^30*z0^2 - x^28*z0^4 + x^31 + x^29*y*z0 - x^29*z0^2 + x^27*y*z0^3 - x^26*y*z0^3 - 2*x^26*z0^4 + x^29 + 2*x^27*y*z0 + 2*x^27*z0^2 + 2*x^25*y*z0^3 + x^25*z0^4 + x^28 - x^26*y*z0 - x^26*z0^2 - x^24*y*z0^3 + x^24*z0^4 + x^27 + x^25*y*z0 - x^23*z0^4 + x^26 + 2*x^22*y*z0^3 - 2*x^25 - x^23*y*z0 + x^23*z0^2 + 2*x^21*y*z0^3 - 2*x^21*z0^4 - x^24 + x^21*y*z0 + 2*x^21*z0^2 + x^19*y*z0^3 - x^22 - 2*x^20*y*z0 - 2*x^20*z0^2 - 2*x^18*y*z0^3 - 2*x^18*z0^4 + x^21 + x^19*z0^2 + 2*x^17*y*z0^3 + 2*x^17*z0^4 - x^18*y*z0 + 2*x^18*z0^2 + x^16*y*z0^3 - x^16*z0^4 - x^19 - 2*x^17*y*z0 + 2*x^15*z0^4 + 2*x^16*y*z0 + x^16*z0^2 - x^14*y*z0^3 - 2*x^14*z0^4 - 2*x^17 - 2*x^15*y*z0 + 2*x^15*z0^2 - 2*x^13*y*z0^3 - x^14*z0^2 + x^12*y*z0^3 + x^12*z0^4 - 2*x^15 - 2*x^13*y*z0 + 2*x^11*y*z0^3 - 2*x^11*z0^4 - x^12*y*z0 - x^12*z0^2 + 2*x^10*z0^4 - 2*x^11*y*z0 + 2*x^9*z0^4 - 2*x^10*y*z0 - 2*x^10*z0^2 + x^8*z0^4 + x^11 + x^9*y*z0 - x^9*z0^2 + x^7*y*z0^3 + x^7*z0^4 - 2*x^10 + 2*x^8*y*z0 - x^6*z0^4 + x^9 - x^7*y*z0 - x^7*z0^2 + x^5*z0^4 + x^8 - x^6*y*z0 - x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 - 2*x^5*y*z0 - 2*x^5*z0^2 + x^3*y*z0^3 + x^4*y*z0 + 2*x^4*z0^2 - 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*z0^2 - x^2*y*z0 + x^2*z0^2 - 2*x^2)/y) * dx, - ((x^61*z0^3 - 2*x^60*z0^3 - x^58*y^2*z0^3 - 2*x^61*z0 + x^59*z0^3 + 2*x^57*y^2*z0^3 + x^60*z0 + 2*x^58*y^2*z0 - 2*x^58*z0^3 - x^56*y^2*z0^3 - 2*x^59*z0 - x^57*y^2*z0 + 2*x^57*z0^3 + x^55*y^2*z0^3 + 2*x^58*z0 + 2*x^56*y^2*z0 - x^56*z0^3 - 2*x^57*z0 + 2*x^55*z0^3 + 2*x^56*z0 + x^54*y^2*z0 - 2*x^54*z0^3 - 2*x^55*z0 + x^53*z0^3 + 2*x^54*z0 - 2*x^52*z0^3 - 2*x^53*z0 + 2*x^51*z0^3 + 2*x^52*z0 - x^50*z0^3 - 2*x^51*z0 + 2*x^49*z0^3 + 2*x^50*z0 - 2*x^48*z0^3 - 2*x^49*z0 + x^47*z0^3 + 2*x^48*z0 - 2*x^46*z0^3 - 2*x^47*z0 + 2*x^45*z0^3 + 2*x^46*z0 - x^44*z0^3 - 2*x^45*z0 + 2*x^43*z0^3 + 2*x^44*z0 - 2*x^42*z0^3 - 2*x^43*z0 + 2*x^41*z0^3 + x^39*y*z0^4 + 2*x^42*z0 - 2*x^40*y*z0^2 - 2*x^40*z0^3 + x^38*y*z0^4 + x^41*z0 - 2*x^39*y*z0^2 + x^39*z0^3 - 2*x^37*y*z0^4 - x^40*y + x^40*z0 + 2*x^38*z0^3 + x^39*z0 + 2*x^37*y*z0^2 + 2*x^37*z0^3 + x^38*z0 + 2*x^36*z0^3 + 2*x^34*y*z0^4 - 2*x^37*y + 2*x^37*z0 - x^35*z0^3 + x^33*y*z0^4 - x^36*y - 2*x^36*z0 - x^34*y*z0^2 - 2*x^34*z0^3 - 2*x^35*z0 - 2*x^33*y*z0^2 - x^33*z0^3 - 2*x^31*y*z0^4 + x^34*y + x^34*z0 - x^32*y*z0^2 + 2*x^32*z0^3 - x^33*y + x^33*z0 + x^29*y*z0^4 + 2*x^32*y + 2*x^32*z0 - x^30*y*z0^2 + x^30*z0^3 - x^28*y*z0^4 + 2*x^31*y - x^31*z0 - x^29*z0^3 + x^27*y*z0^4 - 2*x^30*z0 + 2*x^28*y*z0^2 + x^26*y*z0^4 - 2*x^29*z0 + x^27*y*z0^2 + 2*x^25*y*z0^4 + x^28*y + x^28*z0 + x^26*y*z0^2 - 2*x^24*y*z0^4 - 2*x^27*y - x^27*z0 + 2*x^23*y*z0^4 - x^26*y + 2*x^26*z0 + 2*x^24*z0^3 + x^22*y*z0^4 + x^25*y + 2*x^25*z0 + 2*x^23*y*z0^2 + x^23*z0^3 - x^21*y*z0^4 - x^24*y + x^24*z0 - 2*x^22*y*z0^2 - x^20*y*z0^4 + x^23*y - x^23*z0 - 2*x^19*y*z0^4 - 2*x^22*y - x^22*z0 - x^20*y*z0^2 - 2*x^20*z0^3 + x^18*y*z0^4 - 2*x^21*y - 2*x^21*z0 + x^19*y*z0^2 - 2*x^19*z0^3 - x^17*y*z0^4 - x^20*y + x^20*z0 + 2*x^18*y*z0^2 + x^18*z0^3 + 2*x^16*y*z0^4 + 2*x^19*y - 2*x^19*z0 - 2*x^17*y*z0^2 + 2*x^17*z0^3 - 2*x^15*y*z0^4 - 2*x^18*y - 2*x^18*z0 - x^16*y*z0^2 - x^16*z0^3 - x^14*y*z0^4 - 2*x^15*y*z0^2 + x^15*z0^3 + x^13*y*z0^4 - x^16*y - 2*x^14*z0^3 - 2*x^12*y*z0^4 - 2*x^15*y + 2*x^15*z0 + 2*x^13*y*z0^2 - x^13*z0^3 + x^14*y + x^14*z0 - x^12*y*z0^2 - x^10*y*z0^4 + x^13*z0 - x^11*y*z0^2 + 2*x^9*y*z0^4 + x^12*y - 2*x^12*z0 + 2*x^10*y*z0^2 - x^10*z0^3 + x^8*y*z0^4 + x^11*y - 2*x^9*y*z0^2 + 2*x^9*z0^3 + 2*x^10*y + x^10*z0 + 2*x^8*y*z0^2 + x^8*z0^3 - 2*x^6*y*z0^4 - 2*x^9*y - 2*x^9*z0 + x^7*y*z0^2 - x^7*z0^3 - 2*x^8*y - 2*x^8*z0 - 2*x^6*y*z0^2 - x^6*z0^3 - x^4*y*z0^4 + 2*x^7*y + 2*x^7*z0 - x^5*y*z0^2 + x^3*y*z0^4 - x^6*y - 2*x^4*y*z0^2 + x^4*z0^3 - 2*x^2*y*z0^4 - x^5*y + x^5*z0 + 2*x^3*z0^3 + 2*x^4*y + x^4*z0 - 2*x^2*z0^3 + x^3*y + 2*x^2*y)/y) * dx, - ((x^61*z0^4 - x^60*z0^4 - x^58*y^2*z0^4 + 2*x^61*z0^2 - x^59*z0^4 + x^57*y^2*z0^4 - 2*x^60*z0^2 - 2*x^58*y^2*z0^2 - x^58*z0^4 + x^56*y^2*z0^4 + 2*x^61 + 2*x^57*y^2*z0^2 + x^57*z0^4 - x^60 - 2*x^58*y^2 - 2*x^58*z0^2 + x^56*z0^4 + x^57*y^2 + x^57*z0^2 + x^55*z0^4 - 2*x^58 + x^54*y^2*z0^2 - x^54*z0^4 + x^57 + 2*x^55*z0^2 - x^53*z0^4 - x^54*z0^2 - x^52*z0^4 + 2*x^55 + x^51*z0^4 - x^54 - 2*x^52*z0^2 + x^50*z0^4 + x^51*z0^2 + x^49*z0^4 - 2*x^52 - x^48*z0^4 + x^51 + 2*x^49*z0^2 - x^47*z0^4 - x^48*z0^2 - x^46*z0^4 + 2*x^49 + x^45*z0^4 - x^48 - 2*x^46*z0^2 + x^44*z0^4 + x^45*z0^2 + x^43*z0^4 - 2*x^46 - x^42*z0^4 + x^45 + 2*x^43*z0^2 + x^41*z0^4 - x^42*z0^2 - 2*x^40*y*z0^3 + x^40*z0^4 + 2*x^43 + 2*x^41*z0^2 + 2*x^39*y*z0^3 - x^39*z0^4 - x^42 + x^40*y*z0 - 2*x^40*z0^2 - x^38*y*z0^3 - x^38*z0^4 + 2*x^41 + x^39*y*z0 - x^39*z0^2 - x^37*y*z0^3 + x^37*z0^4 + 2*x^40 + x^38*y*z0 - x^38*z0^2 + x^36*y*z0^3 - x^36*z0^4 + 2*x^39 + x^37*z0^2 - 2*x^35*y*z0^3 + 2*x^38 - 2*x^36*y*z0 + x^36*z0^2 - x^34*y*z0^3 - 2*x^37 - 2*x^35*y*z0 - 2*x^35*z0^2 - x^33*y*z0^3 - 2*x^33*z0^4 + 2*x^36 + 2*x^34*y*z0 - x^32*y*z0^3 - x^32*z0^4 + x^33*y*z0 + x^33*z0^2 - 2*x^31*y*z0^3 - 2*x^34 - x^32*y*z0 - 2*x^32*z0^2 - x^30*y*z0^3 + x^30*z0^4 + 2*x^31*y*z0 - x^29*y*z0^3 + 2*x^29*z0^4 - 2*x^30*z0^2 - 2*x^28*y*z0^3 + 2*x^28*z0^4 + 2*x^29*y*z0 - x^29*z0^2 + x^27*y*z0^3 + x^27*z0^4 + 2*x^30 + 2*x^28*z0^2 + 2*x^26*y*z0^3 + 2*x^26*z0^4 - 2*x^29 - x^27*y*z0 - x^27*z0^2 + x^25*y*z0^3 - 2*x^25*z0^4 + 2*x^28 + x^26*y*z0 - 2*x^24*y*z0^3 - x^24*z0^4 - 2*x^27 + x^25*y*z0 - x^25*z0^2 - x^23*y*z0^3 - x^23*z0^4 + x^26 - x^24*z0^2 + x^22*y*z0^3 - x^22*z0^4 + x^25 - 2*x^23*y*z0 + 2*x^21*y*z0^3 - 2*x^24 - x^22*y*z0 + 2*x^22*z0^2 + 2*x^20*y*z0^3 + 2*x^20*z0^4 - x^21*y*z0 - x^21*z0^2 - 2*x^19*y*z0^3 + x^19*z0^4 + 2*x^22 + 2*x^20*z0^2 - 2*x^18*y*z0^3 + 2*x^18*z0^4 - x^21 - 2*x^19*y*z0 - x^19*z0^2 - x^17*y*z0^3 + 2*x^17*z0^4 - x^20 + x^18*y*z0 - x^18*z0^2 + x^16*y*z0^3 - x^16*z0^4 + x^17*y*z0 + x^17*z0^2 + x^15*y*z0^3 - x^15*z0^4 - 2*x^16*z0^2 - 2*x^14*y*z0^3 + x^14*z0^4 + 2*x^17 - 2*x^15*y*z0 + 2*x^15*z0^2 + x^13*y*z0^3 - 2*x^13*z0^4 + x^16 + 2*x^14*y*z0 - x^14*z0^2 - x^12*y*z0^3 - 2*x^12*z0^4 - 2*x^15 + x^13*y*z0 + 2*x^13*z0^2 - x^11*y*z0^3 - 2*x^11*z0^4 + 2*x^12*y*z0 - x^10*y*z0^3 + x^10*z0^4 + 2*x^13 + 2*x^11*y*z0 - 2*x^11*z0^2 + 2*x^9*y*z0^3 - 2*x^12 + 2*x^10*z0^2 + x^8*y*z0^3 - x^8*z0^4 - 2*x^11 - x^9*z0^2 + x^7*y*z0^3 - x^7*z0^4 + x^10 - x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 - 2*x^9 + 2*x^7*z0^2 + 2*x^5*y*z0^3 + 2*x^5*z0^4 - x^8 - 2*x^6*z0^2 - x^4*y*z0^3 + 2*x^4*z0^4 - x^7 + 2*x^5*y*z0 - x^5*z0^2 - 2*x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 + 2*x^3*z0^2 - x^2*y*z0 - x^3 + 2*x^2)/y) * dx, - ((x^61*z0^4 - x^58*y^2*z0^4 - x^60*z0^2 - x^58*z0^4 + 2*x^61 + x^57*y^2*z0^2 - x^57*z0^4 - 2*x^60 - 2*x^58*y^2 + x^54*y^2*z0^4 + 2*x^57*y^2 + x^57*z0^2 + x^55*z0^4 - 2*x^58 + x^54*z0^4 + 2*x^57 - x^54*z0^2 - x^52*z0^4 + 2*x^55 - x^51*z0^4 - 2*x^54 + x^51*z0^2 + x^49*z0^4 - 2*x^52 + x^48*z0^4 + 2*x^51 - x^48*z0^2 - x^46*z0^4 + 2*x^49 - x^45*z0^4 - 2*x^48 + x^45*z0^2 + x^43*z0^4 - 2*x^46 + x^42*z0^4 + 2*x^45 + 2*x^41*z0^4 - x^42*z0^2 - 2*x^40*y*z0^3 - x^40*z0^4 + 2*x^43 + 2*x^39*z0^4 - 2*x^42 - x^40*z0^2 - 2*x^38*y*z0^3 - x^38*z0^4 + 2*x^41 - x^39*y*z0 + x^39*z0^2 - x^37*y*z0^3 + 2*x^40 + x^38*y*z0 - x^39 - 2*x^37*z0^2 + 2*x^35*y*z0^3 + x^35*z0^4 - x^38 - x^36*z0^2 - x^34*y*z0^3 + 2*x^34*z0^4 - 2*x^37 - 2*x^35*y*z0 - x^35*z0^2 + x^33*y*z0^3 - 2*x^33*z0^4 + x^34*y*z0 + x^34*z0^2 - 2*x^35 - x^33*z0^2 + 2*x^31*y*z0^3 + 2*x^31*z0^4 + x^34 + x^32*y*z0 + 2*x^32*z0^2 + 2*x^30*y*z0^3 - 2*x^30*z0^4 - 2*x^33 - x^31*y*z0 + 2*x^31*z0^2 - x^29*y*z0^3 - x^29*z0^4 + 2*x^30*z0^2 - 2*x^28*y*z0^3 + 2*x^28*z0^4 - 2*x^31 - 2*x^29*y*z0 + 2*x^29*z0^2 + x^27*y*z0^3 - x^30 - 2*x^28*y*z0 - 2*x^26*y*z0^3 + x^26*z0^4 - x^29 - 2*x^27*y*z0 - x^27*z0^2 - x^25*y*z0^3 - 2*x^28 + x^26*y*z0 - 2*x^24*y*z0^3 - 2*x^27 - 2*x^25*y*z0 + x^25*z0^2 - x^23*y*z0^3 - 2*x^23*z0^4 - x^26 - 2*x^24*y*z0 + x^24*z0^2 - 2*x^22*y*z0^3 + 2*x^22*z0^4 + 2*x^25 - x^23*y*z0 - 2*x^23*z0^2 + x^21*y*z0^3 - x^21*z0^4 + x^24 - 2*x^22*y*z0 - 2*x^20*z0^4 + 2*x^23 + x^21*y*z0 - 2*x^21*z0^2 - 2*x^19*z0^4 - 2*x^22 - 2*x^20*y*z0 + 2*x^20*z0^2 - x^18*y*z0^3 + x^18*z0^4 - x^21 - x^19*y*z0 - x^19*z0^2 + 2*x^17*z0^4 - x^20 + x^18*y*z0 + 2*x^16*y*z0^3 + x^19 - x^17*y*z0 + 2*x^17*z0^2 - x^15*y*z0^3 - x^15*z0^4 + 2*x^18 - x^16*y*z0 - x^16*z0^2 - x^14*z0^4 + x^17 + x^15*y*z0 - 2*x^15*z0^2 - 2*x^13*y*z0^3 - x^13*z0^4 - x^14*y*z0 - 2*x^14*z0^2 + 2*x^12*y*z0^3 - x^12*z0^4 + x^13*y*z0 - x^13*z0^2 + 2*x^11*y*z0^3 - x^11*z0^4 + x^14 + 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 + 2*x^11*y*z0 - 2*x^11*z0^2 - 2*x^9*y*z0^3 + x^9*z0^4 - x^10*z0^2 - x^8*y*z0^3 - 2*x^8*z0^4 + 2*x^11 + x^9*y*z0 + x^7*y*z0^3 - 2*x^7*z0^4 + x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 + 2*x^6*y*z0^3 - x^6*z0^4 + x^9 - x^7*y*z0 + x^7*z0^2 - 2*x^5*y*z0^3 - x^8 - x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + 2*x^5*z0^2 - x^3*y*z0^3 - x^3*z0^4 - 2*x^6 + 2*x^4*y*z0 - 2*x^4*z0^2 + 2*x^2*y*z0^3 - x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 + 2*x^3 - 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^61*z0^4 - x^60*z0^4 + x^58*y^2*z0^4 - 2*x^61*z0^2 + x^59*z0^4 + x^57*y^2*z0^4 + 2*x^58*y^2*z0^2 + x^58*z0^4 - x^56*y^2*z0^4 + 2*x^61 + x^57*z0^4 - x^60 - 2*x^58*y^2 + 2*x^58*z0^2 - x^56*z0^4 + x^57*y^2 - x^55*z0^4 + 2*x^58 - x^54*z0^4 + x^57 + x^55*y^2 - 2*x^55*z0^2 + x^53*z0^4 + x^52*z0^4 - 2*x^55 + x^51*z0^4 - x^54 + 2*x^52*z0^2 - x^50*z0^4 - x^49*z0^4 + 2*x^52 - x^48*z0^4 + x^51 - 2*x^49*z0^2 + x^47*z0^4 + x^46*z0^4 - 2*x^49 + x^45*z0^4 - x^48 + 2*x^46*z0^2 - x^44*z0^4 - x^43*z0^4 + 2*x^46 - x^42*z0^4 + x^45 - 2*x^43*z0^2 + x^41*z0^4 + 2*x^40*y*z0^3 - x^40*z0^4 - 2*x^43 - 2*x^41*z0^2 - 2*x^39*y*z0^3 - x^42 - x^40*y*z0 - x^40*z0^2 + 2*x^38*y*z0^3 + 2*x^39*y*z0 + 2*x^39*z0^2 + 2*x^37*y*z0^3 + x^37*z0^4 + x^40 + x^38*y*z0 + x^38*z0^2 - x^36*y*z0^3 - x^36*z0^4 - x^37*y*z0 + 2*x^35*y*z0^3 - x^35*z0^4 + 2*x^38 - 2*x^36*z0^2 + x^34*z0^4 + 2*x^37 + 2*x^35*y*z0 + x^35*z0^2 + x^33*y*z0^3 + 2*x^33*z0^4 + 2*x^36 - 2*x^32*y*z0^3 - 2*x^35 + 2*x^33*y*z0 - x^33*z0^2 - x^31*y*z0^3 - x^34 - x^32*y*z0 - 2*x^32*z0^2 - 2*x^30*y*z0^3 + 2*x^33 + x^31*y*z0 - x^29*y*z0^3 - x^29*z0^4 + 2*x^32 - x^30*y*z0 + 2*x^30*z0^2 + x^28*y*z0^3 - 2*x^28*z0^4 - x^31 + x^29*y*z0 - 2*x^29*z0^2 + 2*x^27*z0^4 + 2*x^30 - 2*x^28*y*z0 - 2*x^28*z0^2 - x^26*y*z0^3 + 2*x^26*z0^4 + x^29 - 2*x^27*y*z0 + x^27*z0^2 + x^25*y*z0^3 - x^25*z0^4 + x^28 + x^26*y*z0 + 2*x^26*z0^2 - 2*x^27 - 2*x^25*y*z0 + 2*x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 + 2*x^26 + 2*x^24*y*z0 - 2*x^22*y*z0^3 - x^22*z0^4 + x^25 + 2*x^23*y*z0 + 2*x^23*z0^2 + x^21*y*z0^3 + 2*x^24 - x^22*y*z0 + x^22*z0^2 + x^20*y*z0^3 + x^20*z0^4 + 2*x^23 - x^21*z0^2 - 2*x^19*y*z0^3 - x^19*z0^4 + x^22 - 2*x^20*y*z0 - 2*x^21 - 2*x^19*y*z0 + 2*x^19*z0^2 + 2*x^17*z0^4 - 2*x^20 + 2*x^18*y*z0 - 2*x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^19 + 2*x^17*y*z0 - 2*x^17*z0^2 + x^15*y*z0^3 + 2*x^15*z0^4 - 2*x^18 - 2*x^16*y*z0 + x^16*z0^2 - 2*x^14*y*z0^3 + x^14*z0^4 + x^17 + x^13*z0^4 + x^16 + 2*x^14*z0^2 - x^12*y*z0^3 + x^12*z0^4 + x^15 - x^13*y*z0 - 2*x^13*z0^2 + 2*x^11*y*z0^3 - 2*x^11*z0^4 + 2*x^14 + 2*x^12*y*z0 + x^12*z0^2 + 2*x^13 + x^11*y*z0 - x^11*z0^2 + 2*x^9*z0^4 + 2*x^10*y*z0 + x^10*z0^2 + x^8*y*z0^3 - x^11 + x^9*y*z0 - x^9*z0^2 - 2*x^7*y*z0^3 + x^7*z0^4 - x^10 - 2*x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 + 2*x^9 - 2*x^7*z0^2 - x^5*y*z0^3 - 2*x^5*z0^4 - x^6*y*z0 - x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 - x^7 - 2*x^5*z0^2 - x^3*y*z0^3 - x^3*z0^4 - x^4*y*z0 + x^4*z0^2 - 2*x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^3*z0^2 - x^2*y*z0 + x^2*z0^2 - x^3 - x^2)/y) * dx, - ((2*x^61*z0^3 - 2*x^58*y^2*z0^3 - 2*x^61*z0 - x^60*z0 + 2*x^58*y^2*z0 + x^58*z0^3 - 2*x^59*z0 + x^57*y^2*z0 + 2*x^55*y^2*z0^3 + x^58*z0 + 2*x^56*y^2*z0 + x^57*z0 + x^55*y^2*z0 - x^55*z0^3 + 2*x^56*z0 - x^55*z0 - x^54*z0 + x^52*z0^3 - 2*x^53*z0 + x^52*z0 + x^51*z0 - x^49*z0^3 + 2*x^50*z0 - x^49*z0 - x^48*z0 + x^46*z0^3 - 2*x^47*z0 + x^46*z0 + x^45*z0 - x^43*z0^3 + 2*x^44*z0 - x^43*z0 + 2*x^41*z0^3 + 2*x^39*y*z0^4 - x^42*z0 + x^40*y*z0^2 + 2*x^40*z0^3 - x^38*y*z0^4 + x^41*z0 - 2*x^39*y*z0^2 + x^39*z0^3 - 2*x^37*y*z0^4 - x^40*y - 2*x^40*z0 - x^38*y*z0^2 - x^38*z0^3 + x^36*y*z0^4 + 2*x^39*y - x^39*z0 + 2*x^37*z0^3 - 2*x^35*y*z0^4 + x^38*z0 - x^36*z0^3 - 2*x^37*y - 2*x^37*z0 + 2*x^35*y*z0^2 + 2*x^35*z0^3 - 2*x^33*y*z0^4 + x^36*y + x^34*y*z0^2 - 2*x^34*z0^3 - x^32*y*z0^4 - 2*x^35*y - 2*x^35*z0 - x^33*y*z0^2 + 2*x^33*z0^3 + x^31*y*z0^4 + 2*x^34*z0 + x^32*y*z0^2 + 2*x^32*z0^3 + 2*x^30*y*z0^4 + x^33*y - x^33*z0 + x^31*y*z0^2 - x^31*z0^3 + x^29*y*z0^4 + x^32*y - 2*x^32*z0 + x^30*y*z0^2 - x^28*y*z0^4 + 2*x^31*y - x^31*z0 - x^29*y*z0^2 - x^29*z0^3 - x^27*y*z0^4 + 2*x^30*y + 2*x^30*z0 - x^28*y*z0^2 - 2*x^28*z0^3 + 2*x^26*y*z0^4 + x^29*y + 2*x^29*z0 + x^27*y*z0^2 + x^27*z0^3 + 2*x^25*y*z0^4 + x^26*y*z0^2 + x^26*z0^3 - x^25*y*z0^2 + x^25*z0^3 - 2*x^23*y*z0^4 - 2*x^26*y + 2*x^26*z0 - x^24*y*z0^2 - x^22*y*z0^4 + 2*x^25*y + 2*x^25*z0 + 2*x^23*y*z0^2 - 2*x^23*z0^3 - 2*x^22*z0^3 - x^20*y*z0^4 + 2*x^23*y + 2*x^23*z0 + 2*x^21*y*z0^2 + x^19*y*z0^4 + 2*x^22*y - 2*x^22*z0 + x^20*y*z0^2 - x^20*z0^3 + 2*x^18*y*z0^4 + x^21*y + 2*x^21*z0 + x^19*y*z0^2 + x^19*z0^3 + x^20*y + x^20*z0 - 2*x^18*y*z0^2 + x^18*z0^3 + x^16*y*z0^4 - x^19*z0 - x^17*y*z0^2 - 2*x^17*z0^3 + 2*x^15*y*z0^4 + x^16*y*z0^2 - x^14*y*z0^4 - x^17*z0 - 2*x^15*y*z0^2 - 2*x^15*z0^3 - x^13*y*z0^4 + 2*x^16*y + x^16*z0 - x^14*y*z0^2 - 2*x^14*z0^3 - x^12*y*z0^4 + x^15*y - x^15*z0 + 2*x^13*y*z0^2 - x^13*z0^3 + x^11*y*z0^4 - x^14*y - x^14*z0 + 2*x^12*y*z0^2 - 2*x^10*y*z0^4 + x^13*y + 2*x^13*z0 - 2*x^11*y*z0^2 - x^11*z0^3 - 2*x^9*y*z0^4 - x^12*y + 2*x^12*z0 - 2*x^10*y*z0^2 + 2*x^10*z0^3 - x^8*y*z0^4 - 2*x^11*y + x^9*y*z0^2 + 2*x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y - 2*x^10*z0 - 2*x^6*y*z0^4 + 2*x^9*y + 2*x^9*z0 - x^5*y*z0^4 - x^8*y + x^8*z0 + x^6*y*z0^2 - x^6*z0^3 - 2*x^4*y*z0^4 + 2*x^7*z0 - 2*x^5*y*z0^2 - x^5*z0^3 + x^3*y*z0^4 + 2*x^6*y - 2*x^6*z0 + x^4*y*z0^2 + x^4*z0^3 + x^5*y - x^3*y*z0^2 + x^3*z0^3 - x^4*y + x^4*z0 - x^2*y*z0^2 + x^2*z0^3 + x^3*y - 2*x^3*z0 - x^2*y)/y) * dx, - ((-2*x^61*z0^4 - 2*x^60*z0^4 + 2*x^58*y^2*z0^4 + 2*x^57*y^2*z0^4 + 2*x^58*z0^4 + x^61 + 2*x^57*z0^4 - 2*x^60 - x^58*y^2 - x^58*z0^2 + 2*x^57*y^2 + x^55*y^2*z0^2 - 2*x^55*z0^4 - x^58 - 2*x^54*z0^4 + 2*x^57 + x^55*z0^2 + 2*x^52*z0^4 + x^55 + 2*x^51*z0^4 - 2*x^54 - x^52*z0^2 - 2*x^49*z0^4 - x^52 - 2*x^48*z0^4 + 2*x^51 + x^49*z0^2 + 2*x^46*z0^4 + x^49 + 2*x^45*z0^4 - 2*x^48 - x^46*z0^2 - 2*x^43*z0^4 - x^46 - 2*x^42*z0^4 + 2*x^45 + x^43*z0^2 + x^41*z0^4 - x^40*y*z0^3 + 2*x^40*z0^4 + x^43 - x^39*z0^4 - 2*x^42 + 2*x^40*z0^2 + 2*x^38*y*z0^3 + 2*x^38*z0^4 + x^41 + x^39*y*z0 - 2*x^37*y*z0^3 - x^37*z0^4 - x^40 + 2*x^38*y*z0 - 2*x^36*z0^4 + x^39 - x^37*y*z0 + 2*x^37*z0^2 - 2*x^35*y*z0^3 - x^35*z0^4 + 2*x^38 + 2*x^36*y*z0 - 2*x^34*z0^4 - x^35*y*z0 + 2*x^35*z0^2 - 2*x^33*y*z0^3 + 2*x^34*y*z0 - 2*x^34*z0^2 - 2*x^32*z0^4 + x^35 - x^33*y*z0 + 2*x^33*z0^2 + x^31*y*z0^3 + 2*x^31*z0^4 + x^34 + x^32*y*z0 + x^32*z0^2 - x^33 + x^31*y*z0 - 2*x^29*y*z0^3 + 2*x^29*z0^4 - x^32 - 2*x^30*y*z0 + x^30*z0^2 - 2*x^31 + x^29*y*z0 + 2*x^29*z0^2 - 2*x^27*y*z0^3 - x^27*z0^4 + x^30 - x^28*y*z0 - 2*x^26*y*z0^3 + 2*x^27*y*z0 + 2*x^27*z0^2 - x^25*y*z0^3 - 2*x^28 + x^26*y*z0 + 2*x^24*z0^4 - x^27 + 2*x^25*y*z0 + x^25*z0^2 - x^23*y*z0^3 + x^23*z0^4 + 2*x^26 + 2*x^24*y*z0 - x^24*z0^2 + 2*x^22*y*z0^3 - x^22*z0^4 + 2*x^25 + 2*x^23*y*z0 - 2*x^23*z0^2 + x^21*y*z0^3 + x^21*z0^4 - x^24 - 2*x^22*y*z0 + x^20*y*z0^3 - 2*x^20*z0^4 + x^23 - x^21*y*z0 - 2*x^21*z0^2 - 2*x^22 + x^20*y*z0 - 2*x^20*z0^2 + 2*x^18*z0^4 - 2*x^19*y*z0 + x^19*z0^2 + x^17*y*z0^3 - 2*x^17*z0^4 + x^20 - 2*x^18*y*z0 + x^18*z0^2 + x^16*y*z0^3 - x^16*z0^4 - x^19 + 2*x^17*y*z0 - 2*x^17*z0^2 - x^15*y*z0^3 - 2*x^15*z0^4 - x^18 - 2*x^16*y*z0 - 2*x^16*z0^2 + x^14*y*z0^3 + 2*x^15*y*z0 - x^15*z0^2 - 2*x^13*y*z0^3 + 2*x^13*z0^4 + 2*x^16 + x^14*y*z0 + 2*x^14*z0^2 + 2*x^12*y*z0^3 - x^12*z0^4 + 2*x^15 - x^13*y*z0 + x^13*z0^2 - 2*x^11*y*z0^3 - 2*x^11*z0^4 - 2*x^14 - 2*x^12*y*z0 - x^12*z0^2 - 2*x^10*y*z0^3 - 2*x^10*z0^4 - 2*x^13 + x^11*y*z0 + 2*x^11*z0^2 + x^9*y*z0^3 - x^9*z0^4 + x^12 + x^10*y*z0 + 2*x^10*z0^2 + 2*x^8*y*z0^3 - x^8*z0^4 - x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 - x^8*y*z0 + x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 + 2*x^7*z0^2 + x^5*y*z0^3 + 2*x^5*z0^4 - 2*x^8 + 2*x^6*y*z0 + x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 + x^7 + 2*x^5*y*z0 + 2*x^5*z0^2 + x^3*y*z0^3 + x^3*z0^4 - x^6 - 2*x^4*y*z0 - 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 + 2*x^3 - 2*x^2)/y) * dx, - ((2*x^61*z0^4 - 2*x^60*z0^4 - 2*x^58*y^2*z0^4 + x^61*z0^2 - x^59*z0^4 + 2*x^57*y^2*z0^4 + 2*x^60*z0^2 - x^58*y^2*z0^2 + 2*x^58*z0^4 + x^56*y^2*z0^4 - 2*x^61 - 2*x^57*y^2*z0^2 + 2*x^57*z0^4 + x^55*y^2*z0^4 - x^60 + 2*x^58*y^2 - x^58*z0^2 + x^56*z0^4 + x^57*y^2 - 2*x^57*z0^2 - 2*x^55*z0^4 + 2*x^58 - 2*x^54*z0^4 + x^57 + x^55*z0^2 - x^53*z0^4 + 2*x^54*z0^2 + 2*x^52*z0^4 - 2*x^55 + 2*x^51*z0^4 - x^54 - x^52*z0^2 + x^50*z0^4 - 2*x^51*z0^2 - 2*x^49*z0^4 + 2*x^52 - 2*x^48*z0^4 + x^51 + x^49*z0^2 - x^47*z0^4 + 2*x^48*z0^2 + 2*x^46*z0^4 - 2*x^49 + 2*x^45*z0^4 - x^48 - x^46*z0^2 + x^44*z0^4 - 2*x^45*z0^2 - 2*x^43*z0^4 + 2*x^46 - 2*x^42*z0^4 + x^45 + x^43*z0^2 + 2*x^42*z0^2 + x^40*y*z0^3 + x^40*z0^4 - 2*x^43 + x^41*z0^2 + x^39*y*z0^3 - 2*x^39*z0^4 - x^42 - 2*x^40*y*z0 - x^40*z0^2 - x^38*y*z0^3 + 2*x^38*z0^4 + x^41 + x^39*y*z0 + 2*x^39*z0^2 + 2*x^37*z0^4 + x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - 2*x^39 - 2*x^37*y*z0 + x^37*z0^2 + x^35*y*z0^3 + x^35*z0^4 - 2*x^36*z0^2 + 2*x^34*y*z0^3 - 2*x^37 - x^35*y*z0 - 2*x^35*z0^2 + 2*x^33*y*z0^3 + 2*x^33*z0^4 - x^34*y*z0 + 2*x^34*z0^2 + x^32*z0^4 + x^35 + 2*x^33*y*z0 - 2*x^33*z0^2 + x^31*z0^4 - 2*x^32*y*z0 + x^30*y*z0^3 + 2*x^30*z0^4 + 2*x^33 + x^31*y*z0 - 2*x^31*z0^2 - 2*x^29*y*z0^3 + x^29*z0^4 - x^32 - 2*x^30*y*z0 - 2*x^30*z0^2 - 2*x^31 - 2*x^29*y*z0 + 2*x^29*z0^2 + x^27*y*z0^3 - x^27*z0^4 + x^30 - 2*x^28*y*z0 + 2*x^28*z0^2 + x^26*y*z0^3 - x^29 - 2*x^27*y*z0 - x^27*z0^2 - x^25*y*z0^3 + x^25*z0^4 + x^28 + x^26*y*z0 - 2*x^26*z0^2 - x^24*y*z0^3 - x^24*z0^4 - x^27 - 2*x^25*y*z0 + x^23*z0^4 - 2*x^26 - 2*x^24*y*z0 - x^24*z0^2 + 2*x^22*z0^4 - 2*x^25 + x^23*z0^2 + 2*x^21*y*z0^3 - 2*x^21*z0^4 + x^24 - x^22*z0^2 + 2*x^20*y*z0^3 + 2*x^20*z0^4 - x^23 + x^21*y*z0 + x^21*z0^2 + x^19*y*z0^3 - x^19*z0^4 - 2*x^22 + x^20*y*z0 + 2*x^20*z0^2 - x^18*y*z0^3 - x^21 - x^19*y*z0 + x^19*z0^2 + 2*x^17*y*z0^3 - 2*x^17*z0^4 + 2*x^20 - 2*x^18*y*z0 - x^18*z0^2 + x^17*y*z0 - x^15*y*z0^3 + x^15*z0^4 - x^18 - 2*x^16*y*z0 - 2*x^16*z0^2 + x^14*y*z0^3 + 2*x^14*z0^4 - 2*x^17 + 2*x^15*y*z0 - 2*x^13*y*z0^3 + x^16 - x^13*y*z0 + x^13*z0^2 - 2*x^11*z0^4 - x^12*y*z0 - x^12*z0^2 - x^10*y*z0^3 + 2*x^10*z0^4 + 2*x^13 + 2*x^9*y*z0^3 - x^12 + x^10*y*z0 + 2*x^10*z0^2 - x^11 + x^9*y*z0 + x^9*z0^2 + x^7*y*z0^3 + 2*x^7*z0^4 - x^10 + x^8*y*z0 - x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^9 + 2*x^5*y*z0^3 - x^5*z0^4 - x^8 - 2*x^6*z0^2 + 2*x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 + 2*x^5*y*z0 - x^5*z0^2 + 2*x^3*y*z0^3 + 2*x^3*z0^4 + x^6 + x^4*z0^2 - 2*x^2*y*z0^3 + x^2*z0^4 - x^5 - 2*x^3*y*z0 + x^2*z0^2 - x^3)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^61*z0^2 + x^59*z0^4 - x^58*y^2*z0^2 - x^56*y^2*z0^4 - x^61 + 2*x^60 + x^58*y^2 - x^58*z0^2 - x^56*z0^4 - x^59 - 2*x^57*y^2 + x^58 + x^56*y^2 - 2*x^57 + x^55*z0^2 + x^53*z0^4 + x^56 - x^55 + 2*x^54 - x^52*z0^2 - x^50*z0^4 - x^53 + x^52 - 2*x^51 + x^49*z0^2 + x^47*z0^4 + x^50 - x^49 + 2*x^48 - x^46*z0^2 - x^44*z0^4 - x^47 + x^46 - 2*x^45 + x^43*z0^2 - 2*x^41*z0^4 + x^44 + x^40*z0^4 - x^43 + x^41*z0^2 + x^39*y*z0^3 + 2*x^39*z0^4 + 2*x^42 - 2*x^40*y*z0 + 2*x^40*z0^2 + 2*x^38*y*z0^3 - x^38*z0^4 + x^41 - x^39*y*z0 - 2*x^39*z0^2 - 2*x^37*y*z0^3 - 2*x^37*z0^4 + x^40 - 2*x^38*y*z0 + 2*x^38*z0^2 - 2*x^36*y*z0^3 - x^39 + 2*x^37*y*z0 - 2*x^37*z0^2 - x^35*y*z0^3 + 2*x^35*z0^4 + x^38 + 2*x^36*y*z0 + 2*x^36*z0^2 + 2*x^34*z0^4 + 2*x^37 - 2*x^35*y*z0 + 2*x^33*y*z0^3 - 2*x^36 + 2*x^34*y*z0 - x^34*z0^2 + 2*x^32*y*z0^3 + x^35 + 2*x^31*y*z0^3 + x^31*z0^4 - x^34 - x^32*z0^2 + 2*x^30*y*z0^3 + 2*x^30*z0^4 + 2*x^33 - 2*x^31*y*z0 - x^31*z0^2 + 2*x^29*z0^4 - x^32 + 2*x^30*y*z0 + x^31 + x^29*y*z0 + x^29*z0^2 + 2*x^27*y*z0^3 - x^27*z0^4 - 2*x^30 + x^28*y*z0 + 2*x^26*y*z0^3 + 2*x^26*z0^4 + 2*x^27*y*z0 + 2*x^27*z0^2 - 2*x^25*y*z0^3 - x^25*z0^4 + 2*x^28 - 2*x^26*y*z0 + 2*x^26*z0^2 + 2*x^24*z0^4 - x^27 + x^25*z0^2 + x^23*y*z0^3 + 2*x^23*z0^4 - 2*x^26 - 2*x^24*y*z0 - x^24*z0^2 + 2*x^22*y*z0^3 - 2*x^22*z0^4 - 2*x^25 - x^23*y*z0 - x^23*z0^2 - 2*x^21*y*z0^3 - x^24 - x^22*y*z0 + 2*x^22*z0^2 + 2*x^20*z0^4 - x^23 - x^21*y*z0 - x^21*z0^2 - x^19*y*z0^3 + x^19*z0^4 - 2*x^22 - x^20*y*z0 + 2*x^20*z0^2 - x^18*y*z0^3 - 2*x^18*z0^4 - x^21 + x^19*y*z0 + 2*x^19*z0^2 - x^17*y*z0^3 + 2*x^20 - 2*x^18*y*z0 - 2*x^18*z0^2 + x^16*y*z0^3 - x^16*z0^4 + 2*x^19 + x^17*y*z0 - 2*x^15*y*z0^3 + x^15*z0^4 - x^18 + x^16*y*z0 + 2*x^16*z0^2 - x^14*y*z0^3 - 2*x^17 + x^15*y*z0 + x^15*z0^2 - 2*x^13*y*z0^3 - x^13*z0^4 + x^16 - 2*x^14*y*z0 - x^14*z0^2 - x^15 - x^13*y*z0 - 2*x^13*z0^2 - x^11*y*z0^3 + x^14 + x^12*y*z0 - x^10*y*z0^3 + 2*x^13 - x^11*y*z0 + 2*x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 + 2*x^10*z0^2 + x^8*y*z0^3 + x^11 - 2*x^9*z0^2 + 2*x^7*y*z0^3 - x^7*z0^4 + 2*x^10 - x^8*y*z0 + 2*x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 - x^7*z0^2 + 2*x^5*y*z0^3 - x^5*z0^4 + 2*x^8 - 2*x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^5*z0^2 - x^3*y*z0^3 - 2*x^3*z0^4 - x^6 - x^4*z0^2 - 2*x^2*z0^4 + x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0 + 2*x^2*z0^2)/y) * dx, - ((2*x^61*z0^4 + x^60*z0^4 - 2*x^58*y^2*z0^4 + 2*x^61*z0^2 - x^57*y^2*z0^4 - 2*x^58*y^2*z0^2 - 2*x^58*z0^4 - x^61 - x^59*z0^2 - x^57*z0^4 + x^58*y^2 - 2*x^58*z0^2 + x^56*y^2*z0^2 + 2*x^55*z0^4 + x^58 + x^56*z0^2 + x^54*z0^4 + 2*x^55*z0^2 - 2*x^52*z0^4 - x^55 - x^53*z0^2 - x^51*z0^4 - 2*x^52*z0^2 + 2*x^49*z0^4 + x^52 + x^50*z0^2 + x^48*z0^4 + 2*x^49*z0^2 - 2*x^46*z0^4 - x^49 - x^47*z0^2 - x^45*z0^4 - 2*x^46*z0^2 + 2*x^43*z0^4 + x^46 + x^44*z0^2 + x^42*z0^4 + 2*x^43*z0^2 - x^41*z0^4 + x^40*y*z0^3 - 2*x^40*z0^4 - x^43 + x^41*z0^2 + 2*x^39*y*z0^3 + 2*x^39*z0^4 + x^40*y*z0 - x^40*z0^2 + 2*x^38*y*z0^3 - 2*x^38*z0^4 - x^41 + x^39*y*z0 + x^39*z0^2 + x^37*y*z0^3 + x^37*z0^4 - 2*x^40 - 2*x^38*y*z0 - x^38*z0^2 - x^36*y*z0^3 - 2*x^36*z0^4 - x^39 - 2*x^37*y*z0 + x^37*z0^2 - x^35*y*z0^3 - x^35*z0^4 - 2*x^38 + x^36*y*z0 + x^36*z0^2 + x^34*y*z0^3 + x^34*z0^4 + x^37 + 2*x^35*y*z0 - 2*x^33*z0^4 + 2*x^36 - 2*x^34*y*z0 - 2*x^34*z0^2 - x^32*y*z0^3 + x^33*y*z0 - x^33*z0^2 - 2*x^31*y*z0^3 - 2*x^34 - 2*x^32*y*z0 - 2*x^32*z0^2 + 2*x^30*z0^4 + 2*x^33 + 2*x^31*y*z0 - x^31*z0^2 + x^29*y*z0^3 + 2*x^29*z0^4 - x^32 - 2*x^30*y*z0 + 2*x^30*z0^2 - x^28*z0^4 + x^29*y*z0 + x^27*y*z0^3 - 2*x^27*z0^4 + x^30 - 2*x^28*y*z0 + x^28*z0^2 - x^26*y*z0^3 + x^26*z0^4 - x^29 + x^27*y*z0 + 2*x^25*y*z0^3 + 2*x^25*z0^4 + x^28 + x^26*y*z0 + 2*x^26*z0^2 - 2*x^24*y*z0^3 + x^24*z0^4 - x^27 + x^25*y*z0 - 2*x^25*z0^2 - x^23*z0^4 - 2*x^26 + 2*x^24*y*z0 + x^24*z0^2 + 2*x^22*y*z0^3 - x^22*z0^4 + x^21*y*z0^3 + 2*x^21*z0^4 + x^24 + x^22*y*z0 - 2*x^22*z0^2 + 2*x^20*z0^4 + 2*x^23 + x^21*y*z0 + x^21*z0^2 + x^19*y*z0^3 + 2*x^19*z0^4 - x^22 - 2*x^20*y*z0 + 2*x^20*z0^2 - 2*x^18*y*z0^3 - 2*x^18*z0^4 + x^21 - 2*x^19*y*z0 + x^19*z0^2 - x^20 + 2*x^18*y*z0 + 2*x^18*z0^2 - 2*x^16*y*z0^3 + 2*x^16*z0^4 - 2*x^19 - x^17*y*z0 - x^17*z0^2 - x^15*y*z0^3 + x^15*z0^4 + x^18 + x^16*y*z0 + x^16*z0^2 - x^14*y*z0^3 + 2*x^14*z0^4 - x^17 - x^15*y*z0 - 2*x^13*y*z0^3 - x^13*z0^4 - 2*x^14*y*z0 + 2*x^12*y*z0^3 + 2*x^12*z0^4 + 2*x^13*y*z0 - x^13*z0^2 - 2*x^11*y*z0^3 - x^11*z0^4 + 2*x^14 - x^12*z0^2 + 2*x^10*y*z0^3 - x^10*z0^4 - x^13 + 2*x^11*y*z0 - 2*x^11*z0^2 - 2*x^9*y*z0^3 - 2*x^9*z0^4 + x^12 - x^10*z0^2 - x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 + 2*x^9*z0^2 - x^10 - x^8*y*z0 - x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 + x^5*z0^4 + x^8 - x^6*y*z0 - 2*x^4*y*z0^3 - x^4*z0^4 + 2*x^7 + 2*x^5*y*z0 - 2*x^5*z0^2 - x^3*y*z0^3 + x^3*z0^4 - 2*x^6 - x^4*z0^2 + 2*x^2*y*z0^3 - 2*x^2*z0^4 + x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0 - x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llAS.holomorphic_diferentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7llAS.holomorphic_diferentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7llAS.holomorphic_diferentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7l AS.holomorphic_diferentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7l=AS.holomorphic_diferentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7l AS.holomorphic_diferentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l10)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lll = AS.holomorphic_differentials_basis2(threshold = 10) -[?7h[?12l[?25h[?2004lIncrease precision. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll = AS.holomorphic_differentials_basis2(threshold = 10)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: lll -[?7h[?12l[?25h[?2004l[?7h[((2*x^31*z0^3 + 2*x^30*z0^3 - 2*x^28*y^2*z0^3 - 2*x^31*z0 + 2*x^29*z0^3 - 2*x^27*y^2*z0^3 + x^30*z0 + 2*x^28*y^2*z0 - 2*x^28*z0^3 - 2*x^26*y^2*z0^3 - 2*x^29*z0 - x^27*y^2*z0 - x^27*z0^3 + 2*x^26*y^2*z0 - 2*x^26*z0^3 - x^24*y^2*z0^3 - x^27*z0 + 2*x^25*y^2*z0 + 2*x^25*z0^3 + 2*x^26*z0 + x^24*z0^3 + 2*x^23*z0^3 + x^24*z0 - 2*x^22*z0^3 - 2*x^23*z0 - x^21*z0^3 - 2*x^20*z0^3 - x^21*z0 + 2*x^19*z0^3 + 2*x^20*z0 + x^18*z0^3 + 2*x^17*z0^3 + x^18*z0 - 2*x^16*z0^3 - 2*x^17*z0 - x^15*z0^3 - 2*x^14*z0^3 - x^15*z0 + 2*x^13*z0^3 + 2*x^14*z0 + x^12*z0^3 + 2*x^11*z0^3 - 2*x^9*y*z0^4 + x^12*z0 - x^10*y*z0^2 + 2*x^10*z0^3 + 2*x^8*y*z0^4 - 2*x^11*z0 + 2*x^9*y*z0^2 - 2*x^9*z0^3 - 2*x^7*y*z0^4 + x^10*y - 2*x^10*z0 - x^8*y*z0^2 + x^8*z0^3 - x^6*y*z0^4 + 2*x^9*y + x^9*z0 + x^7*z0^3 - 2*x^8*z0 + x^6*y*z0^2 + 2*x^6*z0^3 + 2*x^4*y*z0^4 + x^7*y - x^5*y*z0^2 - x^3*y*z0^4 + 2*x^6*z0 - x^4*y*z0^2 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - x^3*y*z0^2 - x^3*z0^3 + x^2*y*z0^2 + 2*x^2*z0^3 - x^3*y + 2*x^3*z0 - 2*x^2*z0 + y)/y) * dx, - ((-x^30*z0^4 + 2*x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 - 2*x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 - 2*x^31 + x^27*z0^4 + 2*x^28*y^2 - 2*x^28*z0^2 + 2*x^26*z0^4 + 2*x^28 - x^24*z0^4 + 2*x^25*z0^2 - 2*x^23*z0^4 - 2*x^25 + x^21*z0^4 - 2*x^22*z0^2 + 2*x^20*z0^4 + 2*x^22 - x^18*z0^4 + 2*x^19*z0^2 - 2*x^17*z0^4 - 2*x^19 + x^15*z0^4 - 2*x^16*z0^2 + 2*x^14*z0^4 + 2*x^16 - x^12*z0^4 + 2*x^13*z0^2 - x^11*z0^4 - 2*x^10*z0^4 - 2*x^13 - 2*x^9*y*z0^3 + x^9*z0^4 - x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 + x^8*z0^4 - x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 + x^7*y*z0^3 - 2*x^10 - x^8*y*z0 + 2*x^8*z0^2 + 2*x^6*y*z0^3 - x^6*z0^4 + x^7*y*z0 + 2*x^7*z0^2 + x^5*y*z0^3 + 2*x^5*z0^4 + x^8 - x^6*y*z0 + 2*x^6*z0^2 + x^4*z0^4 - x^5*y*z0 - x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^6 - x^4*y*z0 - 2*x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^3*y*z0 - 2*x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 - x^3 - x^2 + y*z0)/y) * dx, - ((-x^31*z0^3 + x^30*z0^3 + x^28*y^2*z0^3 + x^31*z0 - x^29*z0^3 - x^27*y^2*z0^3 - x^30*z0 - x^28*y^2*z0 + x^28*z0^3 + x^26*y^2*z0^3 - x^29*z0 + x^27*y^2*z0 - 2*x^27*z0^3 - x^28*z0 + x^26*y^2*z0 + x^26*z0^3 + x^24*y^2*z0^3 + x^27*z0 - x^25*z0^3 + x^26*z0 + 2*x^24*z0^3 + x^25*z0 - x^23*z0^3 - x^24*z0 + x^22*z0^3 - x^23*z0 - 2*x^21*z0^3 - x^22*z0 + x^20*z0^3 + x^21*z0 - x^19*z0^3 + x^20*z0 + 2*x^18*z0^3 + x^19*z0 - x^17*z0^3 - x^18*z0 + x^16*z0^3 - x^17*z0 - 2*x^15*z0^3 - x^16*z0 + x^14*z0^3 + x^15*z0 - x^13*z0^3 + x^14*z0 + 2*x^12*z0^3 + x^13*z0 - x^11*z0^3 + x^9*y*z0^4 - x^12*z0 - 2*x^10*y*z0^2 + 2*x^10*z0^3 + x^8*y*z0^4 - x^11*z0 - x^9*y*z0^2 + 2*x^9*z0^3 + 2*x^10*y - 2*x^10*z0 - x^8*z0^3 - x^6*y*z0^4 - x^9*y - x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 + 2*x^8*y - 2*x^8*z0 + 2*x^6*y*z0^2 + 2*x^6*z0^3 + 2*x^4*y*z0^4 + 2*x^7*y + x^7*z0 - 2*x^5*y*z0^2 + x^5*z0^3 + 2*x^3*y*z0^4 - x^6*y + 2*x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 + 2*x^2*y*z0^4 - x^5*z0 + x^3*y*z0^2 + 2*x^3*z0^3 - x^4*y + x^3*z0 + x^2*y - x^2*z0 + y*z0^2)/y) * dx, - ((2*x^31*z0^4 + 2*x^30*z0^4 - 2*x^28*y^2*z0^4 - 2*x^27*y^2*z0^4 + x^30*z0^2 - 2*x^28*z0^4 - 2*x^31 - x^27*y^2*z0^2 - 2*x^27*z0^4 + x^30 + 2*x^28*y^2 - x^27*y^2 - x^27*z0^2 + 2*x^25*z0^4 + 2*x^28 + 2*x^24*z0^4 - x^27 + x^24*z0^2 - 2*x^22*z0^4 - 2*x^25 - 2*x^21*z0^4 + x^24 - x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 + 2*x^18*z0^4 - x^21 + x^18*z0^2 - 2*x^16*z0^4 - 2*x^19 - 2*x^15*z0^4 + x^18 - x^15*z0^2 + 2*x^13*z0^4 + 2*x^16 + 2*x^12*z0^4 - x^15 + x^11*z0^4 + x^12*z0^2 - x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - x^9*z0^4 + x^12 - x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 - 2*x^7*y*z0^3 - x^7*z0^4 + 2*x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 - x^6*z0^4 + x^9 + x^7*y*z0 + x^7*z0^2 - 2*x^5*y*z0^3 + 2*x^5*z0^4 + x^8 - x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 - 2*x^4*z0^4 - 2*x^5*y*z0 + x^5*z0^2 + 2*x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^4*y*z0 - x^4*z0^2 + x^2*z0^4 - 2*x^5 - x^3*y*z0 + 2*x^2*y*z0 + 2*x^2*z0^2 + y*z0^3 - 2*x^3 - 2*x^2)/y) * dx, - ((-2*x^29*z0^3 + 2*x^30*z0 + 2*x^26*y^2*z0^3 - x^29*z0 - 2*x^27*y^2*z0 + x^27*z0^3 - x^28*z0 + x^26*y^2*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 - 2*x^27*z0 + x^25*y^2*z0 + x^26*z0 - x^24*z0^3 + x^25*z0 - 2*x^23*z0^3 + 2*x^24*z0 - x^23*z0 + x^21*z0^3 - x^22*z0 + 2*x^20*z0^3 - 2*x^21*z0 + x^20*z0 - x^18*z0^3 + x^19*z0 - 2*x^17*z0^3 + 2*x^18*z0 - x^17*z0 + x^15*z0^3 - x^16*z0 + 2*x^14*z0^3 - 2*x^15*z0 + x^14*z0 - x^12*z0^3 + x^13*z0 - 2*x^11*z0^3 + 2*x^12*z0 - x^11*z0 + 2*x^9*z0^3 + 2*x^10*z0 - 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 + x^5*y*z0^4 + 2*x^8*z0 + x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 + 2*x^7*y - x^7*z0 + x^5*z0^3 + x^3*y*z0^4 - x^6*y - x^6*z0 + 2*x^2*y*z0^4 - 2*x^5*z0 + 2*x^3*z0^3 - x^4*y - x^4*z0 - x^2*y*z0^2 - 2*x^2*z0^3 + y*z0^4 - x^3*y - x^3*z0 - 2*x^2*y + 2*x^2*z0)/y) * dx, - ((-x^3 + y^2)/y) * dx, - ((-x^3*z0 + y^2*z0)/y) * dx, - ((-x^3*z0^2 + y^2*z0^2)/y) * dx, - ((-x^3*z0^3 + y^2*z0^3)/y) * dx, - ((-x^3*z0^4 + y^2*z0^4)/y) * dx, - ((2*x^31*z0^3 + x^30*z0^3 - 2*x^28*y^2*z0^3 - x^31*z0 + 2*x^29*z0^3 - x^27*y^2*z0^3 + x^28*y^2*z0 - 2*x^28*z0^3 - 2*x^26*y^2*z0^3 - x^29*z0 + 2*x^27*z0^3 + x^26*y^2*z0 - 2*x^26*z0^3 + 2*x^24*y^2*z0^3 + x^25*y^2*z0 + 2*x^25*z0^3 + x^26*z0 - 2*x^24*z0^3 + 2*x^23*z0^3 - 2*x^22*z0^3 - x^23*z0 + 2*x^21*z0^3 - 2*x^20*z0^3 + 2*x^19*z0^3 + x^20*z0 - 2*x^18*z0^3 + 2*x^17*z0^3 - 2*x^16*z0^3 - x^17*z0 + 2*x^15*z0^3 - 2*x^14*z0^3 + 2*x^13*z0^3 + x^14*z0 - 2*x^12*z0^3 + 2*x^11*z0^3 - 2*x^9*y*z0^4 - x^10*y*z0^2 - x^10*z0^3 + x^8*y*z0^4 - x^11*z0 + x^9*y*z0^2 - 2*x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y - 2*x^10*z0 - 2*x^8*y*z0^2 - x^8*z0^3 + 2*x^6*y*z0^4 + 2*x^9*y + 2*x^9*z0 + 2*x^7*y*z0^2 - x^7*z0^3 + x^5*y*z0^4 + 2*x^8*y + 2*x^8*z0 + 2*x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^4*y*z0^4 + x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 + 2*x^6*y + 2*x^6*z0 + 2*x^4*y*z0^2 - x^4*z0^3 - 2*x^2*y*z0^4 - x^5*y + x^5*z0 + x^3*z0^3 - x^4*y + 2*x^4*z0 + 2*x^2*z0^3 + 2*x^3*y - 2*x^3*z0 + x^2*y + x^2*z0 + x*y)/y) * dx, - ((x^30*z0^4 + 2*x^31*z0^2 - 2*x^29*z0^4 - x^27*y^2*z0^4 + 2*x^30*z0^2 - 2*x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + x^31 - 2*x^27*y^2*z0^2 - x^27*z0^4 - x^28*y^2 - 2*x^28*z0^2 + 2*x^26*z0^4 - 2*x^27*z0^2 - x^28 + x^24*z0^4 + 2*x^25*z0^2 - 2*x^23*z0^4 + 2*x^24*z0^2 + x^25 - x^21*z0^4 - 2*x^22*z0^2 + 2*x^20*z0^4 - 2*x^21*z0^2 - x^22 + x^18*z0^4 + 2*x^19*z0^2 - 2*x^17*z0^4 + 2*x^18*z0^2 + x^19 - x^15*z0^4 - 2*x^16*z0^2 + 2*x^14*z0^4 - 2*x^15*z0^2 - x^16 + x^12*z0^4 + 2*x^13*z0^2 + 2*x^12*z0^2 + x^10*z0^4 + x^13 - 2*x^9*y*z0^3 - 2*x^9*z0^4 - x^10*y*z0 - 2*x^11 - x^9*y*z0 + x^7*y*z0^3 + x^7*z0^4 - x^10 - 2*x^8*z0^2 - x^6*y*z0^3 - x^6*z0^4 + 2*x^9 - x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 - x^5*z0^4 - 2*x^8 + x^4*y*z0^3 + 2*x^4*z0^4 - x^7 - x^5*y*z0 - x^3*y*z0^3 + 2*x^6 - 2*x^4*y*z0 + x^4*z0^2 + x^2*z0^4 + 2*x^5 + x^3*y*z0 + 2*x^2*z0^2 + x^3 + x*y*z0 - 2*x^2)/y) * dx, - ((-x^31*z0 + 2*x^29*z0^3 + x^28*y^2*z0 - 2*x^26*y^2*z0^3 - x^29*z0 + 2*x^27*z0^3 + x^26*y^2*z0 - 2*x^26*z0^3 - 2*x^24*y^2*z0^3 + x^25*y^2*z0 + x^26*z0 - 2*x^24*z0^3 + 2*x^23*z0^3 - x^23*z0 + 2*x^21*z0^3 - 2*x^20*z0^3 + x^20*z0 - 2*x^18*z0^3 + 2*x^17*z0^3 - x^17*z0 + 2*x^15*z0^3 - 2*x^14*z0^3 + x^14*z0 - 2*x^12*z0^3 + 2*x^11*z0^3 - x^10*z0^3 - x^11*z0 + x^9*y*z0^2 + x^9*z0^3 - x^7*y*z0^4 - 2*x^10*y + x^10*z0 + 2*x^8*y*z0^2 + 2*x^8*z0^3 + x^6*y*z0^4 - x^7*y*z0^2 - x^7*z0^3 - x^5*y*z0^4 - 2*x^8*z0 + x^6*z0^3 - 2*x^4*y*z0^4 - x^7*y - x^7*z0 - x^5*z0^3 + x^3*y*z0^4 - 2*x^6*z0 - x^4*y*z0^2 - x^4*z0^3 - 2*x^2*y*z0^4 - x^5*z0 - 2*x^3*y*z0^2 + 2*x^3*z0^3 - 2*x^4*y + x^4*z0 + 2*x^2*y*z0^2 + x^3*y - x^3*z0 + x*y*z0^2 - 2*x^2*z0)/y) * dx, - ((x^31*z0^4 - x^30*z0^4 - x^28*y^2*z0^4 + 2*x^31*z0^2 - x^29*z0^4 + x^27*y^2*z0^4 - 2*x^28*y^2*z0^2 - x^28*z0^4 + x^26*y^2*z0^4 - 2*x^31 + x^27*z0^4 + 2*x^28*y^2 - 2*x^28*z0^2 + x^26*z0^4 + x^25*z0^4 + 2*x^28 - x^24*z0^4 + 2*x^25*z0^2 - x^23*z0^4 - x^22*z0^4 - 2*x^25 + x^21*z0^4 - 2*x^22*z0^2 + x^20*z0^4 + x^19*z0^4 + 2*x^22 - x^18*z0^4 + 2*x^19*z0^2 - x^17*z0^4 - x^16*z0^4 - 2*x^19 + x^15*z0^4 - 2*x^16*z0^2 + x^14*z0^4 + x^13*z0^4 + 2*x^16 - x^12*z0^4 + 2*x^13*z0^2 + 2*x^10*y*z0^3 + x^10*z0^4 - 2*x^13 - 2*x^9*y*z0^3 + x^9*z0^4 - x^10*y*z0 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 - x^7*z0^4 - 2*x^10 + x^8*y*z0 - 2*x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 + 2*x^9 - x^7*z0^2 - 2*x^5*y*z0^3 + x^5*z0^4 + 2*x^8 + x^6*y*z0 - x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^7 - x^5*z0^2 - x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^6 + 2*x^2*y*z0^3 + x^2*z0^4 - x^5 - x^3*y*z0 - x^3*z0^2 + x*y*z0^3 + x^2*y*z0 - 2*x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((x^31*z0^3 + x^30*z0^3 - x^28*y^2*z0^3 - 2*x^31*z0 - x^27*y^2*z0^3 - 2*x^30*z0 + 2*x^28*y^2*z0 - x^28*z0^3 - x^29*z0 + 2*x^27*y^2*z0 - 2*x^27*z0^3 + x^28*z0 + x^26*y^2*z0 + x^24*y^2*z0^3 + 2*x^27*z0 + x^25*y^2*z0 + x^25*z0^3 + x^26*z0 + 2*x^24*z0^3 - x^25*z0 - 2*x^24*z0 - x^22*z0^3 - x^23*z0 - 2*x^21*z0^3 + x^22*z0 + 2*x^21*z0 + x^19*z0^3 + x^20*z0 + 2*x^18*z0^3 - x^19*z0 - 2*x^18*z0 - x^16*z0^3 - x^17*z0 - 2*x^15*z0^3 + x^16*z0 + 2*x^15*z0 + x^13*z0^3 + x^14*z0 + 2*x^12*z0^3 - x^13*z0 - x^9*y*z0^4 - 2*x^12*z0 + 2*x^10*y*z0^2 + x^8*y*z0^4 - x^11*z0 + 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 + x^10*y + x^10*z0 + x^8*y*z0^2 + 2*x^8*z0^3 + x^6*y*z0^4 + x^9*y + x^9*z0 + x^7*y*z0^2 + 2*x^7*z0^3 + 2*x^5*y*z0^4 + 2*x^8*z0 + 2*x^6*y*z0^2 + 2*x^6*z0^3 + x^4*y*z0^4 - 2*x^7*z0 - x^5*y*z0^2 + x^5*z0^3 + 2*x^3*y*z0^4 + x^6*y - 2*x^6*z0 + 2*x^4*y*z0^2 + 2*x^4*z0^3 + 2*x^2*y*z0^4 - 2*x^5*z0 - 2*x^3*y*z0^2 + x^3*z0^3 + x*y*z0^4 - x^4*y + 2*x^4*z0 - 2*x^2*y*z0^2 + 2*x^3*y + 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((-x^31*z0^4 - x^30*z0^4 + x^28*y^2*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 - x^28*y^2*z0^2 + x^28*z0^4 + 2*x^26*y^2*z0^4 + 2*x^31 + x^27*z0^4 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 - x^25*z0^4 - 2*x^28 - x^24*z0^4 + x^25*z0^2 - 2*x^23*z0^4 + x^22*z0^4 + 2*x^25 + x^21*z0^4 - x^22*z0^2 + 2*x^20*z0^4 - x^19*z0^4 - 2*x^22 - x^18*z0^4 + x^19*z0^2 - 2*x^17*z0^4 + x^16*z0^4 + 2*x^19 + x^15*z0^4 - x^16*z0^2 + 2*x^14*z0^4 - x^13*z0^4 - 2*x^16 - x^12*z0^4 + x^13*z0^2 + 2*x^11*z0^4 - 2*x^10*y*z0^3 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 + x^8*z0^4 + 2*x^11 - 2*x^9*y*z0 + x^7*y*z0^3 + x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 + 2*x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^6 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - x^3 + x*y^2)/y) * dx, - ((2*x^30*z0^3 + 2*x^31*z0 - 2*x^29*z0^3 - 2*x^27*y^2*z0^3 - x^30*z0 - 2*x^28*y^2*z0 + 2*x^26*y^2*z0^3 + x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + 2*x^25*y^2*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 - x^24*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 + x^21*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 - x^18*z0 - x^15*z0^3 + x^16*z0 + 2*x^14*z0^3 + x^15*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 - x^12*z0 + 2*x^8*y*z0^4 - 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - x^8*z0 - 2*x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 - 2*x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y - x^6*z0 - x^4*y*z0^2 + x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - 2*x^3*z0^3 + x^4*y + 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y + x^3*z0 + x*y^2*z0 - 2*x^2*z0)/y) * dx, - ((2*x^30*z0^4 + x^31*z0^2 - 2*x^29*z0^4 - 2*x^27*y^2*z0^4 - x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + 2*x^31 - 2*x^27*z0^4 - 2*x^30 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y^2 - 2*x^28 + 2*x^24*z0^4 + 2*x^27 + x^25*z0^2 - 2*x^23*z0^4 + 2*x^25 - 2*x^21*z0^4 - 2*x^24 - x^22*z0^2 + 2*x^20*z0^4 - 2*x^22 + 2*x^18*z0^4 + 2*x^21 + x^19*z0^2 - 2*x^17*z0^4 + 2*x^19 - 2*x^15*z0^4 - 2*x^18 - x^16*z0^2 + 2*x^14*z0^4 - 2*x^16 + 2*x^12*z0^4 + 2*x^15 + x^13*z0^2 + 2*x^11*z0^4 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*z0^4 - 2*x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 + x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 + x*y^2*z0^2 + 2*x^2*y*z0 + x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^31*z0^3 + x^28*y^2*z0^3 - x^31*z0 - 2*x^29*z0^3 + x^30*z0 + x^28*y^2*z0 + x^28*z0^3 + 2*x^26*y^2*z0^3 - 2*x^29*z0 - x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*y^2*z0 + 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - x^25*z0^3 + 2*x^26*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 + x^24*z0 + x^22*z0^3 - 2*x^23*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 - x^21*z0 - x^19*z0^3 + 2*x^20*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 + x^18*z0 + x^16*z0^3 - 2*x^17*z0 - x^15*z0^3 + x^16*z0 + 2*x^14*z0^3 - x^15*z0 - x^13*z0^3 + 2*x^14*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 - 2*x^10*y*z0^2 + x^10*z0^3 - 2*x^11*z0 + x^9*y*z0^2 - x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y + x^8*y*z0^2 - x^6*y*z0^4 - x^9*y - x^9*z0 + 2*x^7*y*z0^2 - 2*x^5*y*z0^4 + x^8*y + 2*x^8*z0 + x^6*y*z0^2 - x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^6*z0 + x^4*z0^3 - x^2*y*z0^4 - x^5*y + x^5*z0 - x^3*y*z0^2 - x^3*z0^3 + x*y^2*z0^3 - 2*x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - 2*x^3*y - 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-2*x^31*z0^4 - x^30*z0^4 + 2*x^28*y^2*z0^4 + x^31*z0^2 + x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 + 2*x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 + 2*x^30 - 2*x^28*y^2 - x^28*z0^2 - x^26*z0^4 - 2*x^27*y^2 - 2*x^27*z0^2 - 2*x^25*z0^4 - 2*x^28 - x^24*z0^4 - 2*x^27 + x^25*z0^2 + x^23*z0^4 + 2*x^24*z0^2 + 2*x^22*z0^4 + 2*x^25 + x^21*z0^4 + 2*x^24 - x^22*z0^2 - x^20*z0^4 - 2*x^21*z0^2 - 2*x^19*z0^4 - 2*x^22 - x^18*z0^4 - 2*x^21 + x^19*z0^2 + x^17*z0^4 + 2*x^18*z0^2 + 2*x^16*z0^4 + 2*x^19 + x^15*z0^4 + 2*x^18 - x^16*z0^2 - x^14*z0^4 - 2*x^15*z0^2 - 2*x^13*z0^4 - 2*x^16 - x^12*z0^4 - 2*x^15 + x^13*z0^2 + 2*x^12*z0^2 + x^10*y*z0^3 + x^10*z0^4 + 2*x^13 - x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 + x^7*z0^4 - 2*x^10 - x^8*y*z0 + x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 - 2*x^7*y*z0 + x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 - x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + x^5*y*z0 + x*y^2*z0^4 - 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^5 + x^2*y^2 + x^2)/y) * dx, - ((-x^5*z0 + x^2*y^2*z0 + x^2*z0)/y) * dx, - ((-x^5*z0^2 + x^2*y^2*z0^2 + x^2*z0^2)/y) * dx, - ((-x^5*z0^3 + x^2*y^2*z0^3 + x^2*z0^3)/y) * dx, - ((-x^5*z0^4 + x^2*y^2*z0^4 + x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^6 + x^3*y^2 + x^3)/y) * dx, - ((-x^6*z0 + x^3*y^2*z0 + x^3*z0)/y) * dx, - ((-x^6*z0^2 + x^3*y^2*z0^2 + x^3*z0^2)/y) * dx, - ((-x^6*z0^3 + x^3*y^2*z0^3 + x^3*z0^3)/y) * dx, - ((-x^6*z0^4 + x^3*y^2*z0^4 + x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^31*z0^4 + x^30*z0^4 - x^28*y^2*z0^4 - x^31*z0^2 + 2*x^29*z0^4 - x^27*y^2*z0^4 + x^28*y^2*z0^2 - x^28*z0^4 - 2*x^26*y^2*z0^4 - 2*x^31 - x^27*z0^4 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 + x^25*z0^4 + 2*x^28 + x^24*z0^4 - x^25*z0^2 + 2*x^23*z0^4 - x^22*z0^4 - 2*x^25 - x^21*z0^4 + x^22*z0^2 - 2*x^20*z0^4 + x^19*z0^4 + 2*x^22 + x^18*z0^4 - x^19*z0^2 + 2*x^17*z0^4 - x^16*z0^4 - 2*x^19 - x^15*z0^4 + x^16*z0^2 - 2*x^14*z0^4 + x^13*z0^4 + 2*x^16 + x^12*z0^4 - x^13*z0^2 - 2*x^11*z0^4 + 2*x^10*y*z0^3 + x^10*z0^4 - 2*x^13 + x^9*y*z0^3 - x^9*z0^4 - 2*x^10*y*z0 + x^10*z0^2 - x^8*z0^4 - 2*x^11 + 2*x^9*y*z0 - x^7*y*z0^3 - x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 - 2*x^7*y*z0 + 2*x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + x^8 - x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 + x^7 + x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^6 + x^4*y^2 - 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 + x^3)/y) * dx, - ((-2*x^30*z0^3 - 2*x^31*z0 + 2*x^29*z0^3 + 2*x^27*y^2*z0^3 + x^30*z0 + 2*x^28*y^2*z0 - 2*x^26*y^2*z0^3 - x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - 2*x^25*y^2*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 + x^24*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 - x^21*z0 - x^18*z0^3 + x^19*z0 + 2*x^17*z0^3 + x^18*z0 + x^15*z0^3 - x^16*z0 - 2*x^14*z0^3 - x^15*z0 - x^12*z0^3 + x^13*z0 + 2*x^11*z0^3 + x^12*z0 - 2*x^8*y*z0^4 + 2*x^9*y*z0^2 - 2*x^9*z0^3 + 2*x^7*y*z0^4 + x^10*y - 2*x^8*y*z0^2 + 2*x^8*z0^3 - x^6*y*z0^4 - x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 - x^8*y + x^8*z0 + 2*x^6*y*z0^2 - x^6*z0^3 + 2*x^4*y*z0^4 + x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - x^3*y*z0^4 + 2*x^6*y + x^6*z0 + x^4*y^2*z0 + x^4*y*z0^2 - x^4*z0^3 - x^2*y*z0^4 - 2*x^5*y - 2*x^5*z0 + 2*x^3*z0^3 - x^4*y - 2*x^4*z0 - 2*x^2*y*z0^2 + 2*x^2*z0^3 - 2*x^3*y - x^3*z0 + 2*x^2*z0)/y) * dx, - ((-2*x^30*z0^4 - x^31*z0^2 + 2*x^29*z0^4 + 2*x^27*y^2*z0^4 + x^28*y^2*z0^2 - 2*x^26*y^2*z0^4 - 2*x^31 + 2*x^27*z0^4 + 2*x^30 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 - 2*x^27*y^2 + 2*x^28 - 2*x^24*z0^4 - 2*x^27 - x^25*z0^2 + 2*x^23*z0^4 - 2*x^25 + 2*x^21*z0^4 + 2*x^24 + x^22*z0^2 - 2*x^20*z0^4 + 2*x^22 - 2*x^18*z0^4 - 2*x^21 - x^19*z0^2 + 2*x^17*z0^4 - 2*x^19 + 2*x^15*z0^4 + 2*x^18 + x^16*z0^2 - 2*x^14*z0^4 + 2*x^16 - 2*x^12*z0^4 - 2*x^15 - x^13*z0^2 - 2*x^11*z0^4 + x^10*z0^4 - 2*x^13 + x^9*y*z0^3 + x^9*z0^4 + 2*x^12 - 2*x^10*y*z0 + 2*x^8*y*z0^3 - 2*x^8*z0^4 - x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*z0^4 + 2*x^8*y*z0 - x^8*z0^2 + x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 - x^8 + 2*x^6*y*z0 + x^6*z0^2 + x^4*y^2*z0^2 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((x^31*z0^3 - x^28*y^2*z0^3 + x^31*z0 + 2*x^29*z0^3 - x^30*z0 - x^28*y^2*z0 - x^28*z0^3 - 2*x^26*y^2*z0^3 + 2*x^29*z0 + x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*y^2*z0 - 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + x^25*z0^3 - 2*x^26*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 - x^24*z0 - x^22*z0^3 + 2*x^23*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 + x^21*z0 + x^19*z0^3 - 2*x^20*z0 - x^18*z0^3 + x^19*z0 + 2*x^17*z0^3 - x^18*z0 - x^16*z0^3 + 2*x^17*z0 + x^15*z0^3 - x^16*z0 - 2*x^14*z0^3 + x^15*z0 + x^13*z0^3 - 2*x^14*z0 - x^12*z0^3 + x^13*z0 + 2*x^11*z0^3 - x^9*y*z0^4 - x^12*z0 + 2*x^10*y*z0^2 - x^10*z0^3 + 2*x^11*z0 - x^9*y*z0^2 + x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y - x^8*y*z0^2 + x^6*y*z0^4 + x^9*y + x^9*z0 - 2*x^7*y*z0^2 - x^7*z0^3 + 2*x^5*y*z0^4 - x^8*y - 2*x^8*z0 - x^6*y*z0^2 + x^4*y^2*z0^3 + x^7*z0 + 2*x^5*y*z0^2 - 2*x^5*z0^3 + x^6*z0 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - x^5*z0 + x^3*y*z0^2 + x^3*z0^3 + 2*x^4*z0 - x^2*y*z0^2 - x^2*z0^3 + 2*x^3*y + 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((2*x^31*z0^4 + x^30*z0^4 - 2*x^28*y^2*z0^4 - x^31*z0^2 - x^29*z0^4 - x^27*y^2*z0^4 - 2*x^30*z0^2 + x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 - 2*x^31 + 2*x^27*y^2*z0^2 - x^27*z0^4 - 2*x^30 + 2*x^28*y^2 + x^28*z0^2 + x^26*z0^4 + 2*x^27*y^2 + 2*x^27*z0^2 + 2*x^25*z0^4 + 2*x^28 + x^24*z0^4 + 2*x^27 - x^25*z0^2 - x^23*z0^4 - 2*x^24*z0^2 - 2*x^22*z0^4 - 2*x^25 - x^21*z0^4 - 2*x^24 + x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 + x^18*z0^4 + 2*x^21 - x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*z0^4 - 2*x^19 - x^15*z0^4 - 2*x^18 + x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + 2*x^13*z0^4 + 2*x^16 + x^12*z0^4 + 2*x^15 - x^13*z0^2 - 2*x^12*z0^2 - x^10*y*z0^3 - x^10*z0^4 - 2*x^13 + x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 + 2*x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*y*z0^3 - 2*x^7*z0^4 + 2*x^10 + x^8*y*z0 - x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 + x^4*y^2*z0^4 - x^9 + 2*x^7*y*z0 - x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^6 + x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^8 + x^5*y^2 + x^5 - x^2)/y) * dx, - ((-x^8*z0 + x^5*y^2*z0 + x^5*z0 - x^2*z0)/y) * dx, - ((-x^8*z0^2 + x^5*y^2*z0^2 + x^5*z0^2 - x^2*z0^2)/y) * dx, - ((-x^8*z0^3 + x^5*y^2*z0^3 + x^5*z0^3 - x^2*z0^3)/y) * dx, - ((-x^8*z0^4 + x^5*y^2*z0^4 + x^5*z0^4 - x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^9 + x^6*y^2 + x^6 - x^3)/y) * dx, - ((-x^9*z0 + x^6*y^2*z0 + x^6*z0 - x^3*z0)/y) * dx, - ((-x^9*z0^2 + x^6*y^2*z0^2 + x^6*z0^2 - x^3*z0^2)/y) * dx, - ((-x^9*z0^3 + x^6*y^2*z0^3 + x^6*z0^3 - x^3*z0^3)/y) * dx, - ((-x^9*z0^4 + x^6*y^2*z0^4 + x^6*z0^4 - x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^31*z0^4 - x^30*z0^4 + x^28*y^2*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 - x^28*y^2*z0^2 + x^28*z0^4 + 2*x^26*y^2*z0^4 + 2*x^31 + x^27*z0^4 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 - x^25*z0^4 - 2*x^28 - x^24*z0^4 + x^25*z0^2 - 2*x^23*z0^4 + x^22*z0^4 + 2*x^25 + x^21*z0^4 - x^22*z0^2 + 2*x^20*z0^4 - x^19*z0^4 - 2*x^22 - x^18*z0^4 + x^19*z0^2 - 2*x^17*z0^4 + x^16*z0^4 + 2*x^19 + x^15*z0^4 - x^16*z0^2 + 2*x^14*z0^4 - x^13*z0^4 - 2*x^16 - x^12*z0^4 + x^13*z0^2 + 2*x^11*z0^4 - 2*x^10*y*z0^3 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 + x^8*z0^4 + 2*x^11 - 2*x^9*y*z0 + x^7*y*z0^3 - x^10 + x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 + x^7*y^2 + 2*x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - x^7 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^6 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - x^3)/y) * dx, - ((2*x^30*z0^3 + 2*x^31*z0 - 2*x^29*z0^3 - 2*x^27*y^2*z0^3 - x^30*z0 - 2*x^28*y^2*z0 + 2*x^26*y^2*z0^3 + x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + 2*x^25*y^2*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 - x^24*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 + x^21*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 - x^18*z0 - x^15*z0^3 + x^16*z0 + 2*x^14*z0^3 + x^15*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 - x^12*z0 + 2*x^8*y*z0^4 - 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y - x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^9*z0 + x^7*y^2*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - x^8*z0 - 2*x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 - x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y - x^6*z0 - x^4*y*z0^2 + x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - 2*x^3*z0^3 + x^4*y + 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y + x^3*z0 - 2*x^2*z0)/y) * dx, - ((2*x^30*z0^4 + x^31*z0^2 - 2*x^29*z0^4 - 2*x^27*y^2*z0^4 - x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + 2*x^31 - 2*x^27*z0^4 - 2*x^30 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y^2 - 2*x^28 + 2*x^24*z0^4 + 2*x^27 + x^25*z0^2 - 2*x^23*z0^4 + 2*x^25 - 2*x^21*z0^4 - 2*x^24 - x^22*z0^2 + 2*x^20*z0^4 - 2*x^22 + 2*x^18*z0^4 + 2*x^21 + x^19*z0^2 - 2*x^17*z0^4 + 2*x^19 - 2*x^15*z0^4 - 2*x^18 - x^16*z0^2 + 2*x^14*z0^4 - 2*x^16 + 2*x^12*z0^4 + 2*x^15 + x^13*z0^2 + 2*x^11*z0^4 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 + x^7*y^2*z0^2 - x^7*z0^4 - 2*x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^31*z0^3 + x^28*y^2*z0^3 - x^31*z0 - 2*x^29*z0^3 + x^30*z0 + x^28*y^2*z0 + x^28*z0^3 + 2*x^26*y^2*z0^3 - 2*x^29*z0 - x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*y^2*z0 + 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - x^25*z0^3 + 2*x^26*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 + x^24*z0 + x^22*z0^3 - 2*x^23*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 - x^21*z0 - x^19*z0^3 + 2*x^20*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 + x^18*z0 + x^16*z0^3 - 2*x^17*z0 - x^15*z0^3 + x^16*z0 + 2*x^14*z0^3 - x^15*z0 - x^13*z0^3 + 2*x^14*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 - 2*x^10*y*z0^2 - 2*x^11*z0 + x^9*y*z0^2 - x^9*z0^3 + x^7*y^2*z0^3 + x^7*y*z0^4 - 2*x^10*y + x^8*y*z0^2 - x^6*y*z0^4 - x^9*y - x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 - 2*x^5*y*z0^4 + x^8*y + 2*x^8*z0 + x^6*y*z0^2 - x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^6*z0 + x^4*z0^3 - x^2*y*z0^4 - x^5*y + x^5*z0 - x^3*y*z0^2 - x^3*z0^3 - 2*x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - 2*x^3*y - 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-2*x^31*z0^4 - x^30*z0^4 + 2*x^28*y^2*z0^4 + x^31*z0^2 + x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 + 2*x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 + 2*x^30 - 2*x^28*y^2 - x^28*z0^2 - x^26*z0^4 - 2*x^27*y^2 - 2*x^27*z0^2 - 2*x^25*z0^4 - 2*x^28 - x^24*z0^4 - 2*x^27 + x^25*z0^2 + x^23*z0^4 + 2*x^24*z0^2 + 2*x^22*z0^4 + 2*x^25 + x^21*z0^4 + 2*x^24 - x^22*z0^2 - x^20*z0^4 - 2*x^21*z0^2 - 2*x^19*z0^4 - 2*x^22 - x^18*z0^4 - 2*x^21 + x^19*z0^2 + x^17*z0^4 + 2*x^18*z0^2 + 2*x^16*z0^4 + 2*x^19 + x^15*z0^4 + 2*x^18 - x^16*z0^2 - x^14*z0^4 - 2*x^15*z0^2 - 2*x^13*z0^4 - 2*x^16 - x^12*z0^4 - 2*x^15 + x^13*z0^2 + 2*x^12*z0^2 + x^10*y*z0^3 + 2*x^13 - x^9*y*z0^3 + 2*x^9*z0^4 + x^7*y^2*z0^4 + 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 - x^8*y*z0 + x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 - 2*x^7*y*z0 + x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 - x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^11 + x^8*y^2 + x^8 - x^5 + x^2)/y) * dx, - ((-x^11*z0 + x^8*y^2*z0 + x^8*z0 - x^5*z0 + x^2*z0)/y) * dx, - ((-x^11*z0^2 + x^8*y^2*z0^2 + x^8*z0^2 - x^5*z0^2 + x^2*z0^2)/y) * dx, - ((-x^11*z0^3 + x^8*y^2*z0^3 + x^8*z0^3 - x^5*z0^3 + x^2*z0^3)/y) * dx, - ((-x^11*z0^4 + x^8*y^2*z0^4 + x^8*z0^4 - x^5*z0^4 + x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^12 + x^9*y^2 + x^9 - x^6 + x^3)/y) * dx, - ((-x^12*z0 + x^9*y^2*z0 + x^9*z0 - x^6*z0 + x^3*z0)/y) * dx, - ((-x^12*z0^2 + x^9*y^2*z0^2 + x^9*z0^2 - x^6*z0^2 + x^3*z0^2)/y) * dx, - ((-x^12*z0^3 + x^9*y^2*z0^3 + x^9*z0^3 - x^6*z0^3 + x^3*z0^3)/y) * dx, - ((-x^12*z0^4 + x^9*y^2*z0^4 + x^9*z0^4 - x^6*z0^4 + x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^31*z0^4 + x^30*z0^4 - x^28*y^2*z0^4 - x^31*z0^2 + 2*x^29*z0^4 - x^27*y^2*z0^4 + x^28*y^2*z0^2 - x^28*z0^4 - 2*x^26*y^2*z0^4 - 2*x^31 - x^27*z0^4 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 + x^25*z0^4 + 2*x^28 + x^24*z0^4 - x^25*z0^2 + 2*x^23*z0^4 - x^22*z0^4 - 2*x^25 - x^21*z0^4 + x^22*z0^2 - 2*x^20*z0^4 + x^19*z0^4 + 2*x^22 + x^18*z0^4 - x^19*z0^2 + 2*x^17*z0^4 - x^16*z0^4 - 2*x^19 - x^15*z0^4 + x^16*z0^2 - 2*x^14*z0^4 + x^13*z0^4 + 2*x^16 + x^12*z0^4 - x^13*z0^2 - 2*x^11*z0^4 + 2*x^10*y*z0^3 + x^10*z0^4 + 2*x^13 + x^9*y*z0^3 - x^9*z0^4 + x^10*y^2 - 2*x^10*y*z0 + x^10*z0^2 - x^8*z0^4 - 2*x^11 + 2*x^9*y*z0 - x^7*y*z0^3 + x^10 - x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 - 2*x^7*y*z0 + 2*x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + x^8 - x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 + x^7 + x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^6 - 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 + x^3)/y) * dx, - ((-2*x^30*z0^3 - 2*x^31*z0 + 2*x^29*z0^3 + 2*x^27*y^2*z0^3 + x^30*z0 + 2*x^28*y^2*z0 - 2*x^26*y^2*z0^3 - x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - 2*x^25*y^2*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 + x^24*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 - x^21*z0 - x^18*z0^3 + x^19*z0 + 2*x^17*z0^3 + x^18*z0 + x^15*z0^3 - x^16*z0 - 2*x^14*z0^3 - x^15*z0 - x^12*z0^3 + 2*x^11*z0^3 + x^12*z0 + x^10*y^2*z0 - 2*x^8*y*z0^4 + 2*x^9*y*z0^2 - 2*x^9*z0^3 + 2*x^7*y*z0^4 + x^10*y + x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 - x^6*y*z0^4 - x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 - x^8*y + x^8*z0 + 2*x^6*y*z0^2 - x^6*z0^3 + 2*x^4*y*z0^4 + x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - x^3*y*z0^4 + 2*x^6*y + x^6*z0 + x^4*y*z0^2 - x^4*z0^3 - x^2*y*z0^4 - 2*x^5*y - 2*x^5*z0 + 2*x^3*z0^3 - x^4*y - 2*x^4*z0 - 2*x^2*y*z0^2 + 2*x^2*z0^3 - 2*x^3*y - x^3*z0 + 2*x^2*z0)/y) * dx, - ((-2*x^30*z0^4 - x^31*z0^2 + 2*x^29*z0^4 + 2*x^27*y^2*z0^4 + x^28*y^2*z0^2 - 2*x^26*y^2*z0^4 - 2*x^31 + 2*x^27*z0^4 + 2*x^30 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 - 2*x^27*y^2 + 2*x^28 - 2*x^24*z0^4 - 2*x^27 - x^25*z0^2 + 2*x^23*z0^4 - 2*x^25 + 2*x^21*z0^4 + 2*x^24 + x^22*z0^2 - 2*x^20*z0^4 + 2*x^22 - 2*x^18*z0^4 - 2*x^21 - x^19*z0^2 + 2*x^17*z0^4 - 2*x^19 + 2*x^15*z0^4 + 2*x^18 + x^16*z0^2 - 2*x^14*z0^4 + 2*x^16 - 2*x^12*z0^4 - 2*x^15 - 2*x^13*z0^2 - 2*x^11*z0^4 + x^10*y^2*z0^2 + x^10*z0^4 - 2*x^13 + x^9*y*z0^3 + x^9*z0^4 + 2*x^12 - 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 - 2*x^8*z0^4 - x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*z0^4 + 2*x^8*y*z0 - x^8*z0^2 + x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 - x^8 + 2*x^6*y*z0 + x^6*z0^2 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((x^31*z0^3 - x^28*y^2*z0^3 + x^31*z0 + 2*x^29*z0^3 - x^30*z0 - x^28*y^2*z0 - x^28*z0^3 - 2*x^26*y^2*z0^3 + 2*x^29*z0 + x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*y^2*z0 - 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + x^25*z0^3 - 2*x^26*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 - x^24*z0 - x^22*z0^3 + 2*x^23*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 + x^21*z0 + x^19*z0^3 - 2*x^20*z0 - x^18*z0^3 + x^19*z0 + 2*x^17*z0^3 - x^18*z0 - x^16*z0^3 + 2*x^17*z0 + x^15*z0^3 - x^16*z0 - 2*x^14*z0^3 + x^15*z0 - 2*x^14*z0 - x^12*z0^3 + x^10*y^2*z0^3 + x^13*z0 + 2*x^11*z0^3 - x^9*y*z0^4 - x^12*z0 + 2*x^10*y*z0^2 + 2*x^11*z0 - x^9*y*z0^2 + x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y - x^8*y*z0^2 + x^6*y*z0^4 + x^9*y + x^9*z0 - 2*x^7*y*z0^2 - x^7*z0^3 + 2*x^5*y*z0^4 - x^8*y - 2*x^8*z0 - x^6*y*z0^2 + x^7*z0 + 2*x^5*y*z0^2 - 2*x^5*z0^3 + x^6*z0 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - x^5*z0 + x^3*y*z0^2 + x^3*z0^3 + 2*x^4*z0 - x^2*y*z0^2 - x^2*z0^3 + 2*x^3*y + 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((2*x^31*z0^4 + x^30*z0^4 - 2*x^28*y^2*z0^4 - x^31*z0^2 - x^29*z0^4 - x^27*y^2*z0^4 - 2*x^30*z0^2 + x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 - 2*x^31 + 2*x^27*y^2*z0^2 - x^27*z0^4 - 2*x^30 + 2*x^28*y^2 + x^28*z0^2 + x^26*z0^4 + 2*x^27*y^2 + 2*x^27*z0^2 + 2*x^25*z0^4 + 2*x^28 + x^24*z0^4 + 2*x^27 - x^25*z0^2 - x^23*z0^4 - 2*x^24*z0^2 - 2*x^22*z0^4 - 2*x^25 - x^21*z0^4 - 2*x^24 + x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 + x^18*z0^4 + 2*x^21 - x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*z0^4 - 2*x^19 - x^15*z0^4 - 2*x^18 + x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + x^13*z0^4 + 2*x^16 + x^12*z0^4 + x^10*y^2*z0^4 + 2*x^15 - x^13*z0^2 - 2*x^12*z0^2 - x^10*y*z0^3 - 2*x^13 + x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 + 2*x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*y*z0^3 - 2*x^7*z0^4 + 2*x^10 + x^8*y*z0 - x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 - x^9 + 2*x^7*y*z0 - x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^6 + x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^14 + x^11*y^2 + x^11 - x^8 + x^5 - x^2)/y) * dx, - ((-x^14*z0 + x^11*y^2*z0 + x^11*z0 - x^8*z0 + x^5*z0 - x^2*z0)/y) * dx, - ((-x^14*z0^2 + x^11*y^2*z0^2 + x^11*z0^2 - x^8*z0^2 + x^5*z0^2 - x^2*z0^2)/y) * dx, - ((-x^14*z0^3 + x^11*y^2*z0^3 + x^11*z0^3 - x^8*z0^3 + x^5*z0^3 - x^2*z0^3)/y) * dx, - ((-x^14*z0^4 + x^11*y^2*z0^4 + x^11*z0^4 - x^8*z0^4 + x^5*z0^4 - x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^15 + x^12*y^2 + x^12 - x^9 + x^6 - x^3)/y) * dx, - ((-x^15*z0 + x^12*y^2*z0 + x^12*z0 - x^9*z0 + x^6*z0 - x^3*z0)/y) * dx, - ((-x^15*z0^2 + x^12*y^2*z0^2 + x^12*z0^2 - x^9*z0^2 + x^6*z0^2 - x^3*z0^2)/y) * dx, - ((-x^15*z0^3 + x^12*y^2*z0^3 + x^12*z0^3 - x^9*z0^3 + x^6*z0^3 - x^3*z0^3)/y) * dx, - ((-x^15*z0^4 + x^12*y^2*z0^4 + x^12*z0^4 - x^9*z0^4 + x^6*z0^4 - x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^31*z0^4 - x^30*z0^4 + x^28*y^2*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 - x^28*y^2*z0^2 + x^28*z0^4 + 2*x^26*y^2*z0^4 + 2*x^31 + x^27*z0^4 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 - x^25*z0^4 - 2*x^28 - x^24*z0^4 + x^25*z0^2 - 2*x^23*z0^4 + x^22*z0^4 + 2*x^25 + x^21*z0^4 - x^22*z0^2 + 2*x^20*z0^4 - x^19*z0^4 - 2*x^22 - x^18*z0^4 + x^19*z0^2 - 2*x^17*z0^4 + x^16*z0^4 + 2*x^19 + x^15*z0^4 - x^16*z0^2 + 2*x^14*z0^4 - x^13*z0^4 + 2*x^16 - x^12*z0^4 + x^13*y^2 + x^13*z0^2 + 2*x^11*z0^4 - 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 + x^8*z0^4 + 2*x^11 - 2*x^9*y*z0 + x^7*y*z0^3 - x^10 + x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 + 2*x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - x^7 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^6 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - x^3)/y) * dx, - ((2*x^30*z0^3 + 2*x^31*z0 - 2*x^29*z0^3 - 2*x^27*y^2*z0^3 - x^30*z0 - 2*x^28*y^2*z0 + 2*x^26*y^2*z0^3 + x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + 2*x^25*y^2*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 - x^24*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 + x^21*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 - x^18*z0 - x^15*z0^3 + 2*x^14*z0^3 + x^15*z0 + x^13*y^2*z0 + x^12*z0^3 - 2*x^11*z0^3 - x^12*z0 + 2*x^8*y*z0^4 - 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y - x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - x^8*z0 - 2*x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 - x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y - x^6*z0 - x^4*y*z0^2 + x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - 2*x^3*z0^3 + x^4*y + 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y + x^3*z0 - 2*x^2*z0)/y) * dx, - ((2*x^30*z0^4 + x^31*z0^2 - 2*x^29*z0^4 - 2*x^27*y^2*z0^4 - x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + 2*x^31 - 2*x^27*z0^4 - 2*x^30 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y^2 - 2*x^28 + 2*x^24*z0^4 + 2*x^27 + x^25*z0^2 - 2*x^23*z0^4 + 2*x^25 - 2*x^21*z0^4 - 2*x^24 - x^22*z0^2 + 2*x^20*z0^4 - 2*x^22 + 2*x^18*z0^4 + 2*x^21 + x^19*z0^2 - 2*x^17*z0^4 + 2*x^19 - 2*x^15*z0^4 - 2*x^18 - 2*x^16*z0^2 + 2*x^14*z0^4 + x^13*y^2*z0^2 - 2*x^16 + 2*x^12*z0^4 + 2*x^15 + 2*x^13*z0^2 + 2*x^11*z0^4 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*z0^4 - 2*x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^31*z0^3 + x^28*y^2*z0^3 - x^31*z0 - 2*x^29*z0^3 + x^30*z0 + x^28*y^2*z0 + x^28*z0^3 + 2*x^26*y^2*z0^3 - 2*x^29*z0 - x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*y^2*z0 + 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - x^25*z0^3 + 2*x^26*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 + x^24*z0 + x^22*z0^3 - 2*x^23*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 - x^21*z0 - x^19*z0^3 + 2*x^20*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 + x^18*z0 - 2*x^17*z0 - x^15*z0^3 + x^13*y^2*z0^3 + x^16*z0 + 2*x^14*z0^3 - x^15*z0 + 2*x^14*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 - 2*x^10*y*z0^2 - 2*x^11*z0 + x^9*y*z0^2 - x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y + x^8*y*z0^2 - x^6*y*z0^4 - x^9*y - x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 - 2*x^5*y*z0^4 + x^8*y + 2*x^8*z0 + x^6*y*z0^2 - x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^6*z0 + x^4*z0^3 - x^2*y*z0^4 - x^5*y + x^5*z0 - x^3*y*z0^2 - x^3*z0^3 - 2*x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - 2*x^3*y - 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-2*x^31*z0^4 - x^30*z0^4 + 2*x^28*y^2*z0^4 + x^31*z0^2 + x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 + 2*x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 + 2*x^30 - 2*x^28*y^2 - x^28*z0^2 - x^26*z0^4 - 2*x^27*y^2 - 2*x^27*z0^2 - 2*x^25*z0^4 - 2*x^28 - x^24*z0^4 - 2*x^27 + x^25*z0^2 + x^23*z0^4 + 2*x^24*z0^2 + 2*x^22*z0^4 + 2*x^25 + x^21*z0^4 + 2*x^24 - x^22*z0^2 - x^20*z0^4 - 2*x^21*z0^2 - 2*x^19*z0^4 - 2*x^22 - x^18*z0^4 - 2*x^21 + x^19*z0^2 + x^17*z0^4 + 2*x^18*z0^2 + x^16*z0^4 + 2*x^19 + x^15*z0^4 + x^13*y^2*z0^4 + 2*x^18 - x^16*z0^2 - x^14*z0^4 - 2*x^15*z0^2 - x^13*z0^4 - 2*x^16 - x^12*z0^4 - 2*x^15 + x^13*z0^2 + 2*x^12*z0^2 + x^10*y*z0^3 + 2*x^13 - x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 - x^8*y*z0 + x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 - 2*x^7*y*z0 + x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 - x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^17 + x^14*y^2 + x^14 - x^11 + x^8 - x^5 + x^2)/y) * dx, - ((-x^17*z0 + x^14*y^2*z0 + x^14*z0 - x^11*z0 + x^8*z0 - x^5*z0 + x^2*z0)/y) * dx, - ((-x^17*z0^2 + x^14*y^2*z0^2 + x^14*z0^2 - x^11*z0^2 + x^8*z0^2 - x^5*z0^2 + x^2*z0^2)/y) * dx, - ((-x^17*z0^3 + x^14*y^2*z0^3 + x^14*z0^3 - x^11*z0^3 + x^8*z0^3 - x^5*z0^3 + x^2*z0^3)/y) * dx, - ((-x^17*z0^4 + x^14*y^2*z0^4 + x^14*z0^4 - x^11*z0^4 + x^8*z0^4 - x^5*z0^4 + x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^18 + x^15*y^2 + x^15 - x^12 + x^9 - x^6 + x^3)/y) * dx, - ((-x^18*z0 + x^15*y^2*z0 + x^15*z0 - x^12*z0 + x^9*z0 - x^6*z0 + x^3*z0)/y) * dx, - ((-x^18*z0^2 + x^15*y^2*z0^2 + x^15*z0^2 - x^12*z0^2 + x^9*z0^2 - x^6*z0^2 + x^3*z0^2)/y) * dx, - ((-x^18*z0^3 + x^15*y^2*z0^3 + x^15*z0^3 - x^12*z0^3 + x^9*z0^3 - x^6*z0^3 + x^3*z0^3)/y) * dx, - ((-x^18*z0^4 + x^15*y^2*z0^4 + x^15*z0^4 - x^12*z0^4 + x^9*z0^4 - x^6*z0^4 + x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^31*z0^4 + x^30*z0^4 - x^28*y^2*z0^4 - x^31*z0^2 + 2*x^29*z0^4 - x^27*y^2*z0^4 + x^28*y^2*z0^2 - x^28*z0^4 - 2*x^26*y^2*z0^4 - 2*x^31 - x^27*z0^4 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 + x^25*z0^4 + 2*x^28 + x^24*z0^4 - x^25*z0^2 + 2*x^23*z0^4 - x^22*z0^4 - 2*x^25 - x^21*z0^4 + x^22*z0^2 - 2*x^20*z0^4 + x^19*z0^4 + 2*x^22 + x^18*z0^4 - x^19*z0^2 + 2*x^17*z0^4 - x^16*z0^4 + 2*x^19 - x^15*z0^4 + x^16*y^2 + x^16*z0^2 - 2*x^14*z0^4 + x^13*z0^4 - 2*x^16 + x^12*z0^4 - x^13*z0^2 - 2*x^11*z0^4 + 2*x^10*y*z0^3 + x^10*z0^4 + 2*x^13 + x^9*y*z0^3 - x^9*z0^4 - 2*x^10*y*z0 + x^10*z0^2 - x^8*z0^4 - 2*x^11 + 2*x^9*y*z0 - x^7*y*z0^3 + x^10 - x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 - 2*x^7*y*z0 + 2*x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + x^8 - x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 + x^7 + x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^6 - 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 + x^3)/y) * dx, - ((-2*x^30*z0^3 - 2*x^31*z0 + 2*x^29*z0^3 + 2*x^27*y^2*z0^3 + x^30*z0 + 2*x^28*y^2*z0 - 2*x^26*y^2*z0^3 - x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - 2*x^25*y^2*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 + x^24*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 - x^21*z0 - x^18*z0^3 + 2*x^17*z0^3 + x^18*z0 + x^16*y^2*z0 + x^15*z0^3 - 2*x^14*z0^3 - x^15*z0 - x^12*z0^3 + 2*x^11*z0^3 + x^12*z0 - 2*x^8*y*z0^4 + 2*x^9*y*z0^2 - 2*x^9*z0^3 + 2*x^7*y*z0^4 + x^10*y + x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 - x^6*y*z0^4 - x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 - x^8*y + x^8*z0 + 2*x^6*y*z0^2 - x^6*z0^3 + 2*x^4*y*z0^4 + x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - x^3*y*z0^4 + 2*x^6*y + x^6*z0 + x^4*y*z0^2 - x^4*z0^3 - x^2*y*z0^4 - 2*x^5*y - 2*x^5*z0 + 2*x^3*z0^3 - x^4*y - 2*x^4*z0 - 2*x^2*y*z0^2 + 2*x^2*z0^3 - 2*x^3*y - x^3*z0 + 2*x^2*z0)/y) * dx, - ((-2*x^30*z0^4 - x^31*z0^2 + 2*x^29*z0^4 + 2*x^27*y^2*z0^4 + x^28*y^2*z0^2 - 2*x^26*y^2*z0^4 - 2*x^31 + 2*x^27*z0^4 + 2*x^30 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 - 2*x^27*y^2 + 2*x^28 - 2*x^24*z0^4 - 2*x^27 - x^25*z0^2 + 2*x^23*z0^4 - 2*x^25 + 2*x^21*z0^4 + 2*x^24 + x^22*z0^2 - 2*x^20*z0^4 + 2*x^22 - 2*x^18*z0^4 - 2*x^21 - 2*x^19*z0^2 + 2*x^17*z0^4 + x^16*y^2*z0^2 - 2*x^19 + 2*x^15*z0^4 + 2*x^18 + 2*x^16*z0^2 - 2*x^14*z0^4 + 2*x^16 - 2*x^12*z0^4 - 2*x^15 - 2*x^13*z0^2 - 2*x^11*z0^4 + x^10*z0^4 - 2*x^13 + x^9*y*z0^3 + x^9*z0^4 + 2*x^12 - 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 - 2*x^8*z0^4 - x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*z0^4 + 2*x^8*y*z0 - x^8*z0^2 + x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 - x^8 + 2*x^6*y*z0 + x^6*z0^2 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((x^31*z0^3 - x^28*y^2*z0^3 + x^31*z0 + 2*x^29*z0^3 - x^30*z0 - x^28*y^2*z0 - x^28*z0^3 - 2*x^26*y^2*z0^3 + 2*x^29*z0 + x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*y^2*z0 - 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + x^25*z0^3 - 2*x^26*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 - x^24*z0 - x^22*z0^3 + 2*x^23*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 + x^21*z0 - 2*x^20*z0 - x^18*z0^3 + x^16*y^2*z0^3 + x^19*z0 + 2*x^17*z0^3 - x^18*z0 + 2*x^17*z0 + x^15*z0^3 - x^16*z0 - 2*x^14*z0^3 + x^15*z0 - 2*x^14*z0 - x^12*z0^3 + x^13*z0 + 2*x^11*z0^3 - x^9*y*z0^4 - x^12*z0 + 2*x^10*y*z0^2 + 2*x^11*z0 - x^9*y*z0^2 + x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y - x^8*y*z0^2 + x^6*y*z0^4 + x^9*y + x^9*z0 - 2*x^7*y*z0^2 - x^7*z0^3 + 2*x^5*y*z0^4 - x^8*y - 2*x^8*z0 - x^6*y*z0^2 + x^7*z0 + 2*x^5*y*z0^2 - 2*x^5*z0^3 + x^6*z0 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - x^5*z0 + x^3*y*z0^2 + x^3*z0^3 + 2*x^4*z0 - x^2*y*z0^2 - x^2*z0^3 + 2*x^3*y + 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((2*x^31*z0^4 + x^30*z0^4 - 2*x^28*y^2*z0^4 - x^31*z0^2 - x^29*z0^4 - x^27*y^2*z0^4 - 2*x^30*z0^2 + x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 - 2*x^31 + 2*x^27*y^2*z0^2 - x^27*z0^4 - 2*x^30 + 2*x^28*y^2 + x^28*z0^2 + x^26*z0^4 + 2*x^27*y^2 + 2*x^27*z0^2 + 2*x^25*z0^4 + 2*x^28 + x^24*z0^4 + 2*x^27 - x^25*z0^2 - x^23*z0^4 - 2*x^24*z0^2 - 2*x^22*z0^4 - 2*x^25 - x^21*z0^4 - 2*x^24 + x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 + x^19*z0^4 + 2*x^22 + x^18*z0^4 + x^16*y^2*z0^4 + 2*x^21 - x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - x^16*z0^4 - 2*x^19 - x^15*z0^4 - 2*x^18 + x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + x^13*z0^4 + 2*x^16 + x^12*z0^4 + 2*x^15 - x^13*z0^2 - 2*x^12*z0^2 - x^10*y*z0^3 - 2*x^13 + x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 + 2*x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*y*z0^3 - 2*x^7*z0^4 + 2*x^10 + x^8*y*z0 - x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 - x^9 + 2*x^7*y*z0 - x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^6 + x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^20 + x^17*y^2 + x^17 - x^14 + x^11 - x^8 + x^5 - x^2)/y) * dx, - ((-x^20*z0 + x^17*y^2*z0 + x^17*z0 - x^14*z0 + x^11*z0 - x^8*z0 + x^5*z0 - x^2*z0)/y) * dx, - ((-x^20*z0^2 + x^17*y^2*z0^2 + x^17*z0^2 - x^14*z0^2 + x^11*z0^2 - x^8*z0^2 + x^5*z0^2 - x^2*z0^2)/y) * dx, - ((-x^20*z0^3 + x^17*y^2*z0^3 + x^17*z0^3 - x^14*z0^3 + x^11*z0^3 - x^8*z0^3 + x^5*z0^3 - x^2*z0^3)/y) * dx, - ((-x^20*z0^4 + x^17*y^2*z0^4 + x^17*z0^4 - x^14*z0^4 + x^11*z0^4 - x^8*z0^4 + x^5*z0^4 - x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^21 + x^18*y^2 + x^18 - x^15 + x^12 - x^9 + x^6 - x^3)/y) * dx, - ((-x^21*z0 + x^18*y^2*z0 + x^18*z0 - x^15*z0 + x^12*z0 - x^9*z0 + x^6*z0 - x^3*z0)/y) * dx, - ((-x^21*z0^2 + x^18*y^2*z0^2 + x^18*z0^2 - x^15*z0^2 + x^12*z0^2 - x^9*z0^2 + x^6*z0^2 - x^3*z0^2)/y) * dx, - ((-x^21*z0^3 + x^18*y^2*z0^3 + x^18*z0^3 - x^15*z0^3 + x^12*z0^3 - x^9*z0^3 + x^6*z0^3 - x^3*z0^3)/y) * dx, - ((-x^21*z0^4 + x^18*y^2*z0^4 + x^18*z0^4 - x^15*z0^4 + x^12*z0^4 - x^9*z0^4 + x^6*z0^4 - x^3*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^31*z0^4 - x^30*z0^4 + x^28*y^2*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 - x^28*y^2*z0^2 + x^28*z0^4 + 2*x^26*y^2*z0^4 + 2*x^31 + x^27*z0^4 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 - x^25*z0^4 - 2*x^28 - x^24*z0^4 + x^25*z0^2 - 2*x^23*z0^4 + x^22*z0^4 + 2*x^25 + x^21*z0^4 - x^22*z0^2 + 2*x^20*z0^4 - x^19*z0^4 + 2*x^22 - x^18*z0^4 + x^19*y^2 + x^19*z0^2 - 2*x^17*z0^4 + x^16*z0^4 - 2*x^19 + x^15*z0^4 - x^16*z0^2 + 2*x^14*z0^4 - x^13*z0^4 + 2*x^16 - x^12*z0^4 + x^13*z0^2 + 2*x^11*z0^4 - 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 + x^8*z0^4 + 2*x^11 - 2*x^9*y*z0 + x^7*y*z0^3 - x^10 + x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 + 2*x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - x^7 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^6 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - x^3)/y) * dx, - ((2*x^30*z0^3 + 2*x^31*z0 - 2*x^29*z0^3 - 2*x^27*y^2*z0^3 - x^30*z0 - 2*x^28*y^2*z0 + 2*x^26*y^2*z0^3 + x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + 2*x^25*y^2*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 - x^24*z0 - x^21*z0^3 + 2*x^20*z0^3 + x^21*z0 + x^19*y^2*z0 + x^18*z0^3 - 2*x^17*z0^3 - x^18*z0 - x^15*z0^3 + 2*x^14*z0^3 + x^15*z0 + x^12*z0^3 - 2*x^11*z0^3 - x^12*z0 + 2*x^8*y*z0^4 - 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y - x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - x^8*z0 - 2*x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 - x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y - x^6*z0 - x^4*y*z0^2 + x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - 2*x^3*z0^3 + x^4*y + 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y + x^3*z0 - 2*x^2*z0)/y) * dx, - ((2*x^30*z0^4 + x^31*z0^2 - 2*x^29*z0^4 - 2*x^27*y^2*z0^4 - x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + 2*x^31 - 2*x^27*z0^4 - 2*x^30 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y^2 - 2*x^28 + 2*x^24*z0^4 + 2*x^27 + x^25*z0^2 - 2*x^23*z0^4 + 2*x^25 - 2*x^21*z0^4 - 2*x^24 - 2*x^22*z0^2 + 2*x^20*z0^4 + x^19*y^2*z0^2 - 2*x^22 + 2*x^18*z0^4 + 2*x^21 + 2*x^19*z0^2 - 2*x^17*z0^4 + 2*x^19 - 2*x^15*z0^4 - 2*x^18 - 2*x^16*z0^2 + 2*x^14*z0^4 - 2*x^16 + 2*x^12*z0^4 + 2*x^15 + 2*x^13*z0^2 + 2*x^11*z0^4 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*z0^4 - 2*x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^31*z0^3 + x^28*y^2*z0^3 - x^31*z0 - 2*x^29*z0^3 + x^30*z0 + x^28*y^2*z0 + x^28*z0^3 + 2*x^26*y^2*z0^3 - 2*x^29*z0 - x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*y^2*z0 + 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - x^25*z0^3 + 2*x^26*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 + x^24*z0 - 2*x^23*z0 - x^21*z0^3 + x^19*y^2*z0^3 + x^22*z0 + 2*x^20*z0^3 - x^21*z0 + 2*x^20*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 + x^18*z0 - 2*x^17*z0 - x^15*z0^3 + x^16*z0 + 2*x^14*z0^3 - x^15*z0 + 2*x^14*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 - 2*x^10*y*z0^2 - 2*x^11*z0 + x^9*y*z0^2 - x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y + x^8*y*z0^2 - x^6*y*z0^4 - x^9*y - x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 - 2*x^5*y*z0^4 + x^8*y + 2*x^8*z0 + x^6*y*z0^2 - x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^6*z0 + x^4*z0^3 - x^2*y*z0^4 - x^5*y + x^5*z0 - x^3*y*z0^2 - x^3*z0^3 - 2*x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - 2*x^3*y - 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-2*x^31*z0^4 - x^30*z0^4 + 2*x^28*y^2*z0^4 + x^31*z0^2 + x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 + 2*x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 + 2*x^30 - 2*x^28*y^2 - x^28*z0^2 - x^26*z0^4 - 2*x^27*y^2 - 2*x^27*z0^2 - 2*x^25*z0^4 - 2*x^28 - x^24*z0^4 - 2*x^27 + x^25*z0^2 + x^23*z0^4 + 2*x^24*z0^2 + x^22*z0^4 + 2*x^25 + x^21*z0^4 + x^19*y^2*z0^4 + 2*x^24 - x^22*z0^2 - x^20*z0^4 - 2*x^21*z0^2 - x^19*z0^4 - 2*x^22 - x^18*z0^4 - 2*x^21 + x^19*z0^2 + x^17*z0^4 + 2*x^18*z0^2 + x^16*z0^4 + 2*x^19 + x^15*z0^4 + 2*x^18 - x^16*z0^2 - x^14*z0^4 - 2*x^15*z0^2 - x^13*z0^4 - 2*x^16 - x^12*z0^4 - 2*x^15 + x^13*z0^2 + 2*x^12*z0^2 + x^10*y*z0^3 + 2*x^13 - x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 - x^8*y*z0 + x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 - 2*x^7*y*z0 + x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 - x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-x^23 + x^20*y^2 + x^20 - x^17 + x^14 - x^11 + x^8 - x^5 + x^2)/y) * dx, - ((-x^23*z0 + x^20*y^2*z0 + x^20*z0 - x^17*z0 + x^14*z0 - x^11*z0 + x^8*z0 - x^5*z0 + x^2*z0)/y) * dx, - ((-x^23*z0^2 + x^20*y^2*z0^2 + x^20*z0^2 - x^17*z0^2 + x^14*z0^2 - x^11*z0^2 + x^8*z0^2 - x^5*z0^2 + x^2*z0^2)/y) * dx, - ((-x^23*z0^3 + x^20*y^2*z0^3 + x^20*z0^3 - x^17*z0^3 + x^14*z0^3 - x^11*z0^3 + x^8*z0^3 - x^5*z0^3 + x^2*z0^3)/y) * dx, - ((-x^23*z0^4 + x^20*y^2*z0^4 + x^20*z0^4 - x^17*z0^4 + x^14*z0^4 - x^11*z0^4 + x^8*z0^4 - x^5*z0^4 + x^2*z0^4)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((2*x^31*z0^4 - x^30*z0^4 - 2*x^28*y^2*z0^4 - 2*x^31*z0^2 - x^29*z0^4 + x^27*y^2*z0^4 - 2*x^30*z0^2 + 2*x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 + 2*x^31 + 2*x^27*y^2*z0^2 + x^27*z0^4 + x^30 - 2*x^28*y^2 + 2*x^28*z0^2 + x^26*z0^4 - x^27*y^2 + 2*x^27*z0^2 + 2*x^25*z0^4 - 2*x^28 - x^24*z0^4 - x^27 - 2*x^25*z0^2 - x^23*z0^4 - 2*x^24*z0^2 - 2*x^22*z0^4 + 2*x^25 + x^21*z0^4 + 2*x^22*z0^2 + x^20*z0^4 + x^21*y^2 + 2*x^21*z0^2 + 2*x^19*z0^4 - 2*x^22 - x^18*z0^4 - 2*x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*z0^4 + 2*x^19 + x^15*z0^4 + 2*x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + 2*x^13*z0^4 - 2*x^16 - x^12*z0^4 - 2*x^13*z0^2 - 2*x^11*z0^4 - 2*x^12*z0^2 - x^10*y*z0^3 + 2*x^13 + 2*x^9*y*z0^3 + x^9*z0^4 + x^10*y*z0 - 2*x^8*y*z0^3 - x^8*z0^4 - x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 - 2*x^7*z0^4 - x^10 - 2*x^8*z0^2 + x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 + 2*x^7*y*z0 - x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 + 2*x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 + 2*x^4*y*z0^3 + 2*x^4*z0^4 - x^7 + 2*x^5*z0^2 - x^3*z0^4 - 2*x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 + x^2*z0^4 + x^5 - x^3*y*z0 - x^2*y*z0 + 2*x^3 - 2*x^2)/y) * dx, - ((x^31*z0^3 + x^30*z0^3 - x^28*y^2*z0^3 + 2*x^31*z0 + 2*x^29*z0^3 - x^27*y^2*z0^3 - x^30*z0 - 2*x^28*y^2*z0 - x^28*z0^3 - 2*x^26*y^2*z0^3 + x^27*y^2*z0 + x^28*z0 - 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + 2*x^25*y^2*z0 + x^25*z0^3 - x^25*z0 + 2*x^23*z0^3 - 2*x^24*z0 - x^22*z0^3 + x^21*y^2*z0 + x^22*z0 - 2*x^20*z0^3 + 2*x^21*z0 + x^19*z0^3 - x^19*z0 + 2*x^17*z0^3 - 2*x^18*z0 - x^16*z0^3 + x^16*z0 - 2*x^14*z0^3 + 2*x^15*z0 + x^13*z0^3 - x^13*z0 + 2*x^11*z0^3 - x^9*y*z0^4 - 2*x^12*z0 + 2*x^10*y*z0^2 - x^10*z0^3 + x^8*y*z0^4 - 2*x^9*y*z0^2 - x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y + x^10*z0 - x^8*y*z0^2 + 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*y + 2*x^7*y*z0^2 - x^7*z0^3 - 2*x^5*y*z0^4 + 2*x^8*y + 2*x^8*z0 + x^6*y*z0^2 - 2*x^6*z0^3 - 2*x^4*y*z0^4 - x^7*y + 2*x^5*z0^3 + 2*x^6*y - 2*x^6*z0 - 2*x^4*y*z0^2 - x^4*z0^3 + x^5*y + 2*x^5*z0 + 2*x^3*y*z0^2 - 2*x^4*y + 2*x^4*z0 + 2*x^2*z0^3 + 2*x^3*y + 2*x^2*z0)/y) * dx, - ((-2*x^31*z0^4 - 2*x^30*z0^4 + 2*x^28*y^2*z0^4 - x^31*z0^2 + x^29*z0^4 + 2*x^27*y^2*z0^4 + x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 - 2*x^31 + 2*x^27*z0^4 - 2*x^30 + 2*x^28*y^2 + x^28*z0^2 - x^26*z0^4 + 2*x^27*y^2 - 2*x^25*z0^4 + 2*x^28 - 2*x^24*z0^4 + 2*x^27 - x^25*z0^2 + x^23*z0^4 - x^24*z0^2 + 2*x^22*z0^4 - 2*x^25 + x^21*y^2*z0^2 + 2*x^21*z0^4 - 2*x^24 + x^22*z0^2 - x^20*z0^4 + x^21*z0^2 - 2*x^19*z0^4 + 2*x^22 - 2*x^18*z0^4 + 2*x^21 - x^19*z0^2 + x^17*z0^4 - x^18*z0^2 + 2*x^16*z0^4 - 2*x^19 + 2*x^15*z0^4 - 2*x^18 + x^16*z0^2 - x^14*z0^4 + x^15*z0^2 - 2*x^13*z0^4 + 2*x^16 - 2*x^12*z0^4 + 2*x^15 - x^13*z0^2 + 2*x^11*z0^4 - x^12*z0^2 + x^10*y*z0^3 - 2*x^13 + x^9*y*z0^3 - x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - 2*x^10*z0^2 - x^8*z0^4 + x^11 + 2*x^9*y*z0 + x^9*z0^2 - x^7*y*z0^3 - x^10 + x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 - 2*x^5*z0^4 + x^6*y*z0 + 2*x^6*z0^2 + 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 - x^5*z0^2 - 2*x^3*y*z0^3 - x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 - x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 + 2*x^2*z0^2 + 2*x^2)/y) * dx, - ((2*x^31*z0^3 - x^30*z0^3 - 2*x^28*y^2*z0^3 - 2*x^31*z0 + x^29*z0^3 + x^27*y^2*z0^3 + x^30*z0 + 2*x^28*y^2*z0 - 2*x^28*z0^3 - x^26*y^2*z0^3 - x^27*y^2*z0 - 2*x^27*z0^3 - 2*x^28*z0 - x^26*z0^3 - 2*x^24*y^2*z0^3 - x^27*z0 - x^25*y^2*z0 + 2*x^25*z0^3 + x^24*z0^3 + 2*x^25*z0 + x^23*z0^3 + x^21*y^2*z0^3 + x^24*z0 - 2*x^22*z0^3 - x^21*z0^3 - 2*x^22*z0 - x^20*z0^3 - x^21*z0 + 2*x^19*z0^3 + x^18*z0^3 + 2*x^19*z0 + x^17*z0^3 + x^18*z0 - 2*x^16*z0^3 - x^15*z0^3 - 2*x^16*z0 - x^14*z0^3 - x^15*z0 + 2*x^13*z0^3 + x^12*z0^3 + 2*x^13*z0 + x^11*z0^3 - 2*x^9*y*z0^4 + x^12*z0 - x^10*y*z0^2 - x^8*y*z0^4 + 2*x^9*y*z0^2 - 2*x^7*y*z0^4 + x^10*y + x^10*z0 - 2*x^8*y*z0^2 - x^8*z0^3 - x^6*y*z0^4 + 2*x^9*y + x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 - x^8*y + 2*x^8*z0 - 2*x^6*z0^3 + x^4*y*z0^4 + 2*x^7*y - 2*x^7*z0 + 2*x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 + x^6*y - 2*x^6*z0 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - 2*x^5*z0 + 2*x^3*y*z0^2 + x^3*z0^3 - 2*x^4*y + x^4*z0 - 2*x^2*y*z0^2 + x^3*y + x^2*y - 2*x^2*z0)/y) * dx, - ((x^31*z0^4 - 2*x^30*z0^4 - x^28*y^2*z0^4 + 2*x^31*z0^2 - x^29*z0^4 + 2*x^27*y^2*z0^4 - 2*x^30*z0^2 - 2*x^28*y^2*z0^2 - x^28*z0^4 + x^26*y^2*z0^4 + x^31 + 2*x^27*y^2*z0^2 + 2*x^27*z0^4 + x^30 - x^28*y^2 - 2*x^28*z0^2 + x^26*z0^4 - x^27*y^2 + 2*x^27*z0^2 + x^25*z0^4 - x^28 + 2*x^24*z0^4 - x^27 + 2*x^25*z0^2 - x^23*z0^4 + x^21*y^2*z0^4 - 2*x^24*z0^2 - x^22*z0^4 + x^25 - 2*x^21*z0^4 + x^24 - 2*x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 + x^19*z0^4 - x^22 + 2*x^18*z0^4 - x^21 + 2*x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - x^16*z0^4 + x^19 - 2*x^15*z0^4 + x^18 - 2*x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + x^13*z0^4 - x^16 + 2*x^12*z0^4 - x^15 + 2*x^13*z0^2 + x^11*z0^4 - 2*x^12*z0^2 + 2*x^10*y*z0^3 + 2*x^10*z0^4 + x^13 - 2*x^9*y*z0^3 + x^12 - x^10*y*z0 - 2*x^8*z0^4 + 2*x^11 - x^9*y*z0 - 2*x^9*z0^2 - 2*x^7*y*z0^3 - x^7*z0^4 - x^8*y*z0 - 2*x^6*y*z0^3 + x^9 - 2*x^7*y*z0 + 2*x^7*z0^2 - x^5*z0^4 - x^6*y*z0 + x^6*z0^2 - 2*x^4*y*z0^3 - 2*x^4*z0^4 + 2*x^7 + 2*x^5*y*z0 + 2*x^5*z0^2 - x^3*y*z0^3 + x^3*z0^4 + x^6 + x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^3*y*z0 + x^3*z0^2 + 2*x^2*y*z0 - 2*x^2*z0^2 + 2*x^3 + 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((2*x^31*z0^4 - 2*x^30*z0^4 - 2*x^28*y^2*z0^4 + 2*x^31*z0^2 - x^29*z0^4 + 2*x^27*y^2*z0^4 + x^30*z0^2 - 2*x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 - x^31 - x^27*y^2*z0^2 + 2*x^27*z0^4 - 2*x^30 + x^28*y^2 - 2*x^28*z0^2 + x^26*z0^4 + 2*x^27*y^2 - x^27*z0^2 + 2*x^25*z0^4 + x^28 - 2*x^24*z0^4 + 2*x^27 + 2*x^25*z0^2 - x^23*z0^4 + x^24*z0^2 - 2*x^22*z0^4 - 2*x^25 + 2*x^21*z0^4 - 2*x^24 + x^22*y^2 - 2*x^22*z0^2 + x^20*z0^4 - x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 - 2*x^18*z0^4 + 2*x^21 + 2*x^19*z0^2 - x^17*z0^4 + x^18*z0^2 - 2*x^16*z0^4 - 2*x^19 + 2*x^15*z0^4 - 2*x^18 - 2*x^16*z0^2 + x^14*z0^4 - x^15*z0^2 + 2*x^13*z0^4 + 2*x^16 - 2*x^12*z0^4 + 2*x^15 + 2*x^13*z0^2 + 2*x^11*z0^4 + x^12*z0^2 - x^10*y*z0^3 - 2*x^13 - 2*x^9*y*z0^3 + x^9*z0^4 - 2*x^12 - x^10*y*z0 + x^10*z0^2 + x^8*y*z0^3 - 2*x^8*z0^4 + x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 - 2*x^10 + x^8*y*z0 - x^8*z0^2 + x^6*y*z0^3 + x^6*z0^4 - 2*x^9 - x^5*y*z0^3 - 2*x^8 + 2*x^6*y*z0 + x^6*z0^2 + x^4*y*z0^3 + x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^5*z0^2 - 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 + x^5 - x^3 - 2*x^2)/y) * dx, - ((2*x^31*z0^3 - 2*x^30*z0^3 - 2*x^28*y^2*z0^3 - x^31*z0 - 2*x^29*z0^3 + 2*x^27*y^2*z0^3 - 2*x^30*z0 + x^28*y^2*z0 - 2*x^28*z0^3 + 2*x^26*y^2*z0^3 + 2*x^27*y^2*z0 - x^27*z0^3 + 2*x^28*z0 + 2*x^26*z0^3 - 2*x^24*y^2*z0^3 + 2*x^27*z0 - x^25*y^2*z0 + 2*x^25*z0^3 + x^24*z0^3 + 2*x^25*z0 - 2*x^23*z0^3 - 2*x^24*z0 + x^22*y^2*z0 - 2*x^22*z0^3 - x^21*z0^3 - 2*x^22*z0 + 2*x^20*z0^3 + 2*x^21*z0 + 2*x^19*z0^3 + x^18*z0^3 + 2*x^19*z0 - 2*x^17*z0^3 - 2*x^18*z0 - 2*x^16*z0^3 - x^15*z0^3 - 2*x^16*z0 + 2*x^14*z0^3 + 2*x^15*z0 + 2*x^13*z0^3 + x^12*z0^3 + 2*x^13*z0 - 2*x^11*z0^3 - 2*x^9*y*z0^4 - 2*x^12*z0 - x^10*y*z0^2 + 2*x^10*z0^3 - 2*x^8*y*z0^4 + x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^10*y - 2*x^10*z0 + 2*x^8*y*z0^2 + 2*x^8*z0^3 + 2*x^6*y*z0^4 + 2*x^9*y + x^7*y*z0^2 + 2*x^5*y*z0^4 - x^8*y - x^6*y*z0^2 - 2*x^6*z0^3 + 2*x^4*y*z0^4 - x^7*y + x^7*z0 - 2*x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - x^6*y + x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 - x^5*y - 2*x^5*z0 - x^3*y*z0^2 + x^3*z0^3 + x^4*y + x^4*z0 - x^2*y*z0^2 + 2*x^2*z0^3 + x^3*y - 2*x^3*z0 + 2*x^2*y + 2*x^2*z0)/y) * dx, - ((x^31*z0^4 + 2*x^30*z0^4 - x^28*y^2*z0^4 - 2*x^31*z0^2 + x^29*z0^4 - 2*x^27*y^2*z0^4 + 2*x^28*y^2*z0^2 - x^28*z0^4 - x^26*y^2*z0^4 + x^31 - 2*x^27*z0^4 + x^30 - x^28*y^2 + 2*x^28*z0^2 - x^26*z0^4 - x^27*y^2 + x^25*z0^4 - x^28 + 2*x^24*z0^4 - x^27 + 2*x^25*z0^2 + x^23*z0^4 + x^22*y^2*z0^2 - x^22*z0^4 + x^25 - 2*x^21*z0^4 + x^24 - 2*x^22*z0^2 - x^20*z0^4 + x^19*z0^4 - x^22 + 2*x^18*z0^4 - x^21 + 2*x^19*z0^2 + x^17*z0^4 - x^16*z0^4 + x^19 - 2*x^15*z0^4 + x^18 - 2*x^16*z0^2 - x^14*z0^4 + x^13*z0^4 - x^16 + 2*x^12*z0^4 - x^15 + 2*x^13*z0^2 - 2*x^11*z0^4 + 2*x^10*y*z0^3 - x^10*z0^4 + x^13 + 2*x^9*y*z0^3 + 2*x^9*z0^4 + x^12 + x^10*y*z0 + 2*x^10*z0^2 - x^8*y*z0^3 + x^8*z0^4 + 2*x^11 - x^9*y*z0 + 2*x^9*z0^2 + 2*x^7*z0^4 - x^10 - 2*x^8*y*z0 - 2*x^8*z0^2 + 2*x^6*y*z0^3 - 2*x^9 + 2*x^7*y*z0 + x^5*y*z0^3 - 2*x^8 - x^6*z0^2 - x^4*y*z0^3 + x^4*z0^4 + x^7 - 2*x^5*y*z0 + 2*x^5*z0^2 + x^3*y*z0^3 + x^3*z0^4 + x^4*z0^2 - x^2*z0^4 + x^5 + 2*x^3*y*z0 - x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 + x^2)/y) * dx, - ((-x^31*z0^3 + x^30*z0^3 + x^28*y^2*z0^3 - x^31*z0 + 2*x^29*z0^3 - x^27*y^2*z0^3 + x^30*z0 + x^28*y^2*z0 + x^28*z0^3 - 2*x^26*y^2*z0^3 + x^29*z0 - x^27*y^2*z0 - x^27*z0^3 - x^26*y^2*z0 - 2*x^26*z0^3 - x^27*z0 + x^25*y^2*z0 - 2*x^25*z0^3 - x^26*z0 + x^24*z0^3 + x^22*y^2*z0^3 + 2*x^23*z0^3 + x^24*z0 + 2*x^22*z0^3 + x^23*z0 - x^21*z0^3 - 2*x^20*z0^3 - x^21*z0 - 2*x^19*z0^3 - x^20*z0 + x^18*z0^3 + 2*x^17*z0^3 + x^18*z0 + 2*x^16*z0^3 + x^17*z0 - x^15*z0^3 - 2*x^14*z0^3 - x^15*z0 - 2*x^13*z0^3 - x^14*z0 + x^12*z0^3 + 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 - 2*x^10*y*z0^2 + x^10*z0^3 + x^8*y*z0^4 + x^11*z0 + x^9*y*z0^2 - x^7*y*z0^4 - 2*x^10*y - x^10*z0 - 2*x^8*z0^3 - 2*x^6*y*z0^4 - x^9*y + 2*x^7*y*z0^2 - x^7*z0^3 + x^5*y*z0^4 - x^8*y - 2*x^8*z0 - 2*x^6*y*z0^2 + x^4*y*z0^4 + x^7*y + 2*x^7*z0 - x^5*y*z0^2 - x^5*z0^3 - 2*x^3*y*z0^4 - 2*x^6*y + x^6*z0 + 2*x^4*y*z0^2 - x^4*z0^3 + x^5*y + 2*x^5*z0 - x^3*z0^3 - x^4*y - x^2*z0^3 + 2*x^3*z0 + 2*x^2*y - 2*x^2*z0)/y) * dx, - ((-x^31*z0^4 + 2*x^30*z0^4 + x^28*y^2*z0^4 + x^31*z0^2 + 2*x^29*z0^4 - 2*x^27*y^2*z0^4 - x^30*z0^2 - x^28*y^2*z0^2 + x^28*z0^4 - 2*x^26*y^2*z0^4 - x^31 + x^27*y^2*z0^2 - 2*x^27*z0^4 - 2*x^30 + x^28*y^2 - x^28*z0^2 - 2*x^26*z0^4 + 2*x^27*y^2 + x^27*z0^2 - 2*x^25*z0^4 + x^28 + 2*x^24*z0^4 + x^22*y^2*z0^4 + 2*x^27 + x^25*z0^2 + 2*x^23*z0^4 - x^24*z0^2 + 2*x^22*z0^4 - x^25 - 2*x^21*z0^4 - 2*x^24 - x^22*z0^2 - 2*x^20*z0^4 + x^21*z0^2 - 2*x^19*z0^4 + x^22 + 2*x^18*z0^4 + 2*x^21 + x^19*z0^2 + 2*x^17*z0^4 - x^18*z0^2 + 2*x^16*z0^4 - x^19 - 2*x^15*z0^4 - 2*x^18 - x^16*z0^2 - 2*x^14*z0^4 + x^15*z0^2 - 2*x^13*z0^4 + x^16 + 2*x^12*z0^4 + 2*x^15 + x^13*z0^2 - x^12*z0^2 - 2*x^10*y*z0^3 + 2*x^10*z0^4 - x^13 - x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 + 2*x^10*z0^2 - 2*x^8*y*z0^3 - x^8*z0^4 - 2*x^11 + x^9*y*z0 - 2*x^7*y*z0^3 + 2*x^7*z0^4 + x^10 + x^8*y*z0 - x^6*y*z0^3 - 2*x^9 - x^7*y*z0 + 2*x^7*z0^2 + x^5*y*z0^3 + x^5*z0^4 - 2*x^8 + 2*x^6*y*z0 - 2*x^6*z0^2 - 2*x^4*y*z0^3 - x^4*z0^4 - 2*x^7 + 2*x^3*z0^4 + 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 - 2*x^5 + x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + x^2*z0^2 - x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^31*z0^4 - x^30*z0^4 - x^28*y^2*z0^4 - x^31*z0^2 - x^29*z0^4 + x^27*y^2*z0^4 + x^30*z0^2 + x^28*y^2*z0^2 - x^28*z0^4 + x^26*y^2*z0^4 - x^31 - x^27*y^2*z0^2 + x^27*z0^4 + x^28*y^2 + x^28*z0^2 + x^26*z0^4 - x^27*z0^2 + x^25*z0^4 + x^28 - x^24*z0^4 - x^25*z0^2 - x^23*z0^4 - x^26 + x^24*z0^2 - x^22*z0^4 - x^25 + x^23*y^2 + x^21*z0^4 + x^22*z0^2 + x^20*z0^4 + x^23 - x^21*z0^2 + x^19*z0^4 + x^22 - x^18*z0^4 - x^19*z0^2 - x^17*z0^4 - x^20 + x^18*z0^2 - x^16*z0^4 - x^19 + x^15*z0^4 + x^16*z0^2 + x^14*z0^4 + x^17 - x^15*z0^2 + x^13*z0^4 + x^16 - x^12*z0^4 - x^13*z0^2 + 2*x^11*z0^4 - x^14 + x^12*z0^2 + 2*x^10*y*z0^3 - 2*x^10*z0^4 - x^13 + x^9*y*z0^3 + x^9*z0^4 - 2*x^10*y*z0 + x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + 2*x^11 + x^9*y*z0 - 2*x^9*z0^2 - x^7*z0^4 + x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 + x^9 - x^7*y*z0 - 2*x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 - 2*x^8 + x^6*y*z0 + 2*x^6*z0^2 + x^4*y*z0^3 - x^7 - x^5*y*z0 - 2*x^5*z0^2 - x^3*y*z0^3 - 2*x^4*y*z0 + x^4*z0^2 + x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 + x^3*z0^2 - 2*x^2*y*z0 + 2*x^2*z0^2 - x^2)/y) * dx, - ((x^31*z0^3 + x^30*z0^3 - x^28*y^2*z0^3 - 2*x^29*z0^3 - x^27*y^2*z0^3 - 2*x^30*z0 - x^28*z0^3 + 2*x^26*y^2*z0^3 + 2*x^27*y^2*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 + 2*x^27*z0 + x^25*z0^3 - x^26*z0 + x^23*y^2*z0 - 2*x^23*z0^3 - 2*x^24*z0 - x^22*z0^3 + x^23*z0 + 2*x^20*z0^3 + 2*x^21*z0 + x^19*z0^3 - x^20*z0 - 2*x^17*z0^3 - 2*x^18*z0 - x^16*z0^3 + x^17*z0 + 2*x^14*z0^3 + 2*x^15*z0 + x^13*z0^3 - x^14*z0 - 2*x^11*z0^3 - x^9*y*z0^4 - 2*x^12*z0 + 2*x^10*y*z0^2 + 2*x^10*z0^3 + x^8*y*z0^4 + x^11*z0 - x^7*y*z0^4 - 2*x^10*z0 - x^8*y*z0^2 - 2*x^8*z0^3 - x^6*y*z0^4 + x^9*y - 2*x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 + x^5*y*z0^4 - 2*x^8*y + x^8*z0 + 2*x^6*z0^3 + 2*x^5*y*z0^2 - 2*x^5*z0^3 - x^6*y - 2*x^6*z0 - 2*x^4*y*z0^2 - x^4*z0^3 - 2*x^2*y*z0^4 + x^5*y - 2*x^5*z0 + x^3*y*z0^2 + 2*x^3*z0^3 - 2*x^4*y - 2*x^4*z0 + 2*x^2*z0^3 - 2*x^3*y - 2*x^3*z0 + 2*x^2*y + x^2*z0)/y) * dx, - ((2*x^31*z0^4 + x^30*z0^4 - 2*x^28*y^2*z0^4 + x^31*z0^2 - x^27*y^2*z0^4 - x^28*y^2*z0^2 - 2*x^28*z0^4 - x^27*z0^4 - x^28*z0^2 + 2*x^25*z0^4 - x^26*z0^2 + x^24*z0^4 + x^25*z0^2 + x^23*y^2*z0^2 - 2*x^22*z0^4 + x^23*z0^2 - x^21*z0^4 - x^22*z0^2 + 2*x^19*z0^4 - x^20*z0^2 + x^18*z0^4 + x^19*z0^2 - 2*x^16*z0^4 + x^17*z0^2 - x^15*z0^4 - x^16*z0^2 + 2*x^13*z0^4 - x^14*z0^2 + x^12*z0^4 + x^13*z0^2 - x^10*y*z0^3 + x^10*z0^4 + x^11*z0^2 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 + x^8*y*z0^3 - 2*x^11 - x^9*z0^2 - x^7*y*z0^3 - x^7*z0^4 + x^10 + x^8*y*z0 + x^8*z0^2 + 2*x^6*z0^4 + 2*x^9 + 2*x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 - x^5*z0^4 + 2*x^8 + 2*x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - x^7 + x^5*z0^2 - 2*x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^4*z0^2 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + x^2*z0^2 - x^3 + 2*x^2)/y) * dx, - ((-2*x^31*z0^3 - 2*x^30*z0^3 + 2*x^28*y^2*z0^3 + 2*x^31*z0 - x^29*z0^3 + 2*x^27*y^2*z0^3 - 2*x^30*z0 - 2*x^28*y^2*z0 + 2*x^28*z0^3 + x^26*y^2*z0^3 - x^29*z0 + 2*x^27*y^2*z0 - x^27*z0^3 + x^26*y^2*z0 - 2*x^24*y^2*z0^3 + 2*x^27*z0 - 2*x^25*y^2*z0 - 2*x^25*z0^3 + x^23*y^2*z0^3 + x^26*z0 + x^24*z0^3 - 2*x^24*z0 + 2*x^22*z0^3 - x^23*z0 - x^21*z0^3 + 2*x^21*z0 - 2*x^19*z0^3 + x^20*z0 + x^18*z0^3 - 2*x^18*z0 + 2*x^16*z0^3 - x^17*z0 - x^15*z0^3 + 2*x^15*z0 - 2*x^13*z0^3 + x^14*z0 + x^12*z0^3 + 2*x^9*y*z0^4 - 2*x^12*z0 + x^10*y*z0^2 - 2*x^10*z0^3 - 2*x^8*y*z0^4 - x^11*z0 - 2*x^9*y*z0^2 - x^7*y*z0^4 - x^10*y - 2*x^10*z0 + x^8*y*z0^2 - x^8*z0^3 - 2*x^6*y*z0^4 - 2*x^9*y - 2*x^9*z0 - 2*x^7*z0^3 - x^5*y*z0^4 - x^8*y + x^8*z0 + x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^7*y - x^7*z0 + x^5*y*z0^2 + 2*x^5*z0^3 - x^6*y + x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^5*y + 2*x^5*z0 + 2*x^3*z0^3 + 2*x^4*z0 + x^2*y*z0^2 + 2*x^2*z0^3 + 2*x^3*y - 2*x^3*z0 + 2*x^2*y + x^2*z0)/y) * dx, - ((-x^30*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 - 2*x^30 - x^28*y^2 - x^28*z0^2 + x^26*z0^4 + 2*x^27*y^2 - 2*x^27*z0^2 + x^23*y^2*z0^4 - x^28 - x^24*z0^4 + 2*x^27 + x^25*z0^2 - x^23*z0^4 + 2*x^24*z0^2 + x^25 + x^21*z0^4 - 2*x^24 - x^22*z0^2 + x^20*z0^4 - 2*x^21*z0^2 - x^22 - x^18*z0^4 + 2*x^21 + x^19*z0^2 - x^17*z0^4 + 2*x^18*z0^2 + x^19 + x^15*z0^4 - 2*x^18 - x^16*z0^2 + x^14*z0^4 - 2*x^15*z0^2 - x^16 - x^12*z0^4 + 2*x^15 + x^13*z0^2 + x^11*z0^4 + 2*x^12*z0^2 + 2*x^10*z0^4 + x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 + 2*x^10*z0^2 - x^8*z0^4 - 2*x^11 - x^9*y*z0 + 2*x^7*z0^4 - x^10 - x^8*y*z0 + x^6*y*z0^3 + x^6*z0^4 - 2*x^9 - x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 + 2*x^8 + 2*x^6*y*z0 - 2*x^6*z0^2 + x^7 + x^5*y*z0 + x^5*z0^2 - 2*x^3*z0^4 - 2*x^4*y*z0 + x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 - x^3*y*z0 - x^2*y*z0 + x^2*z0^2 + x^3 + 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^31*z0^4 - 2*x^30*z0^4 - x^28*y^2*z0^4 + x^31*z0^2 + x^29*z0^4 + 2*x^27*y^2*z0^4 - x^30*z0^2 - x^28*y^2*z0^2 - x^28*z0^4 - x^26*y^2*z0^4 + x^31 + x^27*y^2*z0^2 + 2*x^27*z0^4 - 2*x^30 - x^28*y^2 - x^28*z0^2 - x^26*z0^4 + 2*x^27*y^2 + x^27*z0^2 + x^25*z0^4 - x^28 - 2*x^24*z0^4 + x^27 + x^25*z0^2 + x^23*z0^4 + x^24*y^2 - x^24*z0^2 - x^22*z0^4 + x^25 + 2*x^21*z0^4 - x^24 - x^22*z0^2 - x^20*z0^4 + x^21*z0^2 + x^19*z0^4 - x^22 - 2*x^18*z0^4 + x^21 + x^19*z0^2 + x^17*z0^4 - x^18*z0^2 - x^16*z0^4 + x^19 + 2*x^15*z0^4 - x^18 - x^16*z0^2 - x^14*z0^4 + x^15*z0^2 + x^13*z0^4 - x^16 - 2*x^12*z0^4 + x^15 + x^13*z0^2 - 2*x^11*z0^4 - x^12*z0^2 + 2*x^10*y*z0^3 + x^10*z0^4 + x^13 - x^9*y*z0^3 + 2*x^9*z0^4 - x^12 + 2*x^10*y*z0 + x^10*z0^2 - 2*x^8*y*z0^3 + x^8*z0^4 + 2*x^11 - x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 - 2*x^7*z0^4 - 2*x^10 + 2*x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 + x^9 - x^7*y*z0 - x^7*z0^2 + x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^5*z0^2 + 2*x^3*y*z0^3 - 2*x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*y*z0 + x^3*z0^2 - 2*x^2*y*z0 - 2*x^2*z0^2 + 2*x^2)/y) * dx, - ((-x^31*z0^3 - 2*x^30*z0^3 + x^28*y^2*z0^3 + 2*x^31*z0 + 2*x^27*y^2*z0^3 + x^30*z0 - 2*x^28*y^2*z0 + x^28*z0^3 - x^29*z0 - x^27*y^2*z0 + 2*x^27*z0^3 + 2*x^28*z0 + x^26*y^2*z0 - 2*x^27*z0 + x^25*y^2*z0 - x^25*z0^3 + x^26*z0 + x^24*y^2*z0 - 2*x^24*z0^3 - 2*x^25*z0 + 2*x^24*z0 + x^22*z0^3 - x^23*z0 + 2*x^21*z0^3 + 2*x^22*z0 - 2*x^21*z0 - x^19*z0^3 + x^20*z0 - 2*x^18*z0^3 - 2*x^19*z0 + 2*x^18*z0 + x^16*z0^3 - x^17*z0 + 2*x^15*z0^3 + 2*x^16*z0 - 2*x^15*z0 - x^13*z0^3 + x^14*z0 - 2*x^12*z0^3 - 2*x^13*z0 + x^9*y*z0^4 + 2*x^12*z0 - 2*x^10*y*z0^2 + x^10*z0^3 - 2*x^8*y*z0^4 - x^11*z0 - 2*x^9*y*z0^2 - x^9*z0^3 + x^7*y*z0^4 - x^10*y - 2*x^10*z0 - 2*x^8*y*z0^2 + x^6*y*z0^4 - x^9*y - 2*x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 + x^5*y*z0^4 + x^8*y - 2*x^8*z0 + 2*x^6*y*z0^2 + x^6*z0^3 - x^4*y*z0^4 + x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - 2*x^6*y + x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^2*y*z0^4 - x^5*y + x^5*z0 + x^3*y*z0^2 + 2*x^3*z0^3 - 2*x^2*y*z0^2 - x^2*z0^3 + x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-x^30*z0^4 + x^31*z0^2 + 2*x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 - 2*x^26*y^2*z0^4 - x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 + x^28*y^2 - x^28*z0^2 - 2*x^26*z0^4 + 2*x^27*z0^2 + x^28 + x^24*y^2*z0^2 - x^24*z0^4 + x^25*z0^2 + 2*x^23*z0^4 - 2*x^24*z0^2 - x^25 + x^21*z0^4 - x^22*z0^2 - 2*x^20*z0^4 + 2*x^21*z0^2 + x^22 - x^18*z0^4 + x^19*z0^2 + 2*x^17*z0^4 - 2*x^18*z0^2 - x^19 + x^15*z0^4 - x^16*z0^2 - 2*x^14*z0^4 + 2*x^15*z0^2 + x^16 - x^12*z0^4 + x^13*z0^2 - 2*x^12*z0^2 + 2*x^10*z0^4 - x^13 - x^9*y*z0^3 + 2*x^10*y*z0 - x^8*y*z0^3 - x^8*z0^4 + 2*x^11 + x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 + 2*x^7*z0^4 + x^10 - x^8*y*z0 + 2*x^6*z0^4 - 2*x^9 - 2*x^7*y*z0 + x^7*z0^2 - x^5*y*z0^3 - x^8 - 2*x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*z0^2 - x^3*z0^4 - 2*x^6 - x^4*y*z0 - x^4*z0^2 - 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 + x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 + x^3)/y) * dx, - ((-2*x^31*z0^4 + 2*x^30*z0^4 + 2*x^28*y^2*z0^4 - x^31*z0^2 + x^29*z0^4 - 2*x^27*y^2*z0^4 + 2*x^30*z0^2 + x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 + x^31 - 2*x^27*y^2*z0^2 + 2*x^27*z0^4 - x^28*y^2 + x^28*z0^2 - x^26*z0^4 + x^24*y^2*z0^4 - 2*x^27*z0^2 - 2*x^25*z0^4 - x^28 - 2*x^24*z0^4 - x^25*z0^2 + x^23*z0^4 + 2*x^24*z0^2 + 2*x^22*z0^4 + x^25 + 2*x^21*z0^4 + x^22*z0^2 - x^20*z0^4 - 2*x^21*z0^2 - 2*x^19*z0^4 - x^22 - 2*x^18*z0^4 - x^19*z0^2 + x^17*z0^4 + 2*x^18*z0^2 + 2*x^16*z0^4 + x^19 + 2*x^15*z0^4 + x^16*z0^2 - x^14*z0^4 - 2*x^15*z0^2 - 2*x^13*z0^4 - x^16 - 2*x^12*z0^4 - x^13*z0^2 - 2*x^11*z0^4 + 2*x^12*z0^2 + x^10*y*z0^3 + x^10*z0^4 + x^13 + x^9*y*z0^3 - x^9*z0^4 - 2*x^10*y*z0 - x^10*z0^2 + 2*x^8*y*z0^3 - x^9*y*z0 + x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 + 2*x^8*z0^2 + 2*x^6*y*z0^3 - 2*x^6*z0^4 - 2*x^9 - x^7*y*z0 + x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 - x^8 - 2*x^6*z0^2 - 2*x^4*y*z0^3 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*y*z0 - x^3*y*z0^3 + x^3*z0^4 - 2*x^6 + 2*x^4*y*z0 - 2*x^2*y*z0^3 - x^2*z0^4 + 2*x^5 - 2*x^3*z0^2 + 2*x^2*z0^2 + 2*x^3 + 2*x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((x^31*z0^4 - x^28*y^2*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^30*z0^2 - x^28*y^2*z0^2 - x^28*z0^4 + 2*x^26*y^2*z0^4 + 2*x^31 - x^27*y^2*z0^2 - 2*x^30 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y^2 - x^27*z0^2 + x^25*z0^4 + 2*x^28 + 2*x^27 + x^25*y^2 + x^25*z0^2 - 2*x^23*z0^4 + x^24*z0^2 - x^22*z0^4 - 2*x^25 - 2*x^24 - x^22*z0^2 + 2*x^20*z0^4 - x^21*z0^2 + x^19*z0^4 + 2*x^22 + 2*x^21 + x^19*z0^2 - 2*x^17*z0^4 + x^18*z0^2 - x^16*z0^4 - 2*x^19 - 2*x^18 - x^16*z0^2 + 2*x^14*z0^4 - x^15*z0^2 + x^13*z0^4 + 2*x^16 + 2*x^15 + x^13*z0^2 + 2*x^11*z0^4 + x^12*z0^2 + 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 + 2*x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^9*y*z0 - x^7*y*z0^3 - x^7*z0^4 + 2*x^10 + 2*x^8*y*z0 + 2*x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 - 2*x^7*z0^2 + x^5*y*z0^3 - 2*x^5*z0^4 + x^8 - x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 + x^4*z0^4 - x^5*y*z0 + 2*x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 + x^6 + 2*x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - x^2*z0^4 - 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 - 2*x^2)/y) * dx, - ((2*x^31*z0^4 - x^30*z0^4 - 2*x^28*y^2*z0^4 + 2*x^31*z0^2 - x^29*z0^4 + x^27*y^2*z0^4 - 2*x^30*z0^2 - 2*x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 + x^31 + 2*x^27*y^2*z0^2 + x^27*z0^4 + x^30 - x^28*y^2 + 2*x^28*z0^2 + x^26*z0^4 - x^27*y^2 + 2*x^27*z0^2 + x^25*y^2*z0^2 + 2*x^25*z0^4 - x^28 - x^24*z0^4 - x^27 - 2*x^25*z0^2 - x^23*z0^4 - 2*x^24*z0^2 - 2*x^22*z0^4 + x^25 + x^21*z0^4 + x^24 + 2*x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 + 2*x^19*z0^4 - x^22 - x^18*z0^4 - x^21 - 2*x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*z0^4 + x^19 + x^15*z0^4 + x^18 + 2*x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + 2*x^13*z0^4 - x^16 - x^12*z0^4 - x^15 - 2*x^13*z0^2 + x^11*z0^4 - 2*x^12*z0^2 - x^10*y*z0^3 - x^10*z0^4 + x^13 - 2*x^9*y*z0^3 - 2*x^9*z0^4 + x^12 - x^10*y*z0 - 2*x^8*y*z0^3 + x^11 - x^9*y*z0 + 2*x^7*y*z0^3 - 2*x^7*z0^4 + x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 - 2*x^6*y*z0^3 + 2*x^6*z0^4 + 2*x^9 + 2*x^7*y*z0 - x^5*y*z0^3 - 2*x^4*y*z0^3 - x^7 + x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^4*y*z0 + 2*x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 - x^2)/y) * dx, - ((x^31*z0^3 - x^30*z0^3 - x^28*y^2*z0^3 - 2*x^31*z0 - 2*x^29*z0^3 + x^27*y^2*z0^3 - x^30*z0 + 2*x^28*y^2*z0 - 2*x^28*z0^3 + 2*x^26*y^2*z0^3 + 2*x^29*z0 + x^27*y^2*z0 + x^27*z0^3 + x^25*y^2*z0^3 + 2*x^28*z0 - 2*x^26*y^2*z0 + 2*x^26*z0^3 + x^27*z0 + 2*x^25*z0^3 - 2*x^26*z0 - x^24*z0^3 - 2*x^25*z0 - 2*x^23*z0^3 - x^24*z0 - 2*x^22*z0^3 + 2*x^23*z0 + x^21*z0^3 + 2*x^22*z0 + 2*x^20*z0^3 + x^21*z0 + 2*x^19*z0^3 - 2*x^20*z0 - x^18*z0^3 - 2*x^19*z0 - 2*x^17*z0^3 - x^18*z0 - 2*x^16*z0^3 + 2*x^17*z0 + x^15*z0^3 + 2*x^16*z0 + 2*x^14*z0^3 + x^15*z0 + 2*x^13*z0^3 - 2*x^14*z0 - x^12*z0^3 - 2*x^13*z0 - 2*x^11*z0^3 - x^9*y*z0^4 - x^12*z0 + 2*x^10*y*z0^2 + x^10*z0^3 - x^8*y*z0^4 + 2*x^11*z0 + 2*x^9*y*z0^2 + x^9*z0^3 + x^10*y + x^10*z0 - x^8*z0^3 + x^9*y - 2*x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 + 2*x^8*z0 - x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 - x^5*y*z0^2 - x^5*z0^3 - x^3*y*z0^4 - 2*x^6*y - x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + x^5*z0 - 2*x^3*y*z0^2 + 2*x^3*z0^3 - x^4*y + x^4*z0 - x^2*y*z0^2 - 2*x^2*z0^3 + x^3*y - 2*x^3*z0 - x^2*y - 2*x^2*z0)/y) * dx, - ((2*x^31*z0^4 + x^30*z0^4 - 2*x^28*y^2*z0^4 - x^31*z0^2 - x^27*y^2*z0^4 + x^30*z0^2 + x^28*y^2*z0^2 + 2*x^28*z0^4 + x^31 - x^27*y^2*z0^2 - x^27*z0^4 + x^25*y^2*z0^4 - 2*x^30 - x^28*y^2 + x^28*z0^2 + 2*x^27*y^2 - x^27*z0^2 - 2*x^25*z0^4 - x^28 + x^24*z0^4 + 2*x^27 - x^25*z0^2 + x^24*z0^2 + 2*x^22*z0^4 + x^25 - x^21*z0^4 - 2*x^24 + x^22*z0^2 - x^21*z0^2 - 2*x^19*z0^4 - x^22 + x^18*z0^4 + 2*x^21 - x^19*z0^2 + x^18*z0^2 + 2*x^16*z0^4 + x^19 - x^15*z0^4 - 2*x^18 + x^16*z0^2 - x^15*z0^2 - 2*x^13*z0^4 - x^16 + x^12*z0^4 + 2*x^15 - x^13*z0^2 + 2*x^11*z0^4 + x^12*z0^2 - x^10*y*z0^3 - 2*x^10*z0^4 + x^13 + x^9*y*z0^3 + x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - x^10*z0^2 + 2*x^8*y*z0^3 - x^8*z0^4 + x^11 - x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 - x^7*z0^4 + x^10 - 2*x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 - 2*x^7*y*z0 - x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - 2*x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^7 - 2*x^5*y*z0 + x^3*y*z0^3 - x^3*z0^4 + 2*x^6 + x^4*y*z0 - 2*x^4*z0^2 + 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0 + x^2*z0^2 + x^3 - x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - ((-2*x^31*z0^4 + 2*x^30*z0^4 + 2*x^28*y^2*z0^4 + 2*x^31*z0^2 + x^29*z0^4 - 2*x^27*y^2*z0^4 - 2*x^30*z0^2 - 2*x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 - x^31 + 2*x^27*y^2*z0^2 - 2*x^27*z0^4 + x^28*y^2 - 2*x^28*z0^2 - x^26*z0^4 - x^29 + 2*x^27*z0^2 - 2*x^25*z0^4 + x^28 + x^26*y^2 + 2*x^24*z0^4 + 2*x^25*z0^2 + x^23*z0^4 + x^26 - 2*x^24*z0^2 + 2*x^22*z0^4 - x^25 - 2*x^21*z0^4 - 2*x^22*z0^2 - x^20*z0^4 - x^23 + 2*x^21*z0^2 - 2*x^19*z0^4 + x^22 + 2*x^18*z0^4 + 2*x^19*z0^2 + x^17*z0^4 + x^20 - 2*x^18*z0^2 + 2*x^16*z0^4 - x^19 - 2*x^15*z0^4 - 2*x^16*z0^2 - x^14*z0^4 - x^17 + 2*x^15*z0^2 - 2*x^13*z0^4 + x^16 + 2*x^12*z0^4 + 2*x^13*z0^2 - x^11*z0^4 + x^14 - 2*x^12*z0^2 + x^10*y*z0^3 - x^10*z0^4 - x^13 - 2*x^9*y*z0^3 - x^10*y*z0 - 2*x^8*y*z0^3 + x^8*z0^4 - 2*x^11 + x^9*y*z0 + 2*x^9*z0^2 - x^7*y*z0^3 + x^7*z0^4 - x^10 - x^8*y*z0 + 2*x^8*z0^2 - 2*x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 - 2*x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 - x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 - 2*x^5*z0^2 + x^3*z0^4 + x^6 + x^4*y*z0 - x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - x^3*y*z0 + 2*x^3*z0^2 - x^2*y*z0 - x^2*z0^2 - x^3 - x^2)/y) * dx, - ((2*x^31*z0^4 - 2*x^28*y^2*z0^4 - x^31*z0^2 - x^29*z0^4 + x^30*z0^2 + x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 - x^29*z0^2 - x^27*y^2*z0^2 - x^30 + x^28*z0^2 + x^26*y^2*z0^2 + x^26*z0^4 + x^27*y^2 - x^27*z0^2 + 2*x^25*z0^4 + x^26*z0^2 + x^27 - x^25*z0^2 - x^23*z0^4 + x^24*z0^2 - 2*x^22*z0^4 - x^23*z0^2 - x^24 + x^22*z0^2 + x^20*z0^4 - x^21*z0^2 + 2*x^19*z0^4 + x^20*z0^2 + x^21 - x^19*z0^2 - x^17*z0^4 + x^18*z0^2 - 2*x^16*z0^4 - x^17*z0^2 - x^18 + x^16*z0^2 + x^14*z0^4 - x^15*z0^2 + 2*x^13*z0^4 + x^14*z0^2 + x^15 - x^13*z0^2 - x^11*z0^4 + x^12*z0^2 - x^10*y*z0^3 - x^11*z0^2 + x^9*y*z0^3 + x^9*z0^4 - x^12 - 2*x^10*y*z0 - 2*x^10*z0^2 + x^8*y*z0^3 + x^8*z0^4 - 2*x^11 - 2*x^7*y*z0^3 + x^7*z0^4 + x^10 - 2*x^8*y*z0 - x^6*y*z0^3 + 2*x^6*z0^4 + x^9 + x^7*y*z0 + x^5*y*z0^3 + 2*x^5*z0^4 + x^8 + x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 + 2*x^7 - x^5*y*z0 + x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^4*y*z0 + x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^3*y*z0 + x^3*z0^2 + 2*x^2*y*z0 - 2*x^2*z0^2 + x^3 + x^2)/y) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx, - (0) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C2.polynomial[?7h[?12l[?25h[?25l[?7lgg.monomial_coefficient(y)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = FxRy(y/x)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l![?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l!=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: ggg = [a for a in lll if a.form != 0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llll[?7h[?12l[?25h[?25l[?7len(AS.holomorphic_differentials_basis())[?7h[?12l[?25h[?25l[?7llen([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: len(ggg) -[?7h[?12l[?25h[?2004l[?7h140 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lnu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h9 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in lll:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduction(C2, y^2*a.omega0.h1)/y^2[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls.reduce()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: result = [] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in lll:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lgg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: for a in ggg: -....: [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7l.f[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7l.f[?7h[?12l[?25h[?25l[?7lexponents()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in lll:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l -....: [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnch_points[?7h[?12l[?25h[?25l[?7lsage: AS.branch_points -[?7h[?12l[?25h[?2004l[?7h[0, (-1, 0), (1, 0)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.branch_points[?7h[?12l[?25h[?25l[?7lresult = [][?7h[?12l[?25h[?25l[?7lAS.branch_points[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in lll:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l lll:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lg:[?7h[?12l[?25h[?25l[?7lg:[?7h[?12l[?25h[?25l[?7lg:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in ggg: -....: [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  b = a.expansion((-1, 0)) -....: [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() -....:  -....:  for r in result:[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  for r in result: -....: [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:  if r.expansion((-1, 0)) == b: -....: [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l....:  flag = 0 -....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:  if flag == 1: -....: [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l....:  result += [b] -....: [?7h[?12l[?25h[?25l[?7lsage: for a in ggg: -....:  b = a.expansion((-1, 0)) -....:  flag = 1 -....:  for r in result: -....:  if r.expansion((-1, 0)) == b: -....:  flag = 0 -....:  if flag == 1: -....:  result += [b] -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lresult = [][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: result -[?7h[?12l[?25h[?2004l[?7h[] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lresult[?7h[?12l[?25h[?25l[?7lsage: for a in ggg: -....:  b = a.expansion((-1, 0)) -....:  flag = 1 -....:  for r in result: -....:  if r.expansion((-1, 0)) == b: -....:  flag = 0 -....:  if flag == 1: -....:  result += [b][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lif flag = 1:[?7h[?12l[?25h[?25l[?7lif flag = 1:[?7h[?12l[?25h[?25l[?7lif flag = 1:[?7h[?12l[?25h[?25l[?7lif flag = 1:[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lresult += [b][?7h[?12l[?25h[?25l[?7lresult += [b][?7h[?12l[?25h[?25l[?7lresult += [b][?7h[?12l[?25h[?25l[?7lresult += [b][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7la][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  result += [a] -....: [?7h[?12l[?25h[?25l[?7lsage: for a in ggg: -....:  b = a.expansion((-1, 0)) -....:  flag = 1 -....:  for r in result: -....:  if r.expansion((-1, 0)) == b: -....:  flag = 0 -....:  if flag == 1: -....:  result += [a] -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lresult[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsult[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llt[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: result -[?7h[?12l[?25h[?2004l[?7h[((2*x^31*z0^3 + 2*x^30*z0^3 - 2*x^28*y^2*z0^3 - 2*x^31*z0 + 2*x^29*z0^3 - 2*x^27*y^2*z0^3 + x^30*z0 + 2*x^28*y^2*z0 - 2*x^28*z0^3 - 2*x^26*y^2*z0^3 - 2*x^29*z0 - x^27*y^2*z0 - x^27*z0^3 + 2*x^26*y^2*z0 - 2*x^26*z0^3 - x^24*y^2*z0^3 - x^27*z0 + 2*x^25*y^2*z0 + 2*x^25*z0^3 + 2*x^26*z0 + x^24*z0^3 + 2*x^23*z0^3 + x^24*z0 - 2*x^22*z0^3 - 2*x^23*z0 - x^21*z0^3 - 2*x^20*z0^3 - x^21*z0 + 2*x^19*z0^3 + 2*x^20*z0 + x^18*z0^3 + 2*x^17*z0^3 + x^18*z0 - 2*x^16*z0^3 - 2*x^17*z0 - x^15*z0^3 - 2*x^14*z0^3 - x^15*z0 + 2*x^13*z0^3 + 2*x^14*z0 + x^12*z0^3 + 2*x^11*z0^3 - 2*x^9*y*z0^4 + x^12*z0 - x^10*y*z0^2 + 2*x^10*z0^3 + 2*x^8*y*z0^4 - 2*x^11*z0 + 2*x^9*y*z0^2 - 2*x^9*z0^3 - 2*x^7*y*z0^4 + x^10*y - 2*x^10*z0 - x^8*y*z0^2 + x^8*z0^3 - x^6*y*z0^4 + 2*x^9*y + x^9*z0 + x^7*z0^3 - 2*x^8*z0 + x^6*y*z0^2 + 2*x^6*z0^3 + 2*x^4*y*z0^4 + x^7*y - x^5*y*z0^2 - x^3*y*z0^4 + 2*x^6*z0 - x^4*y*z0^2 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - x^3*y*z0^2 - x^3*z0^3 + x^2*y*z0^2 + 2*x^2*z0^3 - x^3*y + 2*x^3*z0 - 2*x^2*z0 + y)/y) * dx, - ((-x^30*z0^4 + 2*x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 - 2*x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 - 2*x^31 + x^27*z0^4 + 2*x^28*y^2 - 2*x^28*z0^2 + 2*x^26*z0^4 + 2*x^28 - x^24*z0^4 + 2*x^25*z0^2 - 2*x^23*z0^4 - 2*x^25 + x^21*z0^4 - 2*x^22*z0^2 + 2*x^20*z0^4 + 2*x^22 - x^18*z0^4 + 2*x^19*z0^2 - 2*x^17*z0^4 - 2*x^19 + x^15*z0^4 - 2*x^16*z0^2 + 2*x^14*z0^4 + 2*x^16 - x^12*z0^4 + 2*x^13*z0^2 - x^11*z0^4 - 2*x^10*z0^4 - 2*x^13 - 2*x^9*y*z0^3 + x^9*z0^4 - x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 + x^8*z0^4 - x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 + x^7*y*z0^3 - 2*x^10 - x^8*y*z0 + 2*x^8*z0^2 + 2*x^6*y*z0^3 - x^6*z0^4 + x^7*y*z0 + 2*x^7*z0^2 + x^5*y*z0^3 + 2*x^5*z0^4 + x^8 - x^6*y*z0 + 2*x^6*z0^2 + x^4*z0^4 - x^5*y*z0 - x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^6 - x^4*y*z0 - 2*x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^3*y*z0 - 2*x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 - x^3 - x^2 + y*z0)/y) * dx, - ((-x^31*z0^3 + x^30*z0^3 + x^28*y^2*z0^3 + x^31*z0 - x^29*z0^3 - x^27*y^2*z0^3 - x^30*z0 - x^28*y^2*z0 + x^28*z0^3 + x^26*y^2*z0^3 - x^29*z0 + x^27*y^2*z0 - 2*x^27*z0^3 - x^28*z0 + x^26*y^2*z0 + x^26*z0^3 + x^24*y^2*z0^3 + x^27*z0 - x^25*z0^3 + x^26*z0 + 2*x^24*z0^3 + x^25*z0 - x^23*z0^3 - x^24*z0 + x^22*z0^3 - x^23*z0 - 2*x^21*z0^3 - x^22*z0 + x^20*z0^3 + x^21*z0 - x^19*z0^3 + x^20*z0 + 2*x^18*z0^3 + x^19*z0 - x^17*z0^3 - x^18*z0 + x^16*z0^3 - x^17*z0 - 2*x^15*z0^3 - x^16*z0 + x^14*z0^3 + x^15*z0 - x^13*z0^3 + x^14*z0 + 2*x^12*z0^3 + x^13*z0 - x^11*z0^3 + x^9*y*z0^4 - x^12*z0 - 2*x^10*y*z0^2 + 2*x^10*z0^3 + x^8*y*z0^4 - x^11*z0 - x^9*y*z0^2 + 2*x^9*z0^3 + 2*x^10*y - 2*x^10*z0 - x^8*z0^3 - x^6*y*z0^4 - x^9*y - x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 + 2*x^8*y - 2*x^8*z0 + 2*x^6*y*z0^2 + 2*x^6*z0^3 + 2*x^4*y*z0^4 + 2*x^7*y + x^7*z0 - 2*x^5*y*z0^2 + x^5*z0^3 + 2*x^3*y*z0^4 - x^6*y + 2*x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 + 2*x^2*y*z0^4 - x^5*z0 + x^3*y*z0^2 + 2*x^3*z0^3 - x^4*y + x^3*z0 + x^2*y - x^2*z0 + y*z0^2)/y) * dx, - ((2*x^31*z0^4 + 2*x^30*z0^4 - 2*x^28*y^2*z0^4 - 2*x^27*y^2*z0^4 + x^30*z0^2 - 2*x^28*z0^4 - 2*x^31 - x^27*y^2*z0^2 - 2*x^27*z0^4 + x^30 + 2*x^28*y^2 - x^27*y^2 - x^27*z0^2 + 2*x^25*z0^4 + 2*x^28 + 2*x^24*z0^4 - x^27 + x^24*z0^2 - 2*x^22*z0^4 - 2*x^25 - 2*x^21*z0^4 + x^24 - x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 + 2*x^18*z0^4 - x^21 + x^18*z0^2 - 2*x^16*z0^4 - 2*x^19 - 2*x^15*z0^4 + x^18 - x^15*z0^2 + 2*x^13*z0^4 + 2*x^16 + 2*x^12*z0^4 - x^15 + x^11*z0^4 + x^12*z0^2 - x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - x^9*z0^4 + x^12 - x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 - 2*x^7*y*z0^3 - x^7*z0^4 + 2*x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 - x^6*z0^4 + x^9 + x^7*y*z0 + x^7*z0^2 - 2*x^5*y*z0^3 + 2*x^5*z0^4 + x^8 - x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 - 2*x^4*z0^4 - 2*x^5*y*z0 + x^5*z0^2 + 2*x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^4*y*z0 - x^4*z0^2 + x^2*z0^4 - 2*x^5 - x^3*y*z0 + 2*x^2*y*z0 + 2*x^2*z0^2 + y*z0^3 - 2*x^3 - 2*x^2)/y) * dx, - ((-2*x^29*z0^3 + 2*x^30*z0 + 2*x^26*y^2*z0^3 - x^29*z0 - 2*x^27*y^2*z0 + x^27*z0^3 - x^28*z0 + x^26*y^2*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 - 2*x^27*z0 + x^25*y^2*z0 + x^26*z0 - x^24*z0^3 + x^25*z0 - 2*x^23*z0^3 + 2*x^24*z0 - x^23*z0 + x^21*z0^3 - x^22*z0 + 2*x^20*z0^3 - 2*x^21*z0 + x^20*z0 - x^18*z0^3 + x^19*z0 - 2*x^17*z0^3 + 2*x^18*z0 - x^17*z0 + x^15*z0^3 - x^16*z0 + 2*x^14*z0^3 - 2*x^15*z0 + x^14*z0 - x^12*z0^3 + x^13*z0 - 2*x^11*z0^3 + 2*x^12*z0 - x^11*z0 + 2*x^9*z0^3 + 2*x^10*z0 - 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 + x^5*y*z0^4 + 2*x^8*z0 + x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 + 2*x^7*y - x^7*z0 + x^5*z0^3 + x^3*y*z0^4 - x^6*y - x^6*z0 + 2*x^2*y*z0^4 - 2*x^5*z0 + 2*x^3*z0^3 - x^4*y - x^4*z0 - x^2*y*z0^2 - 2*x^2*z0^3 + y*z0^4 - x^3*y - x^3*z0 - 2*x^2*y + 2*x^2*z0)/y) * dx, - ((-x^3 + y^2)/y) * dx, - ((-x^3*z0 + y^2*z0)/y) * dx, - ((-x^3*z0^2 + y^2*z0^2)/y) * dx, - ((-x^3*z0^3 + y^2*z0^3)/y) * dx, - ((-x^3*z0^4 + y^2*z0^4)/y) * dx, - ((2*x^31*z0^3 + x^30*z0^3 - 2*x^28*y^2*z0^3 - x^31*z0 + 2*x^29*z0^3 - x^27*y^2*z0^3 + x^28*y^2*z0 - 2*x^28*z0^3 - 2*x^26*y^2*z0^3 - x^29*z0 + 2*x^27*z0^3 + x^26*y^2*z0 - 2*x^26*z0^3 + 2*x^24*y^2*z0^3 + x^25*y^2*z0 + 2*x^25*z0^3 + x^26*z0 - 2*x^24*z0^3 + 2*x^23*z0^3 - 2*x^22*z0^3 - x^23*z0 + 2*x^21*z0^3 - 2*x^20*z0^3 + 2*x^19*z0^3 + x^20*z0 - 2*x^18*z0^3 + 2*x^17*z0^3 - 2*x^16*z0^3 - x^17*z0 + 2*x^15*z0^3 - 2*x^14*z0^3 + 2*x^13*z0^3 + x^14*z0 - 2*x^12*z0^3 + 2*x^11*z0^3 - 2*x^9*y*z0^4 - x^10*y*z0^2 - x^10*z0^3 + x^8*y*z0^4 - x^11*z0 + x^9*y*z0^2 - 2*x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y - 2*x^10*z0 - 2*x^8*y*z0^2 - x^8*z0^3 + 2*x^6*y*z0^4 + 2*x^9*y + 2*x^9*z0 + 2*x^7*y*z0^2 - x^7*z0^3 + x^5*y*z0^4 + 2*x^8*y + 2*x^8*z0 + 2*x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^4*y*z0^4 + x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 + 2*x^6*y + 2*x^6*z0 + 2*x^4*y*z0^2 - x^4*z0^3 - 2*x^2*y*z0^4 - x^5*y + x^5*z0 + x^3*z0^3 - x^4*y + 2*x^4*z0 + 2*x^2*z0^3 + 2*x^3*y - 2*x^3*z0 + x^2*y + x^2*z0 + x*y)/y) * dx, - ((x^30*z0^4 + 2*x^31*z0^2 - 2*x^29*z0^4 - x^27*y^2*z0^4 + 2*x^30*z0^2 - 2*x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + x^31 - 2*x^27*y^2*z0^2 - x^27*z0^4 - x^28*y^2 - 2*x^28*z0^2 + 2*x^26*z0^4 - 2*x^27*z0^2 - x^28 + x^24*z0^4 + 2*x^25*z0^2 - 2*x^23*z0^4 + 2*x^24*z0^2 + x^25 - x^21*z0^4 - 2*x^22*z0^2 + 2*x^20*z0^4 - 2*x^21*z0^2 - x^22 + x^18*z0^4 + 2*x^19*z0^2 - 2*x^17*z0^4 + 2*x^18*z0^2 + x^19 - x^15*z0^4 - 2*x^16*z0^2 + 2*x^14*z0^4 - 2*x^15*z0^2 - x^16 + x^12*z0^4 + 2*x^13*z0^2 + 2*x^12*z0^2 + x^10*z0^4 + x^13 - 2*x^9*y*z0^3 - 2*x^9*z0^4 - x^10*y*z0 - 2*x^11 - x^9*y*z0 + x^7*y*z0^3 + x^7*z0^4 - x^10 - 2*x^8*z0^2 - x^6*y*z0^3 - x^6*z0^4 + 2*x^9 - x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 - x^5*z0^4 - 2*x^8 + x^4*y*z0^3 + 2*x^4*z0^4 - x^7 - x^5*y*z0 - x^3*y*z0^3 + 2*x^6 - 2*x^4*y*z0 + x^4*z0^2 + x^2*z0^4 + 2*x^5 + x^3*y*z0 + 2*x^2*z0^2 + x^3 + x*y*z0 - 2*x^2)/y) * dx, - ((-x^31*z0 + 2*x^29*z0^3 + x^28*y^2*z0 - 2*x^26*y^2*z0^3 - x^29*z0 + 2*x^27*z0^3 + x^26*y^2*z0 - 2*x^26*z0^3 - 2*x^24*y^2*z0^3 + x^25*y^2*z0 + x^26*z0 - 2*x^24*z0^3 + 2*x^23*z0^3 - x^23*z0 + 2*x^21*z0^3 - 2*x^20*z0^3 + x^20*z0 - 2*x^18*z0^3 + 2*x^17*z0^3 - x^17*z0 + 2*x^15*z0^3 - 2*x^14*z0^3 + x^14*z0 - 2*x^12*z0^3 + 2*x^11*z0^3 - x^10*z0^3 - x^11*z0 + x^9*y*z0^2 + x^9*z0^3 - x^7*y*z0^4 - 2*x^10*y + x^10*z0 + 2*x^8*y*z0^2 + 2*x^8*z0^3 + x^6*y*z0^4 - x^7*y*z0^2 - x^7*z0^3 - x^5*y*z0^4 - 2*x^8*z0 + x^6*z0^3 - 2*x^4*y*z0^4 - x^7*y - x^7*z0 - x^5*z0^3 + x^3*y*z0^4 - 2*x^6*z0 - x^4*y*z0^2 - x^4*z0^3 - 2*x^2*y*z0^4 - x^5*z0 - 2*x^3*y*z0^2 + 2*x^3*z0^3 - 2*x^4*y + x^4*z0 + 2*x^2*y*z0^2 + x^3*y - x^3*z0 + x*y*z0^2 - 2*x^2*z0)/y) * dx, - ((x^31*z0^4 - x^30*z0^4 - x^28*y^2*z0^4 + 2*x^31*z0^2 - x^29*z0^4 + x^27*y^2*z0^4 - 2*x^28*y^2*z0^2 - x^28*z0^4 + x^26*y^2*z0^4 - 2*x^31 + x^27*z0^4 + 2*x^28*y^2 - 2*x^28*z0^2 + x^26*z0^4 + x^25*z0^4 + 2*x^28 - x^24*z0^4 + 2*x^25*z0^2 - x^23*z0^4 - x^22*z0^4 - 2*x^25 + x^21*z0^4 - 2*x^22*z0^2 + x^20*z0^4 + x^19*z0^4 + 2*x^22 - x^18*z0^4 + 2*x^19*z0^2 - x^17*z0^4 - x^16*z0^4 - 2*x^19 + x^15*z0^4 - 2*x^16*z0^2 + x^14*z0^4 + x^13*z0^4 + 2*x^16 - x^12*z0^4 + 2*x^13*z0^2 + 2*x^10*y*z0^3 + x^10*z0^4 - 2*x^13 - 2*x^9*y*z0^3 + x^9*z0^4 - x^10*y*z0 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 - x^7*z0^4 - 2*x^10 + x^8*y*z0 - 2*x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 + 2*x^9 - x^7*z0^2 - 2*x^5*y*z0^3 + x^5*z0^4 + 2*x^8 + x^6*y*z0 - x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^7 - x^5*z0^2 - x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^6 + 2*x^2*y*z0^3 + x^2*z0^4 - x^5 - x^3*y*z0 - x^3*z0^2 + x*y*z0^3 + x^2*y*z0 - 2*x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((x^31*z0^3 + x^30*z0^3 - x^28*y^2*z0^3 - 2*x^31*z0 - x^27*y^2*z0^3 - 2*x^30*z0 + 2*x^28*y^2*z0 - x^28*z0^3 - x^29*z0 + 2*x^27*y^2*z0 - 2*x^27*z0^3 + x^28*z0 + x^26*y^2*z0 + x^24*y^2*z0^3 + 2*x^27*z0 + x^25*y^2*z0 + x^25*z0^3 + x^26*z0 + 2*x^24*z0^3 - x^25*z0 - 2*x^24*z0 - x^22*z0^3 - x^23*z0 - 2*x^21*z0^3 + x^22*z0 + 2*x^21*z0 + x^19*z0^3 + x^20*z0 + 2*x^18*z0^3 - x^19*z0 - 2*x^18*z0 - x^16*z0^3 - x^17*z0 - 2*x^15*z0^3 + x^16*z0 + 2*x^15*z0 + x^13*z0^3 + x^14*z0 + 2*x^12*z0^3 - x^13*z0 - x^9*y*z0^4 - 2*x^12*z0 + 2*x^10*y*z0^2 + x^8*y*z0^4 - x^11*z0 + 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 + x^10*y + x^10*z0 + x^8*y*z0^2 + 2*x^8*z0^3 + x^6*y*z0^4 + x^9*y + x^9*z0 + x^7*y*z0^2 + 2*x^7*z0^3 + 2*x^5*y*z0^4 + 2*x^8*z0 + 2*x^6*y*z0^2 + 2*x^6*z0^3 + x^4*y*z0^4 - 2*x^7*z0 - x^5*y*z0^2 + x^5*z0^3 + 2*x^3*y*z0^4 + x^6*y - 2*x^6*z0 + 2*x^4*y*z0^2 + 2*x^4*z0^3 + 2*x^2*y*z0^4 - 2*x^5*z0 - 2*x^3*y*z0^2 + x^3*z0^3 + x*y*z0^4 - x^4*y + 2*x^4*z0 - 2*x^2*y*z0^2 + 2*x^3*y + 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((-x^31*z0^4 - x^30*z0^4 + x^28*y^2*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 - x^28*y^2*z0^2 + x^28*z0^4 + 2*x^26*y^2*z0^4 + 2*x^31 + x^27*z0^4 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 - x^25*z0^4 - 2*x^28 - x^24*z0^4 + x^25*z0^2 - 2*x^23*z0^4 + x^22*z0^4 + 2*x^25 + x^21*z0^4 - x^22*z0^2 + 2*x^20*z0^4 - x^19*z0^4 - 2*x^22 - x^18*z0^4 + x^19*z0^2 - 2*x^17*z0^4 + x^16*z0^4 + 2*x^19 + x^15*z0^4 - x^16*z0^2 + 2*x^14*z0^4 - x^13*z0^4 - 2*x^16 - x^12*z0^4 + x^13*z0^2 + 2*x^11*z0^4 - 2*x^10*y*z0^3 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 + x^8*z0^4 + 2*x^11 - 2*x^9*y*z0 + x^7*y*z0^3 + x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 + 2*x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^6 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - x^3 + x*y^2)/y) * dx, - ((2*x^30*z0^3 + 2*x^31*z0 - 2*x^29*z0^3 - 2*x^27*y^2*z0^3 - x^30*z0 - 2*x^28*y^2*z0 + 2*x^26*y^2*z0^3 + x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + 2*x^25*y^2*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 - x^24*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 + x^21*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 - x^18*z0 - x^15*z0^3 + x^16*z0 + 2*x^14*z0^3 + x^15*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 - x^12*z0 + 2*x^8*y*z0^4 - 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - x^8*z0 - 2*x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 - 2*x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y - x^6*z0 - x^4*y*z0^2 + x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - 2*x^3*z0^3 + x^4*y + 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y + x^3*z0 + x*y^2*z0 - 2*x^2*z0)/y) * dx, - ((2*x^30*z0^4 + x^31*z0^2 - 2*x^29*z0^4 - 2*x^27*y^2*z0^4 - x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + 2*x^31 - 2*x^27*z0^4 - 2*x^30 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y^2 - 2*x^28 + 2*x^24*z0^4 + 2*x^27 + x^25*z0^2 - 2*x^23*z0^4 + 2*x^25 - 2*x^21*z0^4 - 2*x^24 - x^22*z0^2 + 2*x^20*z0^4 - 2*x^22 + 2*x^18*z0^4 + 2*x^21 + x^19*z0^2 - 2*x^17*z0^4 + 2*x^19 - 2*x^15*z0^4 - 2*x^18 - x^16*z0^2 + 2*x^14*z0^4 - 2*x^16 + 2*x^12*z0^4 + 2*x^15 + x^13*z0^2 + 2*x^11*z0^4 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*z0^4 - 2*x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 + x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 + x*y^2*z0^2 + 2*x^2*y*z0 + x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^31*z0^3 + x^28*y^2*z0^3 - x^31*z0 - 2*x^29*z0^3 + x^30*z0 + x^28*y^2*z0 + x^28*z0^3 + 2*x^26*y^2*z0^3 - 2*x^29*z0 - x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*y^2*z0 + 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - x^25*z0^3 + 2*x^26*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 + x^24*z0 + x^22*z0^3 - 2*x^23*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 - x^21*z0 - x^19*z0^3 + 2*x^20*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 + x^18*z0 + x^16*z0^3 - 2*x^17*z0 - x^15*z0^3 + x^16*z0 + 2*x^14*z0^3 - x^15*z0 - x^13*z0^3 + 2*x^14*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 - 2*x^10*y*z0^2 + x^10*z0^3 - 2*x^11*z0 + x^9*y*z0^2 - x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y + x^8*y*z0^2 - x^6*y*z0^4 - x^9*y - x^9*z0 + 2*x^7*y*z0^2 - 2*x^5*y*z0^4 + x^8*y + 2*x^8*z0 + x^6*y*z0^2 - x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^6*z0 + x^4*z0^3 - x^2*y*z0^4 - x^5*y + x^5*z0 - x^3*y*z0^2 - x^3*z0^3 + x*y^2*z0^3 - 2*x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - 2*x^3*y - 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-2*x^31*z0^4 - x^30*z0^4 + 2*x^28*y^2*z0^4 + x^31*z0^2 + x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 + 2*x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 + 2*x^30 - 2*x^28*y^2 - x^28*z0^2 - x^26*z0^4 - 2*x^27*y^2 - 2*x^27*z0^2 - 2*x^25*z0^4 - 2*x^28 - x^24*z0^4 - 2*x^27 + x^25*z0^2 + x^23*z0^4 + 2*x^24*z0^2 + 2*x^22*z0^4 + 2*x^25 + x^21*z0^4 + 2*x^24 - x^22*z0^2 - x^20*z0^4 - 2*x^21*z0^2 - 2*x^19*z0^4 - 2*x^22 - x^18*z0^4 - 2*x^21 + x^19*z0^2 + x^17*z0^4 + 2*x^18*z0^2 + 2*x^16*z0^4 + 2*x^19 + x^15*z0^4 + 2*x^18 - x^16*z0^2 - x^14*z0^4 - 2*x^15*z0^2 - 2*x^13*z0^4 - 2*x^16 - x^12*z0^4 - 2*x^15 + x^13*z0^2 + 2*x^12*z0^2 + x^10*y*z0^3 + x^10*z0^4 + 2*x^13 - x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 + x^7*z0^4 - 2*x^10 - x^8*y*z0 + x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 - 2*x^7*y*z0 + x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 - x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + x^5*y*z0 + x*y^2*z0^4 - 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^5 + x^2*y^2 + x^2)/y) * dx, - ((-x^5*z0 + x^2*y^2*z0 + x^2*z0)/y) * dx, - ((-x^5*z0^2 + x^2*y^2*z0^2 + x^2*z0^2)/y) * dx, - ((-x^5*z0^3 + x^2*y^2*z0^3 + x^2*z0^3)/y) * dx, - ((-x^5*z0^4 + x^2*y^2*z0^4 + x^2*z0^4)/y) * dx, - ((-x^6 + x^3*y^2 + x^3)/y) * dx, - ((-x^6*z0 + x^3*y^2*z0 + x^3*z0)/y) * dx, - ((-x^6*z0^2 + x^3*y^2*z0^2 + x^3*z0^2)/y) * dx, - ((-x^6*z0^3 + x^3*y^2*z0^3 + x^3*z0^3)/y) * dx, - ((-x^6*z0^4 + x^3*y^2*z0^4 + x^3*z0^4)/y) * dx, - ((x^31*z0^4 + x^30*z0^4 - x^28*y^2*z0^4 - x^31*z0^2 + 2*x^29*z0^4 - x^27*y^2*z0^4 + x^28*y^2*z0^2 - x^28*z0^4 - 2*x^26*y^2*z0^4 - 2*x^31 - x^27*z0^4 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 + x^25*z0^4 + 2*x^28 + x^24*z0^4 - x^25*z0^2 + 2*x^23*z0^4 - x^22*z0^4 - 2*x^25 - x^21*z0^4 + x^22*z0^2 - 2*x^20*z0^4 + x^19*z0^4 + 2*x^22 + x^18*z0^4 - x^19*z0^2 + 2*x^17*z0^4 - x^16*z0^4 - 2*x^19 - x^15*z0^4 + x^16*z0^2 - 2*x^14*z0^4 + x^13*z0^4 + 2*x^16 + x^12*z0^4 - x^13*z0^2 - 2*x^11*z0^4 + 2*x^10*y*z0^3 + x^10*z0^4 - 2*x^13 + x^9*y*z0^3 - x^9*z0^4 - 2*x^10*y*z0 + x^10*z0^2 - x^8*z0^4 - 2*x^11 + 2*x^9*y*z0 - x^7*y*z0^3 - x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 - 2*x^7*y*z0 + 2*x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + x^8 - x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 + x^7 + x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^6 + x^4*y^2 - 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 + x^3)/y) * dx, - ((-2*x^30*z0^3 - 2*x^31*z0 + 2*x^29*z0^3 + 2*x^27*y^2*z0^3 + x^30*z0 + 2*x^28*y^2*z0 - 2*x^26*y^2*z0^3 - x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - 2*x^25*y^2*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 + x^24*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 - x^21*z0 - x^18*z0^3 + x^19*z0 + 2*x^17*z0^3 + x^18*z0 + x^15*z0^3 - x^16*z0 - 2*x^14*z0^3 - x^15*z0 - x^12*z0^3 + x^13*z0 + 2*x^11*z0^3 + x^12*z0 - 2*x^8*y*z0^4 + 2*x^9*y*z0^2 - 2*x^9*z0^3 + 2*x^7*y*z0^4 + x^10*y - 2*x^8*y*z0^2 + 2*x^8*z0^3 - x^6*y*z0^4 - x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 - x^8*y + x^8*z0 + 2*x^6*y*z0^2 - x^6*z0^3 + 2*x^4*y*z0^4 + x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - x^3*y*z0^4 + 2*x^6*y + x^6*z0 + x^4*y^2*z0 + x^4*y*z0^2 - x^4*z0^3 - x^2*y*z0^4 - 2*x^5*y - 2*x^5*z0 + 2*x^3*z0^3 - x^4*y - 2*x^4*z0 - 2*x^2*y*z0^2 + 2*x^2*z0^3 - 2*x^3*y - x^3*z0 + 2*x^2*z0)/y) * dx, - ((-2*x^30*z0^4 - x^31*z0^2 + 2*x^29*z0^4 + 2*x^27*y^2*z0^4 + x^28*y^2*z0^2 - 2*x^26*y^2*z0^4 - 2*x^31 + 2*x^27*z0^4 + 2*x^30 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 - 2*x^27*y^2 + 2*x^28 - 2*x^24*z0^4 - 2*x^27 - x^25*z0^2 + 2*x^23*z0^4 - 2*x^25 + 2*x^21*z0^4 + 2*x^24 + x^22*z0^2 - 2*x^20*z0^4 + 2*x^22 - 2*x^18*z0^4 - 2*x^21 - x^19*z0^2 + 2*x^17*z0^4 - 2*x^19 + 2*x^15*z0^4 + 2*x^18 + x^16*z0^2 - 2*x^14*z0^4 + 2*x^16 - 2*x^12*z0^4 - 2*x^15 - x^13*z0^2 - 2*x^11*z0^4 + x^10*z0^4 - 2*x^13 + x^9*y*z0^3 + x^9*z0^4 + 2*x^12 - 2*x^10*y*z0 + 2*x^8*y*z0^3 - 2*x^8*z0^4 - x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*z0^4 + 2*x^8*y*z0 - x^8*z0^2 + x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 - x^8 + 2*x^6*y*z0 + x^6*z0^2 + x^4*y^2*z0^2 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((x^31*z0^3 - x^28*y^2*z0^3 + x^31*z0 + 2*x^29*z0^3 - x^30*z0 - x^28*y^2*z0 - x^28*z0^3 - 2*x^26*y^2*z0^3 + 2*x^29*z0 + x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*y^2*z0 - 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + x^25*z0^3 - 2*x^26*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 - x^24*z0 - x^22*z0^3 + 2*x^23*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 + x^21*z0 + x^19*z0^3 - 2*x^20*z0 - x^18*z0^3 + x^19*z0 + 2*x^17*z0^3 - x^18*z0 - x^16*z0^3 + 2*x^17*z0 + x^15*z0^3 - x^16*z0 - 2*x^14*z0^3 + x^15*z0 + x^13*z0^3 - 2*x^14*z0 - x^12*z0^3 + x^13*z0 + 2*x^11*z0^3 - x^9*y*z0^4 - x^12*z0 + 2*x^10*y*z0^2 - x^10*z0^3 + 2*x^11*z0 - x^9*y*z0^2 + x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y - x^8*y*z0^2 + x^6*y*z0^4 + x^9*y + x^9*z0 - 2*x^7*y*z0^2 - x^7*z0^3 + 2*x^5*y*z0^4 - x^8*y - 2*x^8*z0 - x^6*y*z0^2 + x^4*y^2*z0^3 + x^7*z0 + 2*x^5*y*z0^2 - 2*x^5*z0^3 + x^6*z0 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - x^5*z0 + x^3*y*z0^2 + x^3*z0^3 + 2*x^4*z0 - x^2*y*z0^2 - x^2*z0^3 + 2*x^3*y + 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((2*x^31*z0^4 + x^30*z0^4 - 2*x^28*y^2*z0^4 - x^31*z0^2 - x^29*z0^4 - x^27*y^2*z0^4 - 2*x^30*z0^2 + x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 - 2*x^31 + 2*x^27*y^2*z0^2 - x^27*z0^4 - 2*x^30 + 2*x^28*y^2 + x^28*z0^2 + x^26*z0^4 + 2*x^27*y^2 + 2*x^27*z0^2 + 2*x^25*z0^4 + 2*x^28 + x^24*z0^4 + 2*x^27 - x^25*z0^2 - x^23*z0^4 - 2*x^24*z0^2 - 2*x^22*z0^4 - 2*x^25 - x^21*z0^4 - 2*x^24 + x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 + x^18*z0^4 + 2*x^21 - x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*z0^4 - 2*x^19 - x^15*z0^4 - 2*x^18 + x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + 2*x^13*z0^4 + 2*x^16 + x^12*z0^4 + 2*x^15 - x^13*z0^2 - 2*x^12*z0^2 - x^10*y*z0^3 - x^10*z0^4 - 2*x^13 + x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 + 2*x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*y*z0^3 - 2*x^7*z0^4 + 2*x^10 + x^8*y*z0 - x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 + x^4*y^2*z0^4 - x^9 + 2*x^7*y*z0 - x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^6 + x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((-x^8 + x^5*y^2 + x^5 - x^2)/y) * dx, - ((-x^8*z0 + x^5*y^2*z0 + x^5*z0 - x^2*z0)/y) * dx, - ((-x^8*z0^2 + x^5*y^2*z0^2 + x^5*z0^2 - x^2*z0^2)/y) * dx, - ((-x^8*z0^3 + x^5*y^2*z0^3 + x^5*z0^3 - x^2*z0^3)/y) * dx, - ((-x^8*z0^4 + x^5*y^2*z0^4 + x^5*z0^4 - x^2*z0^4)/y) * dx, - ((-x^9 + x^6*y^2 + x^6 - x^3)/y) * dx, - ((-x^9*z0 + x^6*y^2*z0 + x^6*z0 - x^3*z0)/y) * dx, - ((-x^9*z0^2 + x^6*y^2*z0^2 + x^6*z0^2 - x^3*z0^2)/y) * dx, - ((-x^9*z0^3 + x^6*y^2*z0^3 + x^6*z0^3 - x^3*z0^3)/y) * dx, - ((-x^9*z0^4 + x^6*y^2*z0^4 + x^6*z0^4 - x^3*z0^4)/y) * dx, - ((-x^31*z0^4 - x^30*z0^4 + x^28*y^2*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 - x^28*y^2*z0^2 + x^28*z0^4 + 2*x^26*y^2*z0^4 + 2*x^31 + x^27*z0^4 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 - x^25*z0^4 - 2*x^28 - x^24*z0^4 + x^25*z0^2 - 2*x^23*z0^4 + x^22*z0^4 + 2*x^25 + x^21*z0^4 - x^22*z0^2 + 2*x^20*z0^4 - x^19*z0^4 - 2*x^22 - x^18*z0^4 + x^19*z0^2 - 2*x^17*z0^4 + x^16*z0^4 + 2*x^19 + x^15*z0^4 - x^16*z0^2 + 2*x^14*z0^4 - x^13*z0^4 - 2*x^16 - x^12*z0^4 + x^13*z0^2 + 2*x^11*z0^4 - 2*x^10*y*z0^3 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 + x^8*z0^4 + 2*x^11 - 2*x^9*y*z0 + x^7*y*z0^3 - x^10 + x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 + x^7*y^2 + 2*x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - x^7 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^6 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - x^3)/y) * dx, - ((2*x^30*z0^3 + 2*x^31*z0 - 2*x^29*z0^3 - 2*x^27*y^2*z0^3 - x^30*z0 - 2*x^28*y^2*z0 + 2*x^26*y^2*z0^3 + x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + 2*x^25*y^2*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 - x^24*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 + x^21*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 - x^18*z0 - x^15*z0^3 + x^16*z0 + 2*x^14*z0^3 + x^15*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 - x^12*z0 + 2*x^8*y*z0^4 - 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y - x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^9*z0 + x^7*y^2*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - x^8*z0 - 2*x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 - x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y - x^6*z0 - x^4*y*z0^2 + x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - 2*x^3*z0^3 + x^4*y + 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y + x^3*z0 - 2*x^2*z0)/y) * dx, - ((2*x^30*z0^4 + x^31*z0^2 - 2*x^29*z0^4 - 2*x^27*y^2*z0^4 - x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + 2*x^31 - 2*x^27*z0^4 - 2*x^30 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y^2 - 2*x^28 + 2*x^24*z0^4 + 2*x^27 + x^25*z0^2 - 2*x^23*z0^4 + 2*x^25 - 2*x^21*z0^4 - 2*x^24 - x^22*z0^2 + 2*x^20*z0^4 - 2*x^22 + 2*x^18*z0^4 + 2*x^21 + x^19*z0^2 - 2*x^17*z0^4 + 2*x^19 - 2*x^15*z0^4 - 2*x^18 - x^16*z0^2 + 2*x^14*z0^4 - 2*x^16 + 2*x^12*z0^4 + 2*x^15 + x^13*z0^2 + 2*x^11*z0^4 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 + x^7*y^2*z0^2 - x^7*z0^4 - 2*x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^31*z0^3 + x^28*y^2*z0^3 - x^31*z0 - 2*x^29*z0^3 + x^30*z0 + x^28*y^2*z0 + x^28*z0^3 + 2*x^26*y^2*z0^3 - 2*x^29*z0 - x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*y^2*z0 + 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - x^25*z0^3 + 2*x^26*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 + x^24*z0 + x^22*z0^3 - 2*x^23*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 - x^21*z0 - x^19*z0^3 + 2*x^20*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 + x^18*z0 + x^16*z0^3 - 2*x^17*z0 - x^15*z0^3 + x^16*z0 + 2*x^14*z0^3 - x^15*z0 - x^13*z0^3 + 2*x^14*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 - 2*x^10*y*z0^2 - 2*x^11*z0 + x^9*y*z0^2 - x^9*z0^3 + x^7*y^2*z0^3 + x^7*y*z0^4 - 2*x^10*y + x^8*y*z0^2 - x^6*y*z0^4 - x^9*y - x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 - 2*x^5*y*z0^4 + x^8*y + 2*x^8*z0 + x^6*y*z0^2 - x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^6*z0 + x^4*z0^3 - x^2*y*z0^4 - x^5*y + x^5*z0 - x^3*y*z0^2 - x^3*z0^3 - 2*x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - 2*x^3*y - 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-2*x^31*z0^4 - x^30*z0^4 + 2*x^28*y^2*z0^4 + x^31*z0^2 + x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 + 2*x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 + 2*x^30 - 2*x^28*y^2 - x^28*z0^2 - x^26*z0^4 - 2*x^27*y^2 - 2*x^27*z0^2 - 2*x^25*z0^4 - 2*x^28 - x^24*z0^4 - 2*x^27 + x^25*z0^2 + x^23*z0^4 + 2*x^24*z0^2 + 2*x^22*z0^4 + 2*x^25 + x^21*z0^4 + 2*x^24 - x^22*z0^2 - x^20*z0^4 - 2*x^21*z0^2 - 2*x^19*z0^4 - 2*x^22 - x^18*z0^4 - 2*x^21 + x^19*z0^2 + x^17*z0^4 + 2*x^18*z0^2 + 2*x^16*z0^4 + 2*x^19 + x^15*z0^4 + 2*x^18 - x^16*z0^2 - x^14*z0^4 - 2*x^15*z0^2 - 2*x^13*z0^4 - 2*x^16 - x^12*z0^4 - 2*x^15 + x^13*z0^2 + 2*x^12*z0^2 + x^10*y*z0^3 + 2*x^13 - x^9*y*z0^3 + 2*x^9*z0^4 + x^7*y^2*z0^4 + 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 - x^8*y*z0 + x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 - 2*x^7*y*z0 + x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 - x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^11 + x^8*y^2 + x^8 - x^5 + x^2)/y) * dx, - ((-x^11*z0 + x^8*y^2*z0 + x^8*z0 - x^5*z0 + x^2*z0)/y) * dx, - ((-x^11*z0^2 + x^8*y^2*z0^2 + x^8*z0^2 - x^5*z0^2 + x^2*z0^2)/y) * dx, - ((-x^11*z0^3 + x^8*y^2*z0^3 + x^8*z0^3 - x^5*z0^3 + x^2*z0^3)/y) * dx, - ((-x^11*z0^4 + x^8*y^2*z0^4 + x^8*z0^4 - x^5*z0^4 + x^2*z0^4)/y) * dx, - ((-x^12 + x^9*y^2 + x^9 - x^6 + x^3)/y) * dx, - ((-x^12*z0 + x^9*y^2*z0 + x^9*z0 - x^6*z0 + x^3*z0)/y) * dx, - ((-x^12*z0^2 + x^9*y^2*z0^2 + x^9*z0^2 - x^6*z0^2 + x^3*z0^2)/y) * dx, - ((-x^12*z0^3 + x^9*y^2*z0^3 + x^9*z0^3 - x^6*z0^3 + x^3*z0^3)/y) * dx, - ((-x^12*z0^4 + x^9*y^2*z0^4 + x^9*z0^4 - x^6*z0^4 + x^3*z0^4)/y) * dx, - ((x^31*z0^4 + x^30*z0^4 - x^28*y^2*z0^4 - x^31*z0^2 + 2*x^29*z0^4 - x^27*y^2*z0^4 + x^28*y^2*z0^2 - x^28*z0^4 - 2*x^26*y^2*z0^4 - 2*x^31 - x^27*z0^4 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 + x^25*z0^4 + 2*x^28 + x^24*z0^4 - x^25*z0^2 + 2*x^23*z0^4 - x^22*z0^4 - 2*x^25 - x^21*z0^4 + x^22*z0^2 - 2*x^20*z0^4 + x^19*z0^4 + 2*x^22 + x^18*z0^4 - x^19*z0^2 + 2*x^17*z0^4 - x^16*z0^4 - 2*x^19 - x^15*z0^4 + x^16*z0^2 - 2*x^14*z0^4 + x^13*z0^4 + 2*x^16 + x^12*z0^4 - x^13*z0^2 - 2*x^11*z0^4 + 2*x^10*y*z0^3 + x^10*z0^4 + 2*x^13 + x^9*y*z0^3 - x^9*z0^4 + x^10*y^2 - 2*x^10*y*z0 + x^10*z0^2 - x^8*z0^4 - 2*x^11 + 2*x^9*y*z0 - x^7*y*z0^3 + x^10 - x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 - 2*x^7*y*z0 + 2*x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + x^8 - x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 + x^7 + x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^6 - 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 + x^3)/y) * dx, - ((-2*x^30*z0^3 - 2*x^31*z0 + 2*x^29*z0^3 + 2*x^27*y^2*z0^3 + x^30*z0 + 2*x^28*y^2*z0 - 2*x^26*y^2*z0^3 - x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - 2*x^25*y^2*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 + x^24*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 - x^21*z0 - x^18*z0^3 + x^19*z0 + 2*x^17*z0^3 + x^18*z0 + x^15*z0^3 - x^16*z0 - 2*x^14*z0^3 - x^15*z0 - x^12*z0^3 + 2*x^11*z0^3 + x^12*z0 + x^10*y^2*z0 - 2*x^8*y*z0^4 + 2*x^9*y*z0^2 - 2*x^9*z0^3 + 2*x^7*y*z0^4 + x^10*y + x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 - x^6*y*z0^4 - x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 - x^8*y + x^8*z0 + 2*x^6*y*z0^2 - x^6*z0^3 + 2*x^4*y*z0^4 + x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - x^3*y*z0^4 + 2*x^6*y + x^6*z0 + x^4*y*z0^2 - x^4*z0^3 - x^2*y*z0^4 - 2*x^5*y - 2*x^5*z0 + 2*x^3*z0^3 - x^4*y - 2*x^4*z0 - 2*x^2*y*z0^2 + 2*x^2*z0^3 - 2*x^3*y - x^3*z0 + 2*x^2*z0)/y) * dx, - ((-2*x^30*z0^4 - x^31*z0^2 + 2*x^29*z0^4 + 2*x^27*y^2*z0^4 + x^28*y^2*z0^2 - 2*x^26*y^2*z0^4 - 2*x^31 + 2*x^27*z0^4 + 2*x^30 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 - 2*x^27*y^2 + 2*x^28 - 2*x^24*z0^4 - 2*x^27 - x^25*z0^2 + 2*x^23*z0^4 - 2*x^25 + 2*x^21*z0^4 + 2*x^24 + x^22*z0^2 - 2*x^20*z0^4 + 2*x^22 - 2*x^18*z0^4 - 2*x^21 - x^19*z0^2 + 2*x^17*z0^4 - 2*x^19 + 2*x^15*z0^4 + 2*x^18 + x^16*z0^2 - 2*x^14*z0^4 + 2*x^16 - 2*x^12*z0^4 - 2*x^15 - 2*x^13*z0^2 - 2*x^11*z0^4 + x^10*y^2*z0^2 + x^10*z0^4 - 2*x^13 + x^9*y*z0^3 + x^9*z0^4 + 2*x^12 - 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 - 2*x^8*z0^4 - x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*z0^4 + 2*x^8*y*z0 - x^8*z0^2 + x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 - x^8 + 2*x^6*y*z0 + x^6*z0^2 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((x^31*z0^3 - x^28*y^2*z0^3 + x^31*z0 + 2*x^29*z0^3 - x^30*z0 - x^28*y^2*z0 - x^28*z0^3 - 2*x^26*y^2*z0^3 + 2*x^29*z0 + x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*y^2*z0 - 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + x^25*z0^3 - 2*x^26*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 - x^24*z0 - x^22*z0^3 + 2*x^23*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 + x^21*z0 + x^19*z0^3 - 2*x^20*z0 - x^18*z0^3 + x^19*z0 + 2*x^17*z0^3 - x^18*z0 - x^16*z0^3 + 2*x^17*z0 + x^15*z0^3 - x^16*z0 - 2*x^14*z0^3 + x^15*z0 - 2*x^14*z0 - x^12*z0^3 + x^10*y^2*z0^3 + x^13*z0 + 2*x^11*z0^3 - x^9*y*z0^4 - x^12*z0 + 2*x^10*y*z0^2 + 2*x^11*z0 - x^9*y*z0^2 + x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y - x^8*y*z0^2 + x^6*y*z0^4 + x^9*y + x^9*z0 - 2*x^7*y*z0^2 - x^7*z0^3 + 2*x^5*y*z0^4 - x^8*y - 2*x^8*z0 - x^6*y*z0^2 + x^7*z0 + 2*x^5*y*z0^2 - 2*x^5*z0^3 + x^6*z0 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - x^5*z0 + x^3*y*z0^2 + x^3*z0^3 + 2*x^4*z0 - x^2*y*z0^2 - x^2*z0^3 + 2*x^3*y + 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((2*x^31*z0^4 + x^30*z0^4 - 2*x^28*y^2*z0^4 - x^31*z0^2 - x^29*z0^4 - x^27*y^2*z0^4 - 2*x^30*z0^2 + x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 - 2*x^31 + 2*x^27*y^2*z0^2 - x^27*z0^4 - 2*x^30 + 2*x^28*y^2 + x^28*z0^2 + x^26*z0^4 + 2*x^27*y^2 + 2*x^27*z0^2 + 2*x^25*z0^4 + 2*x^28 + x^24*z0^4 + 2*x^27 - x^25*z0^2 - x^23*z0^4 - 2*x^24*z0^2 - 2*x^22*z0^4 - 2*x^25 - x^21*z0^4 - 2*x^24 + x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 + x^18*z0^4 + 2*x^21 - x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*z0^4 - 2*x^19 - x^15*z0^4 - 2*x^18 + x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + x^13*z0^4 + 2*x^16 + x^12*z0^4 + x^10*y^2*z0^4 + 2*x^15 - x^13*z0^2 - 2*x^12*z0^2 - x^10*y*z0^3 - 2*x^13 + x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 + 2*x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*y*z0^3 - 2*x^7*z0^4 + 2*x^10 + x^8*y*z0 - x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 - x^9 + 2*x^7*y*z0 - x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^6 + x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((-x^14 + x^11*y^2 + x^11 - x^8 + x^5 - x^2)/y) * dx, - ((-x^14*z0 + x^11*y^2*z0 + x^11*z0 - x^8*z0 + x^5*z0 - x^2*z0)/y) * dx, - ((-x^14*z0^2 + x^11*y^2*z0^2 + x^11*z0^2 - x^8*z0^2 + x^5*z0^2 - x^2*z0^2)/y) * dx, - ((-x^14*z0^3 + x^11*y^2*z0^3 + x^11*z0^3 - x^8*z0^3 + x^5*z0^3 - x^2*z0^3)/y) * dx, - ((-x^14*z0^4 + x^11*y^2*z0^4 + x^11*z0^4 - x^8*z0^4 + x^5*z0^4 - x^2*z0^4)/y) * dx, - ((-x^15 + x^12*y^2 + x^12 - x^9 + x^6 - x^3)/y) * dx, - ((-x^15*z0 + x^12*y^2*z0 + x^12*z0 - x^9*z0 + x^6*z0 - x^3*z0)/y) * dx, - ((-x^15*z0^2 + x^12*y^2*z0^2 + x^12*z0^2 - x^9*z0^2 + x^6*z0^2 - x^3*z0^2)/y) * dx, - ((-x^15*z0^3 + x^12*y^2*z0^3 + x^12*z0^3 - x^9*z0^3 + x^6*z0^3 - x^3*z0^3)/y) * dx, - ((-x^15*z0^4 + x^12*y^2*z0^4 + x^12*z0^4 - x^9*z0^4 + x^6*z0^4 - x^3*z0^4)/y) * dx, - ((-x^31*z0^4 - x^30*z0^4 + x^28*y^2*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 - x^28*y^2*z0^2 + x^28*z0^4 + 2*x^26*y^2*z0^4 + 2*x^31 + x^27*z0^4 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 - x^25*z0^4 - 2*x^28 - x^24*z0^4 + x^25*z0^2 - 2*x^23*z0^4 + x^22*z0^4 + 2*x^25 + x^21*z0^4 - x^22*z0^2 + 2*x^20*z0^4 - x^19*z0^4 - 2*x^22 - x^18*z0^4 + x^19*z0^2 - 2*x^17*z0^4 + x^16*z0^4 + 2*x^19 + x^15*z0^4 - x^16*z0^2 + 2*x^14*z0^4 - x^13*z0^4 + 2*x^16 - x^12*z0^4 + x^13*y^2 + x^13*z0^2 + 2*x^11*z0^4 - 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 + x^8*z0^4 + 2*x^11 - 2*x^9*y*z0 + x^7*y*z0^3 - x^10 + x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 + 2*x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - x^7 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^6 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - x^3)/y) * dx, - ((2*x^30*z0^3 + 2*x^31*z0 - 2*x^29*z0^3 - 2*x^27*y^2*z0^3 - x^30*z0 - 2*x^28*y^2*z0 + 2*x^26*y^2*z0^3 + x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + 2*x^25*y^2*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 - x^24*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 + x^21*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 - x^18*z0 - x^15*z0^3 + 2*x^14*z0^3 + x^15*z0 + x^13*y^2*z0 + x^12*z0^3 - 2*x^11*z0^3 - x^12*z0 + 2*x^8*y*z0^4 - 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y - x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - x^8*z0 - 2*x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 - x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y - x^6*z0 - x^4*y*z0^2 + x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - 2*x^3*z0^3 + x^4*y + 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y + x^3*z0 - 2*x^2*z0)/y) * dx, - ((2*x^30*z0^4 + x^31*z0^2 - 2*x^29*z0^4 - 2*x^27*y^2*z0^4 - x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + 2*x^31 - 2*x^27*z0^4 - 2*x^30 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y^2 - 2*x^28 + 2*x^24*z0^4 + 2*x^27 + x^25*z0^2 - 2*x^23*z0^4 + 2*x^25 - 2*x^21*z0^4 - 2*x^24 - x^22*z0^2 + 2*x^20*z0^4 - 2*x^22 + 2*x^18*z0^4 + 2*x^21 + x^19*z0^2 - 2*x^17*z0^4 + 2*x^19 - 2*x^15*z0^4 - 2*x^18 - 2*x^16*z0^2 + 2*x^14*z0^4 + x^13*y^2*z0^2 - 2*x^16 + 2*x^12*z0^4 + 2*x^15 + 2*x^13*z0^2 + 2*x^11*z0^4 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*z0^4 - 2*x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^31*z0^3 + x^28*y^2*z0^3 - x^31*z0 - 2*x^29*z0^3 + x^30*z0 + x^28*y^2*z0 + x^28*z0^3 + 2*x^26*y^2*z0^3 - 2*x^29*z0 - x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*y^2*z0 + 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - x^25*z0^3 + 2*x^26*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 + x^24*z0 + x^22*z0^3 - 2*x^23*z0 - x^21*z0^3 + x^22*z0 + 2*x^20*z0^3 - x^21*z0 - x^19*z0^3 + 2*x^20*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 + x^18*z0 - 2*x^17*z0 - x^15*z0^3 + x^13*y^2*z0^3 + x^16*z0 + 2*x^14*z0^3 - x^15*z0 + 2*x^14*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 - 2*x^10*y*z0^2 - 2*x^11*z0 + x^9*y*z0^2 - x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y + x^8*y*z0^2 - x^6*y*z0^4 - x^9*y - x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 - 2*x^5*y*z0^4 + x^8*y + 2*x^8*z0 + x^6*y*z0^2 - x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^6*z0 + x^4*z0^3 - x^2*y*z0^4 - x^5*y + x^5*z0 - x^3*y*z0^2 - x^3*z0^3 - 2*x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - 2*x^3*y - 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-2*x^31*z0^4 - x^30*z0^4 + 2*x^28*y^2*z0^4 + x^31*z0^2 + x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 + 2*x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 + 2*x^30 - 2*x^28*y^2 - x^28*z0^2 - x^26*z0^4 - 2*x^27*y^2 - 2*x^27*z0^2 - 2*x^25*z0^4 - 2*x^28 - x^24*z0^4 - 2*x^27 + x^25*z0^2 + x^23*z0^4 + 2*x^24*z0^2 + 2*x^22*z0^4 + 2*x^25 + x^21*z0^4 + 2*x^24 - x^22*z0^2 - x^20*z0^4 - 2*x^21*z0^2 - 2*x^19*z0^4 - 2*x^22 - x^18*z0^4 - 2*x^21 + x^19*z0^2 + x^17*z0^4 + 2*x^18*z0^2 + x^16*z0^4 + 2*x^19 + x^15*z0^4 + x^13*y^2*z0^4 + 2*x^18 - x^16*z0^2 - x^14*z0^4 - 2*x^15*z0^2 - x^13*z0^4 - 2*x^16 - x^12*z0^4 - 2*x^15 + x^13*z0^2 + 2*x^12*z0^2 + x^10*y*z0^3 + 2*x^13 - x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 - x^8*y*z0 + x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 - 2*x^7*y*z0 + x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 - x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^17 + x^14*y^2 + x^14 - x^11 + x^8 - x^5 + x^2)/y) * dx, - ((-x^17*z0 + x^14*y^2*z0 + x^14*z0 - x^11*z0 + x^8*z0 - x^5*z0 + x^2*z0)/y) * dx, - ((-x^17*z0^2 + x^14*y^2*z0^2 + x^14*z0^2 - x^11*z0^2 + x^8*z0^2 - x^5*z0^2 + x^2*z0^2)/y) * dx, - ((-x^17*z0^3 + x^14*y^2*z0^3 + x^14*z0^3 - x^11*z0^3 + x^8*z0^3 - x^5*z0^3 + x^2*z0^3)/y) * dx, - ((-x^17*z0^4 + x^14*y^2*z0^4 + x^14*z0^4 - x^11*z0^4 + x^8*z0^4 - x^5*z0^4 + x^2*z0^4)/y) * dx, - ((-x^18 + x^15*y^2 + x^15 - x^12 + x^9 - x^6 + x^3)/y) * dx, - ((-x^18*z0 + x^15*y^2*z0 + x^15*z0 - x^12*z0 + x^9*z0 - x^6*z0 + x^3*z0)/y) * dx, - ((-x^18*z0^2 + x^15*y^2*z0^2 + x^15*z0^2 - x^12*z0^2 + x^9*z0^2 - x^6*z0^2 + x^3*z0^2)/y) * dx, - ((-x^18*z0^3 + x^15*y^2*z0^3 + x^15*z0^3 - x^12*z0^3 + x^9*z0^3 - x^6*z0^3 + x^3*z0^3)/y) * dx, - ((-x^18*z0^4 + x^15*y^2*z0^4 + x^15*z0^4 - x^12*z0^4 + x^9*z0^4 - x^6*z0^4 + x^3*z0^4)/y) * dx, - ((x^31*z0^4 + x^30*z0^4 - x^28*y^2*z0^4 - x^31*z0^2 + 2*x^29*z0^4 - x^27*y^2*z0^4 + x^28*y^2*z0^2 - x^28*z0^4 - 2*x^26*y^2*z0^4 - 2*x^31 - x^27*z0^4 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 + x^25*z0^4 + 2*x^28 + x^24*z0^4 - x^25*z0^2 + 2*x^23*z0^4 - x^22*z0^4 - 2*x^25 - x^21*z0^4 + x^22*z0^2 - 2*x^20*z0^4 + x^19*z0^4 + 2*x^22 + x^18*z0^4 - x^19*z0^2 + 2*x^17*z0^4 - x^16*z0^4 + 2*x^19 - x^15*z0^4 + x^16*y^2 + x^16*z0^2 - 2*x^14*z0^4 + x^13*z0^4 - 2*x^16 + x^12*z0^4 - x^13*z0^2 - 2*x^11*z0^4 + 2*x^10*y*z0^3 + x^10*z0^4 + 2*x^13 + x^9*y*z0^3 - x^9*z0^4 - 2*x^10*y*z0 + x^10*z0^2 - x^8*z0^4 - 2*x^11 + 2*x^9*y*z0 - x^7*y*z0^3 + x^10 - x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 - 2*x^7*y*z0 + 2*x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 + x^8 - x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 - 2*x^4*z0^4 + x^7 + x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^6 - 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 + x^3)/y) * dx, - ((-2*x^30*z0^3 - 2*x^31*z0 + 2*x^29*z0^3 + 2*x^27*y^2*z0^3 + x^30*z0 + 2*x^28*y^2*z0 - 2*x^26*y^2*z0^3 - x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - 2*x^25*y^2*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 + x^24*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 - x^21*z0 - x^18*z0^3 + 2*x^17*z0^3 + x^18*z0 + x^16*y^2*z0 + x^15*z0^3 - 2*x^14*z0^3 - x^15*z0 - x^12*z0^3 + 2*x^11*z0^3 + x^12*z0 - 2*x^8*y*z0^4 + 2*x^9*y*z0^2 - 2*x^9*z0^3 + 2*x^7*y*z0^4 + x^10*y + x^10*z0 - 2*x^8*y*z0^2 + 2*x^8*z0^3 - x^6*y*z0^4 - x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 - x^8*y + x^8*z0 + 2*x^6*y*z0^2 - x^6*z0^3 + 2*x^4*y*z0^4 + x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - x^3*y*z0^4 + 2*x^6*y + x^6*z0 + x^4*y*z0^2 - x^4*z0^3 - x^2*y*z0^4 - 2*x^5*y - 2*x^5*z0 + 2*x^3*z0^3 - x^4*y - 2*x^4*z0 - 2*x^2*y*z0^2 + 2*x^2*z0^3 - 2*x^3*y - x^3*z0 + 2*x^2*z0)/y) * dx, - ((-2*x^30*z0^4 - x^31*z0^2 + 2*x^29*z0^4 + 2*x^27*y^2*z0^4 + x^28*y^2*z0^2 - 2*x^26*y^2*z0^4 - 2*x^31 + 2*x^27*z0^4 + 2*x^30 + 2*x^28*y^2 + x^28*z0^2 - 2*x^26*z0^4 - 2*x^27*y^2 + 2*x^28 - 2*x^24*z0^4 - 2*x^27 - x^25*z0^2 + 2*x^23*z0^4 - 2*x^25 + 2*x^21*z0^4 + 2*x^24 + x^22*z0^2 - 2*x^20*z0^4 + 2*x^22 - 2*x^18*z0^4 - 2*x^21 - 2*x^19*z0^2 + 2*x^17*z0^4 + x^16*y^2*z0^2 - 2*x^19 + 2*x^15*z0^4 + 2*x^18 + 2*x^16*z0^2 - 2*x^14*z0^4 + 2*x^16 - 2*x^12*z0^4 - 2*x^15 - 2*x^13*z0^2 - 2*x^11*z0^4 + x^10*z0^4 - 2*x^13 + x^9*y*z0^3 + x^9*z0^4 + 2*x^12 - 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 - 2*x^8*z0^4 - x^11 + 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*z0^4 + 2*x^8*y*z0 - x^8*z0^2 + x^6*z0^4 - 2*x^9 - x^7*y*z0 - 2*x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 - x^8 + 2*x^6*y*z0 + x^6*z0^2 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*z0^2 + x^3*y*z0^3 - 2*x^3*z0^4 - 2*x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((x^31*z0^3 - x^28*y^2*z0^3 + x^31*z0 + 2*x^29*z0^3 - x^30*z0 - x^28*y^2*z0 - x^28*z0^3 - 2*x^26*y^2*z0^3 + 2*x^29*z0 + x^27*y^2*z0 + x^27*z0^3 - x^28*z0 - 2*x^26*y^2*z0 - 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + x^25*z0^3 - 2*x^26*z0 - x^24*z0^3 + x^25*z0 + 2*x^23*z0^3 - x^24*z0 - x^22*z0^3 + 2*x^23*z0 + x^21*z0^3 - x^22*z0 - 2*x^20*z0^3 + x^21*z0 - 2*x^20*z0 - x^18*z0^3 + x^16*y^2*z0^3 + x^19*z0 + 2*x^17*z0^3 - x^18*z0 + 2*x^17*z0 + x^15*z0^3 - x^16*z0 - 2*x^14*z0^3 + x^15*z0 - 2*x^14*z0 - x^12*z0^3 + x^13*z0 + 2*x^11*z0^3 - x^9*y*z0^4 - x^12*z0 + 2*x^10*y*z0^2 + 2*x^11*z0 - x^9*y*z0^2 + x^9*z0^3 - x^7*y*z0^4 + 2*x^10*y - x^8*y*z0^2 + x^6*y*z0^4 + x^9*y + x^9*z0 - 2*x^7*y*z0^2 - x^7*z0^3 + 2*x^5*y*z0^4 - x^8*y - 2*x^8*z0 - x^6*y*z0^2 + x^7*z0 + 2*x^5*y*z0^2 - 2*x^5*z0^3 + x^6*z0 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - x^5*z0 + x^3*y*z0^2 + x^3*z0^3 + 2*x^4*z0 - x^2*y*z0^2 - x^2*z0^3 + 2*x^3*y + 2*x^3*z0 + x^2*y + x^2*z0)/y) * dx, - ((2*x^31*z0^4 + x^30*z0^4 - 2*x^28*y^2*z0^4 - x^31*z0^2 - x^29*z0^4 - x^27*y^2*z0^4 - 2*x^30*z0^2 + x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 - 2*x^31 + 2*x^27*y^2*z0^2 - x^27*z0^4 - 2*x^30 + 2*x^28*y^2 + x^28*z0^2 + x^26*z0^4 + 2*x^27*y^2 + 2*x^27*z0^2 + 2*x^25*z0^4 + 2*x^28 + x^24*z0^4 + 2*x^27 - x^25*z0^2 - x^23*z0^4 - 2*x^24*z0^2 - 2*x^22*z0^4 - 2*x^25 - x^21*z0^4 - 2*x^24 + x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 + x^19*z0^4 + 2*x^22 + x^18*z0^4 + x^16*y^2*z0^4 + 2*x^21 - x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - x^16*z0^4 - 2*x^19 - x^15*z0^4 - 2*x^18 + x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + x^13*z0^4 + 2*x^16 + x^12*z0^4 + 2*x^15 - x^13*z0^2 - 2*x^12*z0^2 - x^10*y*z0^3 - 2*x^13 + x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 - 2*x^8*z0^4 + 2*x^11 + 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*y*z0^3 - 2*x^7*z0^4 + 2*x^10 + x^8*y*z0 - x^8*z0^2 - 2*x^6*y*z0^3 - 2*x^6*z0^4 - x^9 + 2*x^7*y*z0 - x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 + x^6*z0^2 + 2*x^4*y*z0^3 - x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^6 + x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + x^3*z0^2 - x^2*y*z0 - 2*x^2*z0^2 + 2*x^3 + x^2)/y) * dx, - ((-x^20 + x^17*y^2 + x^17 - x^14 + x^11 - x^8 + x^5 - x^2)/y) * dx, - ((-x^20*z0 + x^17*y^2*z0 + x^17*z0 - x^14*z0 + x^11*z0 - x^8*z0 + x^5*z0 - x^2*z0)/y) * dx, - ((-x^20*z0^2 + x^17*y^2*z0^2 + x^17*z0^2 - x^14*z0^2 + x^11*z0^2 - x^8*z0^2 + x^5*z0^2 - x^2*z0^2)/y) * dx, - ((-x^20*z0^3 + x^17*y^2*z0^3 + x^17*z0^3 - x^14*z0^3 + x^11*z0^3 - x^8*z0^3 + x^5*z0^3 - x^2*z0^3)/y) * dx, - ((-x^20*z0^4 + x^17*y^2*z0^4 + x^17*z0^4 - x^14*z0^4 + x^11*z0^4 - x^8*z0^4 + x^5*z0^4 - x^2*z0^4)/y) * dx, - ((-x^21 + x^18*y^2 + x^18 - x^15 + x^12 - x^9 + x^6 - x^3)/y) * dx, - ((-x^21*z0 + x^18*y^2*z0 + x^18*z0 - x^15*z0 + x^12*z0 - x^9*z0 + x^6*z0 - x^3*z0)/y) * dx, - ((-x^21*z0^2 + x^18*y^2*z0^2 + x^18*z0^2 - x^15*z0^2 + x^12*z0^2 - x^9*z0^2 + x^6*z0^2 - x^3*z0^2)/y) * dx, - ((-x^21*z0^3 + x^18*y^2*z0^3 + x^18*z0^3 - x^15*z0^3 + x^12*z0^3 - x^9*z0^3 + x^6*z0^3 - x^3*z0^3)/y) * dx, - ((-x^21*z0^4 + x^18*y^2*z0^4 + x^18*z0^4 - x^15*z0^4 + x^12*z0^4 - x^9*z0^4 + x^6*z0^4 - x^3*z0^4)/y) * dx, - ((-x^31*z0^4 - x^30*z0^4 + x^28*y^2*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 - x^28*y^2*z0^2 + x^28*z0^4 + 2*x^26*y^2*z0^4 + 2*x^31 + x^27*z0^4 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 - x^25*z0^4 - 2*x^28 - x^24*z0^4 + x^25*z0^2 - 2*x^23*z0^4 + x^22*z0^4 + 2*x^25 + x^21*z0^4 - x^22*z0^2 + 2*x^20*z0^4 - x^19*z0^4 + 2*x^22 - x^18*z0^4 + x^19*y^2 + x^19*z0^2 - 2*x^17*z0^4 + x^16*z0^4 - 2*x^19 + x^15*z0^4 - x^16*z0^2 + 2*x^14*z0^4 - x^13*z0^4 + 2*x^16 - x^12*z0^4 + x^13*z0^2 + 2*x^11*z0^4 - 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 - x^10*z0^2 + x^8*z0^4 + 2*x^11 - 2*x^9*y*z0 + x^7*y*z0^3 - x^10 + x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 + x^6*z0^4 + 2*x^7*y*z0 - 2*x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - x^8 + x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 - x^7 - x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^6 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 - x^2*z0^2 - x^3)/y) * dx, - ((2*x^30*z0^3 + 2*x^31*z0 - 2*x^29*z0^3 - 2*x^27*y^2*z0^3 - x^30*z0 - 2*x^28*y^2*z0 + 2*x^26*y^2*z0^3 + x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + 2*x^25*y^2*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 - x^24*z0 - x^21*z0^3 + 2*x^20*z0^3 + x^21*z0 + x^19*y^2*z0 + x^18*z0^3 - 2*x^17*z0^3 - x^18*z0 - x^15*z0^3 + 2*x^14*z0^3 + x^15*z0 + x^12*z0^3 - 2*x^11*z0^3 - x^12*z0 + 2*x^8*y*z0^4 - 2*x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y - x^10*z0 + 2*x^8*y*z0^2 - 2*x^8*z0^3 + x^6*y*z0^4 + x^9*z0 + x^7*y*z0^2 - 2*x^7*z0^3 + 2*x^5*y*z0^4 + x^8*y - x^8*z0 - 2*x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 - x^7*z0 + x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - 2*x^6*y - x^6*z0 - x^4*y*z0^2 + x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + 2*x^5*z0 - 2*x^3*z0^3 + x^4*y + 2*x^4*z0 + 2*x^2*y*z0^2 - 2*x^2*z0^3 + 2*x^3*y + x^3*z0 - 2*x^2*z0)/y) * dx, - ((2*x^30*z0^4 + x^31*z0^2 - 2*x^29*z0^4 - 2*x^27*y^2*z0^4 - x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + 2*x^31 - 2*x^27*z0^4 - 2*x^30 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y^2 - 2*x^28 + 2*x^24*z0^4 + 2*x^27 + x^25*z0^2 - 2*x^23*z0^4 + 2*x^25 - 2*x^21*z0^4 - 2*x^24 - 2*x^22*z0^2 + 2*x^20*z0^4 + x^19*y^2*z0^2 - 2*x^22 + 2*x^18*z0^4 + 2*x^21 + 2*x^19*z0^2 - 2*x^17*z0^4 + 2*x^19 - 2*x^15*z0^4 - 2*x^18 - 2*x^16*z0^2 + 2*x^14*z0^4 - 2*x^16 + 2*x^12*z0^4 + 2*x^15 + 2*x^13*z0^2 + 2*x^11*z0^4 - x^10*z0^4 + 2*x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 - x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 - x^7*z0^4 - 2*x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 + x^5*z0^4 + x^8 - 2*x^6*y*z0 - x^6*z0^2 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*z0^2 - x^3*y*z0^3 + 2*x^3*z0^4 + 2*x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 + 2*x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^31*z0^3 + x^28*y^2*z0^3 - x^31*z0 - 2*x^29*z0^3 + x^30*z0 + x^28*y^2*z0 + x^28*z0^3 + 2*x^26*y^2*z0^3 - 2*x^29*z0 - x^27*y^2*z0 - x^27*z0^3 + x^28*z0 + 2*x^26*y^2*z0 + 2*x^26*z0^3 + x^24*y^2*z0^3 - x^27*z0 - x^25*z0^3 + 2*x^26*z0 + x^24*z0^3 - x^25*z0 - 2*x^23*z0^3 + x^24*z0 - 2*x^23*z0 - x^21*z0^3 + x^19*y^2*z0^3 + x^22*z0 + 2*x^20*z0^3 - x^21*z0 + 2*x^20*z0 + x^18*z0^3 - x^19*z0 - 2*x^17*z0^3 + x^18*z0 - 2*x^17*z0 - x^15*z0^3 + x^16*z0 + 2*x^14*z0^3 - x^15*z0 + 2*x^14*z0 + x^12*z0^3 - x^13*z0 - 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 - 2*x^10*y*z0^2 - 2*x^11*z0 + x^9*y*z0^2 - x^9*z0^3 + x^7*y*z0^4 - 2*x^10*y + x^8*y*z0^2 - x^6*y*z0^4 - x^9*y - x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 - 2*x^5*y*z0^4 + x^8*y + 2*x^8*z0 + x^6*y*z0^2 - x^7*z0 - 2*x^5*y*z0^2 + 2*x^5*z0^3 - x^6*z0 + x^4*z0^3 - x^2*y*z0^4 - x^5*y + x^5*z0 - x^3*y*z0^2 - x^3*z0^3 - 2*x^4*z0 + x^2*y*z0^2 + x^2*z0^3 - 2*x^3*y - 2*x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-2*x^31*z0^4 - x^30*z0^4 + 2*x^28*y^2*z0^4 + x^31*z0^2 + x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 + 2*x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 + 2*x^30 - 2*x^28*y^2 - x^28*z0^2 - x^26*z0^4 - 2*x^27*y^2 - 2*x^27*z0^2 - 2*x^25*z0^4 - 2*x^28 - x^24*z0^4 - 2*x^27 + x^25*z0^2 + x^23*z0^4 + 2*x^24*z0^2 + x^22*z0^4 + 2*x^25 + x^21*z0^4 + x^19*y^2*z0^4 + 2*x^24 - x^22*z0^2 - x^20*z0^4 - 2*x^21*z0^2 - x^19*z0^4 - 2*x^22 - x^18*z0^4 - 2*x^21 + x^19*z0^2 + x^17*z0^4 + 2*x^18*z0^2 + x^16*z0^4 + 2*x^19 + x^15*z0^4 + 2*x^18 - x^16*z0^2 - x^14*z0^4 - 2*x^15*z0^2 - x^13*z0^4 - 2*x^16 - x^12*z0^4 - 2*x^15 + x^13*z0^2 + 2*x^12*z0^2 + x^10*y*z0^3 + 2*x^13 - x^9*y*z0^3 + 2*x^9*z0^4 + 2*x^12 + 2*x^10*y*z0 + x^10*z0^2 + 2*x^8*y*z0^3 + 2*x^8*z0^4 - 2*x^11 - 2*x^9*y*z0 - 2*x^9*z0^2 + x^7*y*z0^3 + 2*x^7*z0^4 - 2*x^10 - x^8*y*z0 + x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 + x^9 - 2*x^7*y*z0 + x^5*y*z0^3 - 2*x^5*z0^4 - 2*x^8 + x^6*y*z0 - x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 + x^5*y*z0 - 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 - x^2)/y) * dx, - ((-x^23 + x^20*y^2 + x^20 - x^17 + x^14 - x^11 + x^8 - x^5 + x^2)/y) * dx, - ((-x^23*z0 + x^20*y^2*z0 + x^20*z0 - x^17*z0 + x^14*z0 - x^11*z0 + x^8*z0 - x^5*z0 + x^2*z0)/y) * dx, - ((-x^23*z0^2 + x^20*y^2*z0^2 + x^20*z0^2 - x^17*z0^2 + x^14*z0^2 - x^11*z0^2 + x^8*z0^2 - x^5*z0^2 + x^2*z0^2)/y) * dx, - ((-x^23*z0^3 + x^20*y^2*z0^3 + x^20*z0^3 - x^17*z0^3 + x^14*z0^3 - x^11*z0^3 + x^8*z0^3 - x^5*z0^3 + x^2*z0^3)/y) * dx, - ((-x^23*z0^4 + x^20*y^2*z0^4 + x^20*z0^4 - x^17*z0^4 + x^14*z0^4 - x^11*z0^4 + x^8*z0^4 - x^5*z0^4 + x^2*z0^4)/y) * dx, - ((2*x^31*z0^4 - x^30*z0^4 - 2*x^28*y^2*z0^4 - 2*x^31*z0^2 - x^29*z0^4 + x^27*y^2*z0^4 - 2*x^30*z0^2 + 2*x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 + 2*x^31 + 2*x^27*y^2*z0^2 + x^27*z0^4 + x^30 - 2*x^28*y^2 + 2*x^28*z0^2 + x^26*z0^4 - x^27*y^2 + 2*x^27*z0^2 + 2*x^25*z0^4 - 2*x^28 - x^24*z0^4 - x^27 - 2*x^25*z0^2 - x^23*z0^4 - 2*x^24*z0^2 - 2*x^22*z0^4 + 2*x^25 + x^21*z0^4 + 2*x^22*z0^2 + x^20*z0^4 + x^21*y^2 + 2*x^21*z0^2 + 2*x^19*z0^4 - 2*x^22 - x^18*z0^4 - 2*x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*z0^4 + 2*x^19 + x^15*z0^4 + 2*x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + 2*x^13*z0^4 - 2*x^16 - x^12*z0^4 - 2*x^13*z0^2 - 2*x^11*z0^4 - 2*x^12*z0^2 - x^10*y*z0^3 + 2*x^13 + 2*x^9*y*z0^3 + x^9*z0^4 + x^10*y*z0 - 2*x^8*y*z0^3 - x^8*z0^4 - x^11 - 2*x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 - 2*x^7*z0^4 - x^10 - 2*x^8*z0^2 + x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 + 2*x^7*y*z0 - x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 + 2*x^8 - 2*x^6*y*z0 - 2*x^6*z0^2 + 2*x^4*y*z0^3 + 2*x^4*z0^4 - x^7 + 2*x^5*z0^2 - x^3*z0^4 - 2*x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 + x^2*z0^4 + x^5 - x^3*y*z0 - x^2*y*z0 + 2*x^3 - 2*x^2)/y) * dx, - ((x^31*z0^3 + x^30*z0^3 - x^28*y^2*z0^3 + 2*x^31*z0 + 2*x^29*z0^3 - x^27*y^2*z0^3 - x^30*z0 - 2*x^28*y^2*z0 - x^28*z0^3 - 2*x^26*y^2*z0^3 + x^27*y^2*z0 + x^28*z0 - 2*x^26*z0^3 - x^24*y^2*z0^3 + x^27*z0 + 2*x^25*y^2*z0 + x^25*z0^3 - x^25*z0 + 2*x^23*z0^3 - 2*x^24*z0 - x^22*z0^3 + x^21*y^2*z0 + x^22*z0 - 2*x^20*z0^3 + 2*x^21*z0 + x^19*z0^3 - x^19*z0 + 2*x^17*z0^3 - 2*x^18*z0 - x^16*z0^3 + x^16*z0 - 2*x^14*z0^3 + 2*x^15*z0 + x^13*z0^3 - x^13*z0 + 2*x^11*z0^3 - x^9*y*z0^4 - 2*x^12*z0 + 2*x^10*y*z0^2 - x^10*z0^3 + x^8*y*z0^4 - 2*x^9*y*z0^2 - x^9*z0^3 - 2*x^7*y*z0^4 - x^10*y + x^10*z0 - x^8*y*z0^2 + 2*x^8*z0^3 + 2*x^6*y*z0^4 + x^9*y + 2*x^7*y*z0^2 - x^7*z0^3 - 2*x^5*y*z0^4 + 2*x^8*y + 2*x^8*z0 + x^6*y*z0^2 - 2*x^6*z0^3 - 2*x^4*y*z0^4 - x^7*y + 2*x^5*z0^3 + 2*x^6*y - 2*x^6*z0 - 2*x^4*y*z0^2 - x^4*z0^3 + x^5*y + 2*x^5*z0 + 2*x^3*y*z0^2 - 2*x^4*y + 2*x^4*z0 + 2*x^2*z0^3 + 2*x^3*y + 2*x^2*z0)/y) * dx, - ((-2*x^31*z0^4 - 2*x^30*z0^4 + 2*x^28*y^2*z0^4 - x^31*z0^2 + x^29*z0^4 + 2*x^27*y^2*z0^4 + x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 - 2*x^31 + 2*x^27*z0^4 - 2*x^30 + 2*x^28*y^2 + x^28*z0^2 - x^26*z0^4 + 2*x^27*y^2 - 2*x^25*z0^4 + 2*x^28 - 2*x^24*z0^4 + 2*x^27 - x^25*z0^2 + x^23*z0^4 - x^24*z0^2 + 2*x^22*z0^4 - 2*x^25 + x^21*y^2*z0^2 + 2*x^21*z0^4 - 2*x^24 + x^22*z0^2 - x^20*z0^4 + x^21*z0^2 - 2*x^19*z0^4 + 2*x^22 - 2*x^18*z0^4 + 2*x^21 - x^19*z0^2 + x^17*z0^4 - x^18*z0^2 + 2*x^16*z0^4 - 2*x^19 + 2*x^15*z0^4 - 2*x^18 + x^16*z0^2 - x^14*z0^4 + x^15*z0^2 - 2*x^13*z0^4 + 2*x^16 - 2*x^12*z0^4 + 2*x^15 - x^13*z0^2 + 2*x^11*z0^4 - x^12*z0^2 + x^10*y*z0^3 - 2*x^13 + x^9*y*z0^3 - x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - 2*x^10*z0^2 - x^8*z0^4 + x^11 + 2*x^9*y*z0 + x^9*z0^2 - x^7*y*z0^3 - x^10 + x^8*y*z0 + x^8*z0^2 - x^6*z0^4 + 2*x^9 + x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 - 2*x^5*z0^4 + x^6*y*z0 + 2*x^6*z0^2 + 2*x^4*y*z0^3 + x^4*z0^4 - 2*x^7 - x^5*z0^2 - 2*x^3*y*z0^3 - x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 - 2*x^2*y*z0^3 - 2*x^2*z0^4 - x^5 + 2*x^3*y*z0 - 2*x^3*z0^2 + 2*x^2*z0^2 + 2*x^2)/y) * dx, - ((2*x^31*z0^3 - x^30*z0^3 - 2*x^28*y^2*z0^3 - 2*x^31*z0 + x^29*z0^3 + x^27*y^2*z0^3 + x^30*z0 + 2*x^28*y^2*z0 - 2*x^28*z0^3 - x^26*y^2*z0^3 - x^27*y^2*z0 - 2*x^27*z0^3 - 2*x^28*z0 - x^26*z0^3 - 2*x^24*y^2*z0^3 - x^27*z0 - x^25*y^2*z0 + 2*x^25*z0^3 + x^24*z0^3 + 2*x^25*z0 + x^23*z0^3 + x^21*y^2*z0^3 + x^24*z0 - 2*x^22*z0^3 - x^21*z0^3 - 2*x^22*z0 - x^20*z0^3 - x^21*z0 + 2*x^19*z0^3 + x^18*z0^3 + 2*x^19*z0 + x^17*z0^3 + x^18*z0 - 2*x^16*z0^3 - x^15*z0^3 - 2*x^16*z0 - x^14*z0^3 - x^15*z0 + 2*x^13*z0^3 + x^12*z0^3 + 2*x^13*z0 + x^11*z0^3 - 2*x^9*y*z0^4 + x^12*z0 - x^10*y*z0^2 - x^8*y*z0^4 + 2*x^9*y*z0^2 - 2*x^7*y*z0^4 + x^10*y + x^10*z0 - 2*x^8*y*z0^2 - x^8*z0^3 - x^6*y*z0^4 + 2*x^9*y + x^9*z0 - x^7*y*z0^2 + 2*x^7*z0^3 - x^5*y*z0^4 - x^8*y + 2*x^8*z0 - 2*x^6*z0^3 + x^4*y*z0^4 + 2*x^7*y - 2*x^7*z0 + 2*x^5*y*z0^2 + 2*x^5*z0^3 + 2*x^3*y*z0^4 + x^6*y - 2*x^6*z0 - x^4*z0^3 + x^2*y*z0^4 + x^5*y - 2*x^5*z0 + 2*x^3*y*z0^2 + x^3*z0^3 - 2*x^4*y + x^4*z0 - 2*x^2*y*z0^2 + x^3*y + x^2*y - 2*x^2*z0)/y) * dx, - ((x^31*z0^4 - 2*x^30*z0^4 - x^28*y^2*z0^4 + 2*x^31*z0^2 - x^29*z0^4 + 2*x^27*y^2*z0^4 - 2*x^30*z0^2 - 2*x^28*y^2*z0^2 - x^28*z0^4 + x^26*y^2*z0^4 + x^31 + 2*x^27*y^2*z0^2 + 2*x^27*z0^4 + x^30 - x^28*y^2 - 2*x^28*z0^2 + x^26*z0^4 - x^27*y^2 + 2*x^27*z0^2 + x^25*z0^4 - x^28 + 2*x^24*z0^4 - x^27 + 2*x^25*z0^2 - x^23*z0^4 + x^21*y^2*z0^4 - 2*x^24*z0^2 - x^22*z0^4 + x^25 - 2*x^21*z0^4 + x^24 - 2*x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 + x^19*z0^4 - x^22 + 2*x^18*z0^4 - x^21 + 2*x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - x^16*z0^4 + x^19 - 2*x^15*z0^4 + x^18 - 2*x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + x^13*z0^4 - x^16 + 2*x^12*z0^4 - x^15 + 2*x^13*z0^2 + x^11*z0^4 - 2*x^12*z0^2 + 2*x^10*y*z0^3 + 2*x^10*z0^4 + x^13 - 2*x^9*y*z0^3 + x^12 - x^10*y*z0 - 2*x^8*z0^4 + 2*x^11 - x^9*y*z0 - 2*x^9*z0^2 - 2*x^7*y*z0^3 - x^7*z0^4 - x^8*y*z0 - 2*x^6*y*z0^3 + x^9 - 2*x^7*y*z0 + 2*x^7*z0^2 - x^5*z0^4 - x^6*y*z0 + x^6*z0^2 - 2*x^4*y*z0^3 - 2*x^4*z0^4 + 2*x^7 + 2*x^5*y*z0 + 2*x^5*z0^2 - x^3*y*z0^3 + x^3*z0^4 + x^6 + x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^3*y*z0 + x^3*z0^2 + 2*x^2*y*z0 - 2*x^2*z0^2 + 2*x^3 + 2*x^2)/y) * dx, - ((2*x^31*z0^4 - 2*x^30*z0^4 - 2*x^28*y^2*z0^4 + 2*x^31*z0^2 - x^29*z0^4 + 2*x^27*y^2*z0^4 + x^30*z0^2 - 2*x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 - x^31 - x^27*y^2*z0^2 + 2*x^27*z0^4 - 2*x^30 + x^28*y^2 - 2*x^28*z0^2 + x^26*z0^4 + 2*x^27*y^2 - x^27*z0^2 + 2*x^25*z0^4 + x^28 - 2*x^24*z0^4 + 2*x^27 + 2*x^25*z0^2 - x^23*z0^4 + x^24*z0^2 - 2*x^22*z0^4 - 2*x^25 + 2*x^21*z0^4 - 2*x^24 + x^22*y^2 - 2*x^22*z0^2 + x^20*z0^4 - x^21*z0^2 + 2*x^19*z0^4 + 2*x^22 - 2*x^18*z0^4 + 2*x^21 + 2*x^19*z0^2 - x^17*z0^4 + x^18*z0^2 - 2*x^16*z0^4 - 2*x^19 + 2*x^15*z0^4 - 2*x^18 - 2*x^16*z0^2 + x^14*z0^4 - x^15*z0^2 + 2*x^13*z0^4 + 2*x^16 - 2*x^12*z0^4 + 2*x^15 + 2*x^13*z0^2 + 2*x^11*z0^4 + x^12*z0^2 - x^10*y*z0^3 - 2*x^13 - 2*x^9*y*z0^3 + x^9*z0^4 - 2*x^12 - x^10*y*z0 + x^10*z0^2 + x^8*y*z0^3 - 2*x^8*z0^4 + x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 - 2*x^10 + x^8*y*z0 - x^8*z0^2 + x^6*y*z0^3 + x^6*z0^4 - 2*x^9 - x^5*y*z0^3 - 2*x^8 + 2*x^6*y*z0 + x^6*z0^2 + x^4*y*z0^3 + x^4*z0^4 + 2*x^7 - x^5*y*z0 + 2*x^5*z0^2 - 2*x^3*y*z0^3 + 2*x^3*z0^4 - x^6 + 2*x^4*y*z0 + 2*x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 + x^5 - x^3 - 2*x^2)/y) * dx, - ((2*x^31*z0^3 - 2*x^30*z0^3 - 2*x^28*y^2*z0^3 - x^31*z0 - 2*x^29*z0^3 + 2*x^27*y^2*z0^3 - 2*x^30*z0 + x^28*y^2*z0 - 2*x^28*z0^3 + 2*x^26*y^2*z0^3 + 2*x^27*y^2*z0 - x^27*z0^3 + 2*x^28*z0 + 2*x^26*z0^3 - 2*x^24*y^2*z0^3 + 2*x^27*z0 - x^25*y^2*z0 + 2*x^25*z0^3 + x^24*z0^3 + 2*x^25*z0 - 2*x^23*z0^3 - 2*x^24*z0 + x^22*y^2*z0 - 2*x^22*z0^3 - x^21*z0^3 - 2*x^22*z0 + 2*x^20*z0^3 + 2*x^21*z0 + 2*x^19*z0^3 + x^18*z0^3 + 2*x^19*z0 - 2*x^17*z0^3 - 2*x^18*z0 - 2*x^16*z0^3 - x^15*z0^3 - 2*x^16*z0 + 2*x^14*z0^3 + 2*x^15*z0 + 2*x^13*z0^3 + x^12*z0^3 + 2*x^13*z0 - 2*x^11*z0^3 - 2*x^9*y*z0^4 - 2*x^12*z0 - x^10*y*z0^2 + 2*x^10*z0^3 - 2*x^8*y*z0^4 + x^9*y*z0^2 + 2*x^9*z0^3 - 2*x^10*y - 2*x^10*z0 + 2*x^8*y*z0^2 + 2*x^8*z0^3 + 2*x^6*y*z0^4 + 2*x^9*y + x^7*y*z0^2 + 2*x^5*y*z0^4 - x^8*y - x^6*y*z0^2 - 2*x^6*z0^3 + 2*x^4*y*z0^4 - x^7*y + x^7*z0 - 2*x^5*y*z0^2 - 2*x^5*z0^3 + x^3*y*z0^4 - x^6*y + x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 - x^5*y - 2*x^5*z0 - x^3*y*z0^2 + x^3*z0^3 + x^4*y + x^4*z0 - x^2*y*z0^2 + 2*x^2*z0^3 + x^3*y - 2*x^3*z0 + 2*x^2*y + 2*x^2*z0)/y) * dx, - ((x^31*z0^4 + 2*x^30*z0^4 - x^28*y^2*z0^4 - 2*x^31*z0^2 + x^29*z0^4 - 2*x^27*y^2*z0^4 + 2*x^28*y^2*z0^2 - x^28*z0^4 - x^26*y^2*z0^4 + x^31 - 2*x^27*z0^4 + x^30 - x^28*y^2 + 2*x^28*z0^2 - x^26*z0^4 - x^27*y^2 + x^25*z0^4 - x^28 + 2*x^24*z0^4 - x^27 + 2*x^25*z0^2 + x^23*z0^4 + x^22*y^2*z0^2 - x^22*z0^4 + x^25 - 2*x^21*z0^4 + x^24 - 2*x^22*z0^2 - x^20*z0^4 + x^19*z0^4 - x^22 + 2*x^18*z0^4 - x^21 + 2*x^19*z0^2 + x^17*z0^4 - x^16*z0^4 + x^19 - 2*x^15*z0^4 + x^18 - 2*x^16*z0^2 - x^14*z0^4 + x^13*z0^4 - x^16 + 2*x^12*z0^4 - x^15 + 2*x^13*z0^2 - 2*x^11*z0^4 + 2*x^10*y*z0^3 - x^10*z0^4 + x^13 + 2*x^9*y*z0^3 + 2*x^9*z0^4 + x^12 + x^10*y*z0 + 2*x^10*z0^2 - x^8*y*z0^3 + x^8*z0^4 + 2*x^11 - x^9*y*z0 + 2*x^9*z0^2 + 2*x^7*z0^4 - x^10 - 2*x^8*y*z0 - 2*x^8*z0^2 + 2*x^6*y*z0^3 - 2*x^9 + 2*x^7*y*z0 + x^5*y*z0^3 - 2*x^8 - x^6*z0^2 - x^4*y*z0^3 + x^4*z0^4 + x^7 - 2*x^5*y*z0 + 2*x^5*z0^2 + x^3*y*z0^3 + x^3*z0^4 + x^4*z0^2 - x^2*z0^4 + x^5 + 2*x^3*y*z0 - x^3*z0^2 + 2*x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 + x^2)/y) * dx, - ((-x^31*z0^3 + x^30*z0^3 + x^28*y^2*z0^3 - x^31*z0 + 2*x^29*z0^3 - x^27*y^2*z0^3 + x^30*z0 + x^28*y^2*z0 + x^28*z0^3 - 2*x^26*y^2*z0^3 + x^29*z0 - x^27*y^2*z0 - x^27*z0^3 - x^26*y^2*z0 - 2*x^26*z0^3 - x^27*z0 + x^25*y^2*z0 - 2*x^25*z0^3 - x^26*z0 + x^24*z0^3 + x^22*y^2*z0^3 + 2*x^23*z0^3 + x^24*z0 + 2*x^22*z0^3 + x^23*z0 - x^21*z0^3 - 2*x^20*z0^3 - x^21*z0 - 2*x^19*z0^3 - x^20*z0 + x^18*z0^3 + 2*x^17*z0^3 + x^18*z0 + 2*x^16*z0^3 + x^17*z0 - x^15*z0^3 - 2*x^14*z0^3 - x^15*z0 - 2*x^13*z0^3 - x^14*z0 + x^12*z0^3 + 2*x^11*z0^3 + x^9*y*z0^4 + x^12*z0 - 2*x^10*y*z0^2 + x^10*z0^3 + x^8*y*z0^4 + x^11*z0 + x^9*y*z0^2 - x^7*y*z0^4 - 2*x^10*y - x^10*z0 - 2*x^8*z0^3 - 2*x^6*y*z0^4 - x^9*y + 2*x^7*y*z0^2 - x^7*z0^3 + x^5*y*z0^4 - x^8*y - 2*x^8*z0 - 2*x^6*y*z0^2 + x^4*y*z0^4 + x^7*y + 2*x^7*z0 - x^5*y*z0^2 - x^5*z0^3 - 2*x^3*y*z0^4 - 2*x^6*y + x^6*z0 + 2*x^4*y*z0^2 - x^4*z0^3 + x^5*y + 2*x^5*z0 - x^3*z0^3 - x^4*y - x^2*z0^3 + 2*x^3*z0 + 2*x^2*y - 2*x^2*z0)/y) * dx, - ((-x^31*z0^4 + 2*x^30*z0^4 + x^28*y^2*z0^4 + x^31*z0^2 + 2*x^29*z0^4 - 2*x^27*y^2*z0^4 - x^30*z0^2 - x^28*y^2*z0^2 + x^28*z0^4 - 2*x^26*y^2*z0^4 - x^31 + x^27*y^2*z0^2 - 2*x^27*z0^4 - 2*x^30 + x^28*y^2 - x^28*z0^2 - 2*x^26*z0^4 + 2*x^27*y^2 + x^27*z0^2 - 2*x^25*z0^4 + x^28 + 2*x^24*z0^4 + x^22*y^2*z0^4 + 2*x^27 + x^25*z0^2 + 2*x^23*z0^4 - x^24*z0^2 + 2*x^22*z0^4 - x^25 - 2*x^21*z0^4 - 2*x^24 - x^22*z0^2 - 2*x^20*z0^4 + x^21*z0^2 - 2*x^19*z0^4 + x^22 + 2*x^18*z0^4 + 2*x^21 + x^19*z0^2 + 2*x^17*z0^4 - x^18*z0^2 + 2*x^16*z0^4 - x^19 - 2*x^15*z0^4 - 2*x^18 - x^16*z0^2 - 2*x^14*z0^4 + x^15*z0^2 - 2*x^13*z0^4 + x^16 + 2*x^12*z0^4 + 2*x^15 + x^13*z0^2 - x^12*z0^2 - 2*x^10*y*z0^3 + 2*x^10*z0^4 - x^13 - x^9*y*z0^3 - 2*x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 + 2*x^10*z0^2 - 2*x^8*y*z0^3 - x^8*z0^4 - 2*x^11 + x^9*y*z0 - 2*x^7*y*z0^3 + 2*x^7*z0^4 + x^10 + x^8*y*z0 - x^6*y*z0^3 - 2*x^9 - x^7*y*z0 + 2*x^7*z0^2 + x^5*y*z0^3 + x^5*z0^4 - 2*x^8 + 2*x^6*y*z0 - 2*x^6*z0^2 - 2*x^4*y*z0^3 - x^4*z0^4 - 2*x^7 + 2*x^3*z0^4 + 2*x^6 - x^4*y*z0 + x^4*z0^2 - x^2*y*z0^3 - x^2*z0^4 - 2*x^5 + x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + x^2*z0^2 - x^3 + x^2)/y) * dx, - ((x^31*z0^4 - x^30*z0^4 - x^28*y^2*z0^4 - x^31*z0^2 - x^29*z0^4 + x^27*y^2*z0^4 + x^30*z0^2 + x^28*y^2*z0^2 - x^28*z0^4 + x^26*y^2*z0^4 - x^31 - x^27*y^2*z0^2 + x^27*z0^4 + x^28*y^2 + x^28*z0^2 + x^26*z0^4 - x^27*z0^2 + x^25*z0^4 + x^28 - x^24*z0^4 - x^25*z0^2 - x^23*z0^4 - x^26 + x^24*z0^2 - x^22*z0^4 - x^25 + x^23*y^2 + x^21*z0^4 + x^22*z0^2 + x^20*z0^4 + x^23 - x^21*z0^2 + x^19*z0^4 + x^22 - x^18*z0^4 - x^19*z0^2 - x^17*z0^4 - x^20 + x^18*z0^2 - x^16*z0^4 - x^19 + x^15*z0^4 + x^16*z0^2 + x^14*z0^4 + x^17 - x^15*z0^2 + x^13*z0^4 + x^16 - x^12*z0^4 - x^13*z0^2 + 2*x^11*z0^4 - x^14 + x^12*z0^2 + 2*x^10*y*z0^3 - 2*x^10*z0^4 - x^13 + x^9*y*z0^3 + x^9*z0^4 - 2*x^10*y*z0 + x^10*z0^2 - 2*x^8*y*z0^3 + 2*x^8*z0^4 + 2*x^11 + x^9*y*z0 - 2*x^9*z0^2 - x^7*z0^4 + x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 + x^6*y*z0^3 - x^6*z0^4 + x^9 - x^7*y*z0 - 2*x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 - 2*x^8 + x^6*y*z0 + 2*x^6*z0^2 + x^4*y*z0^3 - x^7 - x^5*y*z0 - 2*x^5*z0^2 - x^3*y*z0^3 - 2*x^4*y*z0 + x^4*z0^2 + x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 + x^3*z0^2 - 2*x^2*y*z0 + 2*x^2*z0^2 - x^2)/y) * dx, - ((x^31*z0^3 + x^30*z0^3 - x^28*y^2*z0^3 - 2*x^29*z0^3 - x^27*y^2*z0^3 - 2*x^30*z0 - x^28*z0^3 + 2*x^26*y^2*z0^3 + 2*x^27*y^2*z0 + 2*x^26*z0^3 - x^24*y^2*z0^3 + 2*x^27*z0 + x^25*z0^3 - x^26*z0 + x^23*y^2*z0 - 2*x^23*z0^3 - 2*x^24*z0 - x^22*z0^3 + x^23*z0 + 2*x^20*z0^3 + 2*x^21*z0 + x^19*z0^3 - x^20*z0 - 2*x^17*z0^3 - 2*x^18*z0 - x^16*z0^3 + x^17*z0 + 2*x^14*z0^3 + 2*x^15*z0 + x^13*z0^3 - x^14*z0 - 2*x^11*z0^3 - x^9*y*z0^4 - 2*x^12*z0 + 2*x^10*y*z0^2 + 2*x^10*z0^3 + x^8*y*z0^4 + x^11*z0 - x^7*y*z0^4 - 2*x^10*z0 - x^8*y*z0^2 - 2*x^8*z0^3 - x^6*y*z0^4 + x^9*y - 2*x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 + x^5*y*z0^4 - 2*x^8*y + x^8*z0 + 2*x^6*z0^3 + 2*x^5*y*z0^2 - 2*x^5*z0^3 - x^6*y - 2*x^6*z0 - 2*x^4*y*z0^2 - x^4*z0^3 - 2*x^2*y*z0^4 + x^5*y - 2*x^5*z0 + x^3*y*z0^2 + 2*x^3*z0^3 - 2*x^4*y - 2*x^4*z0 + 2*x^2*z0^3 - 2*x^3*y - 2*x^3*z0 + 2*x^2*y + x^2*z0)/y) * dx, - ((2*x^31*z0^4 + x^30*z0^4 - 2*x^28*y^2*z0^4 + x^31*z0^2 - x^27*y^2*z0^4 - x^28*y^2*z0^2 - 2*x^28*z0^4 - x^27*z0^4 - x^28*z0^2 + 2*x^25*z0^4 - x^26*z0^2 + x^24*z0^4 + x^25*z0^2 + x^23*y^2*z0^2 - 2*x^22*z0^4 + x^23*z0^2 - x^21*z0^4 - x^22*z0^2 + 2*x^19*z0^4 - x^20*z0^2 + x^18*z0^4 + x^19*z0^2 - 2*x^16*z0^4 + x^17*z0^2 - x^15*z0^4 - x^16*z0^2 + 2*x^13*z0^4 - x^14*z0^2 + x^12*z0^4 + x^13*z0^2 - x^10*y*z0^3 + x^10*z0^4 + x^11*z0^2 - x^9*y*z0^3 + x^9*z0^4 + 2*x^10*y*z0 + x^8*y*z0^3 - 2*x^11 - x^9*z0^2 - x^7*y*z0^3 - x^7*z0^4 + x^10 + x^8*y*z0 + x^8*z0^2 + 2*x^6*z0^4 + 2*x^9 + 2*x^7*y*z0 + 2*x^7*z0^2 - x^5*y*z0^3 - x^5*z0^4 + 2*x^8 + 2*x^6*z0^2 - 2*x^4*y*z0^3 + x^4*z0^4 - x^7 + x^5*z0^2 - 2*x^3*y*z0^3 + 2*x^3*z0^4 - 2*x^4*z0^2 + 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + x^2*z0^2 - x^3 + 2*x^2)/y) * dx, - ((-2*x^31*z0^3 - 2*x^30*z0^3 + 2*x^28*y^2*z0^3 + 2*x^31*z0 - x^29*z0^3 + 2*x^27*y^2*z0^3 - 2*x^30*z0 - 2*x^28*y^2*z0 + 2*x^28*z0^3 + x^26*y^2*z0^3 - x^29*z0 + 2*x^27*y^2*z0 - x^27*z0^3 + x^26*y^2*z0 - 2*x^24*y^2*z0^3 + 2*x^27*z0 - 2*x^25*y^2*z0 - 2*x^25*z0^3 + x^23*y^2*z0^3 + x^26*z0 + x^24*z0^3 - 2*x^24*z0 + 2*x^22*z0^3 - x^23*z0 - x^21*z0^3 + 2*x^21*z0 - 2*x^19*z0^3 + x^20*z0 + x^18*z0^3 - 2*x^18*z0 + 2*x^16*z0^3 - x^17*z0 - x^15*z0^3 + 2*x^15*z0 - 2*x^13*z0^3 + x^14*z0 + x^12*z0^3 + 2*x^9*y*z0^4 - 2*x^12*z0 + x^10*y*z0^2 - 2*x^10*z0^3 - 2*x^8*y*z0^4 - x^11*z0 - 2*x^9*y*z0^2 - x^7*y*z0^4 - x^10*y - 2*x^10*z0 + x^8*y*z0^2 - x^8*z0^3 - 2*x^6*y*z0^4 - 2*x^9*y - 2*x^9*z0 - 2*x^7*z0^3 - x^5*y*z0^4 - x^8*y + x^8*z0 + x^6*y*z0^2 + 2*x^6*z0^3 - 2*x^7*y - x^7*z0 + x^5*y*z0^2 + 2*x^5*z0^3 - x^6*y + x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^5*y + 2*x^5*z0 + 2*x^3*z0^3 + 2*x^4*z0 + x^2*y*z0^2 + 2*x^2*z0^3 + 2*x^3*y - 2*x^3*z0 + 2*x^2*y + x^2*z0)/y) * dx, - ((-x^30*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 + 2*x^26*y^2*z0^4 + x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 - 2*x^30 - x^28*y^2 - x^28*z0^2 + x^26*z0^4 + 2*x^27*y^2 - 2*x^27*z0^2 + x^23*y^2*z0^4 - x^28 - x^24*z0^4 + 2*x^27 + x^25*z0^2 - x^23*z0^4 + 2*x^24*z0^2 + x^25 + x^21*z0^4 - 2*x^24 - x^22*z0^2 + x^20*z0^4 - 2*x^21*z0^2 - x^22 - x^18*z0^4 + 2*x^21 + x^19*z0^2 - x^17*z0^4 + 2*x^18*z0^2 + x^19 + x^15*z0^4 - 2*x^18 - x^16*z0^2 + x^14*z0^4 - 2*x^15*z0^2 - x^16 - x^12*z0^4 + 2*x^15 + x^13*z0^2 + x^11*z0^4 + 2*x^12*z0^2 + 2*x^10*z0^4 + x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 + 2*x^10*z0^2 - x^8*z0^4 - 2*x^11 - x^9*y*z0 + 2*x^7*z0^4 - x^10 - x^8*y*z0 + x^6*y*z0^3 + x^6*z0^4 - 2*x^9 - x^7*z0^2 + x^5*y*z0^3 - x^5*z0^4 + 2*x^8 + 2*x^6*y*z0 - 2*x^6*z0^2 + x^7 + x^5*y*z0 + x^5*z0^2 - 2*x^3*z0^4 - 2*x^4*y*z0 + x^4*z0^2 + 2*x^2*y*z0^3 + 2*x^2*z0^4 + 2*x^5 - x^3*y*z0 - x^2*y*z0 + x^2*z0^2 + x^3 + 2*x^2)/y) * dx, - ((x^31*z0^4 - 2*x^30*z0^4 - x^28*y^2*z0^4 + x^31*z0^2 + x^29*z0^4 + 2*x^27*y^2*z0^4 - x^30*z0^2 - x^28*y^2*z0^2 - x^28*z0^4 - x^26*y^2*z0^4 + x^31 + x^27*y^2*z0^2 + 2*x^27*z0^4 - 2*x^30 - x^28*y^2 - x^28*z0^2 - x^26*z0^4 + 2*x^27*y^2 + x^27*z0^2 + x^25*z0^4 - x^28 - 2*x^24*z0^4 + x^27 + x^25*z0^2 + x^23*z0^4 + x^24*y^2 - x^24*z0^2 - x^22*z0^4 + x^25 + 2*x^21*z0^4 - x^24 - x^22*z0^2 - x^20*z0^4 + x^21*z0^2 + x^19*z0^4 - x^22 - 2*x^18*z0^4 + x^21 + x^19*z0^2 + x^17*z0^4 - x^18*z0^2 - x^16*z0^4 + x^19 + 2*x^15*z0^4 - x^18 - x^16*z0^2 - x^14*z0^4 + x^15*z0^2 + x^13*z0^4 - x^16 - 2*x^12*z0^4 + x^15 + x^13*z0^2 - 2*x^11*z0^4 - x^12*z0^2 + 2*x^10*y*z0^3 + x^10*z0^4 + x^13 - x^9*y*z0^3 + 2*x^9*z0^4 - x^12 + 2*x^10*y*z0 + x^10*z0^2 - 2*x^8*y*z0^3 + x^8*z0^4 + 2*x^11 - x^9*y*z0 + 2*x^9*z0^2 - 2*x^7*y*z0^3 - 2*x^7*z0^4 - 2*x^10 + 2*x^8*y*z0 + x^8*z0^2 + x^6*y*z0^3 + x^9 - x^7*y*z0 - x^7*z0^2 + x^5*y*z0^3 + 2*x^5*z0^4 + 2*x^8 - x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^5*z0^2 + 2*x^3*y*z0^3 - 2*x^4*y*z0 - x^4*z0^2 - 2*x^2*y*z0^3 - x^2*z0^4 - 2*x^5 - x^3*y*z0 + x^3*z0^2 - 2*x^2*y*z0 - 2*x^2*z0^2 + 2*x^2)/y) * dx, - ((-x^31*z0^3 - 2*x^30*z0^3 + x^28*y^2*z0^3 + 2*x^31*z0 + 2*x^27*y^2*z0^3 + x^30*z0 - 2*x^28*y^2*z0 + x^28*z0^3 - x^29*z0 - x^27*y^2*z0 + 2*x^27*z0^3 + 2*x^28*z0 + x^26*y^2*z0 - 2*x^27*z0 + x^25*y^2*z0 - x^25*z0^3 + x^26*z0 + x^24*y^2*z0 - 2*x^24*z0^3 - 2*x^25*z0 + 2*x^24*z0 + x^22*z0^3 - x^23*z0 + 2*x^21*z0^3 + 2*x^22*z0 - 2*x^21*z0 - x^19*z0^3 + x^20*z0 - 2*x^18*z0^3 - 2*x^19*z0 + 2*x^18*z0 + x^16*z0^3 - x^17*z0 + 2*x^15*z0^3 + 2*x^16*z0 - 2*x^15*z0 - x^13*z0^3 + x^14*z0 - 2*x^12*z0^3 - 2*x^13*z0 + x^9*y*z0^4 + 2*x^12*z0 - 2*x^10*y*z0^2 + x^10*z0^3 - 2*x^8*y*z0^4 - x^11*z0 - 2*x^9*y*z0^2 - x^9*z0^3 + x^7*y*z0^4 - x^10*y - 2*x^10*z0 - 2*x^8*y*z0^2 + x^6*y*z0^4 - x^9*y - 2*x^9*z0 + 2*x^7*y*z0^2 + x^7*z0^3 + x^5*y*z0^4 + x^8*y - 2*x^8*z0 + 2*x^6*y*z0^2 + x^6*z0^3 - x^4*y*z0^4 + x^7*z0 - x^5*y*z0^2 + 2*x^5*z0^3 - 2*x^6*y + x^6*z0 + x^4*y*z0^2 + 2*x^4*z0^3 - 2*x^2*y*z0^4 - x^5*y + x^5*z0 + x^3*y*z0^2 + 2*x^3*z0^3 - 2*x^2*y*z0^2 - x^2*z0^3 + x^3*z0 - x^2*y - x^2*z0)/y) * dx, - ((-x^30*z0^4 + x^31*z0^2 + 2*x^29*z0^4 + x^27*y^2*z0^4 + 2*x^30*z0^2 - x^28*y^2*z0^2 - 2*x^26*y^2*z0^4 - x^31 - 2*x^27*y^2*z0^2 + x^27*z0^4 + x^28*y^2 - x^28*z0^2 - 2*x^26*z0^4 + 2*x^27*z0^2 + x^28 + x^24*y^2*z0^2 - x^24*z0^4 + x^25*z0^2 + 2*x^23*z0^4 - 2*x^24*z0^2 - x^25 + x^21*z0^4 - x^22*z0^2 - 2*x^20*z0^4 + 2*x^21*z0^2 + x^22 - x^18*z0^4 + x^19*z0^2 + 2*x^17*z0^4 - 2*x^18*z0^2 - x^19 + x^15*z0^4 - x^16*z0^2 - 2*x^14*z0^4 + 2*x^15*z0^2 + x^16 - x^12*z0^4 + x^13*z0^2 - 2*x^12*z0^2 + 2*x^10*z0^4 - x^13 - x^9*y*z0^3 + 2*x^10*y*z0 - x^8*y*z0^3 - x^8*z0^4 + 2*x^11 + x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 + 2*x^7*z0^4 + x^10 - x^8*y*z0 + 2*x^6*z0^4 - 2*x^9 - 2*x^7*y*z0 + x^7*z0^2 - x^5*y*z0^3 - x^8 - 2*x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 + 2*x^4*z0^4 + 2*x^7 + 2*x^5*z0^2 - x^3*z0^4 - 2*x^6 - x^4*y*z0 - x^4*z0^2 - 2*x^2*z0^4 + 2*x^5 + 2*x^3*y*z0 + x^3*z0^2 + 2*x^2*y*z0 + x^2*z0^2 + x^3)/y) * dx, - ((-2*x^31*z0^4 + 2*x^30*z0^4 + 2*x^28*y^2*z0^4 - x^31*z0^2 + x^29*z0^4 - 2*x^27*y^2*z0^4 + 2*x^30*z0^2 + x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 + x^31 - 2*x^27*y^2*z0^2 + 2*x^27*z0^4 - x^28*y^2 + x^28*z0^2 - x^26*z0^4 + x^24*y^2*z0^4 - 2*x^27*z0^2 - 2*x^25*z0^4 - x^28 - 2*x^24*z0^4 - x^25*z0^2 + x^23*z0^4 + 2*x^24*z0^2 + 2*x^22*z0^4 + x^25 + 2*x^21*z0^4 + x^22*z0^2 - x^20*z0^4 - 2*x^21*z0^2 - 2*x^19*z0^4 - x^22 - 2*x^18*z0^4 - x^19*z0^2 + x^17*z0^4 + 2*x^18*z0^2 + 2*x^16*z0^4 + x^19 + 2*x^15*z0^4 + x^16*z0^2 - x^14*z0^4 - 2*x^15*z0^2 - 2*x^13*z0^4 - x^16 - 2*x^12*z0^4 - x^13*z0^2 - 2*x^11*z0^4 + 2*x^12*z0^2 + x^10*y*z0^3 + x^10*z0^4 + x^13 + x^9*y*z0^3 - x^9*z0^4 - 2*x^10*y*z0 - x^10*z0^2 + 2*x^8*y*z0^3 - x^9*y*z0 + x^9*z0^2 - x^7*y*z0^3 + 2*x^7*z0^4 + 2*x^8*z0^2 + 2*x^6*y*z0^3 - 2*x^6*z0^4 - 2*x^9 - x^7*y*z0 + x^7*z0^2 - 2*x^5*y*z0^3 - x^5*z0^4 - x^8 - 2*x^6*z0^2 - 2*x^4*y*z0^3 - 2*x^4*z0^4 - 2*x^7 - 2*x^5*y*z0 - x^3*y*z0^3 + x^3*z0^4 - 2*x^6 + 2*x^4*y*z0 - 2*x^2*y*z0^3 - x^2*z0^4 + 2*x^5 - 2*x^3*z0^2 + 2*x^2*z0^2 + 2*x^3 + 2*x^2)/y) * dx, - ((x^31*z0^4 - x^28*y^2*z0^4 + x^31*z0^2 - 2*x^29*z0^4 + x^30*z0^2 - x^28*y^2*z0^2 - x^28*z0^4 + 2*x^26*y^2*z0^4 + 2*x^31 - x^27*y^2*z0^2 - 2*x^30 - 2*x^28*y^2 - x^28*z0^2 + 2*x^26*z0^4 + 2*x^27*y^2 - x^27*z0^2 + x^25*z0^4 + 2*x^28 + 2*x^27 + x^25*y^2 + x^25*z0^2 - 2*x^23*z0^4 + x^24*z0^2 - x^22*z0^4 - 2*x^25 - 2*x^24 - x^22*z0^2 + 2*x^20*z0^4 - x^21*z0^2 + x^19*z0^4 + 2*x^22 + 2*x^21 + x^19*z0^2 - 2*x^17*z0^4 + x^18*z0^2 - x^16*z0^4 - 2*x^19 - 2*x^18 - x^16*z0^2 + 2*x^14*z0^4 - x^15*z0^2 + x^13*z0^4 + 2*x^16 + 2*x^15 + x^13*z0^2 + 2*x^11*z0^4 + x^12*z0^2 + 2*x^10*y*z0^3 - x^10*z0^4 - 2*x^13 - x^9*y*z0^3 - x^9*z0^4 - 2*x^12 + 2*x^10*y*z0 + 2*x^8*y*z0^3 - 2*x^8*z0^4 - 2*x^9*y*z0 - x^7*y*z0^3 - x^7*z0^4 + 2*x^10 + 2*x^8*y*z0 + 2*x^8*z0^2 + 2*x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 - 2*x^7*z0^2 + x^5*y*z0^3 - 2*x^5*z0^4 + x^8 - x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 + x^4*z0^4 - x^5*y*z0 + 2*x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 + x^6 + 2*x^4*y*z0 - x^4*z0^2 + x^2*y*z0^3 - x^2*z0^4 - 2*x^3*y*z0 - x^3*z0^2 + x^2*y*z0 + 2*x^2*z0^2 - 2*x^3 - 2*x^2)/y) * dx, - ((2*x^31*z0^4 - x^30*z0^4 - 2*x^28*y^2*z0^4 + 2*x^31*z0^2 - x^29*z0^4 + x^27*y^2*z0^4 - 2*x^30*z0^2 - 2*x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 + x^31 + 2*x^27*y^2*z0^2 + x^27*z0^4 + x^30 - x^28*y^2 + 2*x^28*z0^2 + x^26*z0^4 - x^27*y^2 + 2*x^27*z0^2 + x^25*y^2*z0^2 + 2*x^25*z0^4 - x^28 - x^24*z0^4 - x^27 - 2*x^25*z0^2 - x^23*z0^4 - 2*x^24*z0^2 - 2*x^22*z0^4 + x^25 + x^21*z0^4 + x^24 + 2*x^22*z0^2 + x^20*z0^4 + 2*x^21*z0^2 + 2*x^19*z0^4 - x^22 - x^18*z0^4 - x^21 - 2*x^19*z0^2 - x^17*z0^4 - 2*x^18*z0^2 - 2*x^16*z0^4 + x^19 + x^15*z0^4 + x^18 + 2*x^16*z0^2 + x^14*z0^4 + 2*x^15*z0^2 + 2*x^13*z0^4 - x^16 - x^12*z0^4 - x^15 - 2*x^13*z0^2 + x^11*z0^4 - 2*x^12*z0^2 - x^10*y*z0^3 - x^10*z0^4 + x^13 - 2*x^9*y*z0^3 - 2*x^9*z0^4 + x^12 - x^10*y*z0 - 2*x^8*y*z0^3 + x^11 - x^9*y*z0 + 2*x^7*y*z0^3 - 2*x^7*z0^4 + x^10 + 2*x^8*y*z0 - 2*x^8*z0^2 - 2*x^6*y*z0^3 + 2*x^6*z0^4 + 2*x^9 + 2*x^7*y*z0 - x^5*y*z0^3 - 2*x^4*y*z0^3 - x^7 + x^5*y*z0 - 2*x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^4*y*z0 + 2*x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^5 - x^3*z0^2 - 2*x^2*y*z0 - x^2)/y) * dx, - ((x^31*z0^3 - x^30*z0^3 - x^28*y^2*z0^3 - 2*x^31*z0 - 2*x^29*z0^3 + x^27*y^2*z0^3 - x^30*z0 + 2*x^28*y^2*z0 - 2*x^28*z0^3 + 2*x^26*y^2*z0^3 + 2*x^29*z0 + x^27*y^2*z0 + x^27*z0^3 + x^25*y^2*z0^3 + 2*x^28*z0 - 2*x^26*y^2*z0 + 2*x^26*z0^3 + x^27*z0 + 2*x^25*z0^3 - 2*x^26*z0 - x^24*z0^3 - 2*x^25*z0 - 2*x^23*z0^3 - x^24*z0 - 2*x^22*z0^3 + 2*x^23*z0 + x^21*z0^3 + 2*x^22*z0 + 2*x^20*z0^3 + x^21*z0 + 2*x^19*z0^3 - 2*x^20*z0 - x^18*z0^3 - 2*x^19*z0 - 2*x^17*z0^3 - x^18*z0 - 2*x^16*z0^3 + 2*x^17*z0 + x^15*z0^3 + 2*x^16*z0 + 2*x^14*z0^3 + x^15*z0 + 2*x^13*z0^3 - 2*x^14*z0 - x^12*z0^3 - 2*x^13*z0 - 2*x^11*z0^3 - x^9*y*z0^4 - x^12*z0 + 2*x^10*y*z0^2 + x^10*z0^3 - x^8*y*z0^4 + 2*x^11*z0 + 2*x^9*y*z0^2 + x^9*z0^3 + x^10*y + x^10*z0 - x^8*z0^3 + x^9*y - 2*x^9*z0 - 2*x^7*y*z0^2 + 2*x^7*z0^3 - 2*x^5*y*z0^4 + 2*x^8*z0 - x^6*y*z0^2 + x^6*z0^3 - 2*x^4*y*z0^4 - x^5*y*z0^2 - x^5*z0^3 - x^3*y*z0^4 - 2*x^6*y - x^4*z0^3 + x^2*y*z0^4 + 2*x^5*y + x^5*z0 - 2*x^3*y*z0^2 + 2*x^3*z0^3 - x^4*y + x^4*z0 - x^2*y*z0^2 - 2*x^2*z0^3 + x^3*y - 2*x^3*z0 - x^2*y - 2*x^2*z0)/y) * dx, - ((2*x^31*z0^4 + x^30*z0^4 - 2*x^28*y^2*z0^4 - x^31*z0^2 - x^27*y^2*z0^4 + x^30*z0^2 + x^28*y^2*z0^2 + 2*x^28*z0^4 + x^31 - x^27*y^2*z0^2 - x^27*z0^4 + x^25*y^2*z0^4 - 2*x^30 - x^28*y^2 + x^28*z0^2 + 2*x^27*y^2 - x^27*z0^2 - 2*x^25*z0^4 - x^28 + x^24*z0^4 + 2*x^27 - x^25*z0^2 + x^24*z0^2 + 2*x^22*z0^4 + x^25 - x^21*z0^4 - 2*x^24 + x^22*z0^2 - x^21*z0^2 - 2*x^19*z0^4 - x^22 + x^18*z0^4 + 2*x^21 - x^19*z0^2 + x^18*z0^2 + 2*x^16*z0^4 + x^19 - x^15*z0^4 - 2*x^18 + x^16*z0^2 - x^15*z0^2 - 2*x^13*z0^4 - x^16 + x^12*z0^4 + 2*x^15 - x^13*z0^2 + 2*x^11*z0^4 + x^12*z0^2 - x^10*y*z0^3 - 2*x^10*z0^4 + x^13 + x^9*y*z0^3 + x^9*z0^4 - 2*x^12 - 2*x^10*y*z0 - x^10*z0^2 + 2*x^8*y*z0^3 - x^8*z0^4 + x^11 - x^9*y*z0 - 2*x^9*z0^2 + 2*x^7*y*z0^3 - x^7*z0^4 + x^10 - 2*x^8*y*z0 - x^8*z0^2 - x^6*y*z0^3 - 2*x^6*z0^4 + 2*x^9 - 2*x^7*y*z0 - x^7*z0^2 + 2*x^5*y*z0^3 + x^5*z0^4 - 2*x^6*y*z0 - 2*x^6*z0^2 + x^4*y*z0^3 + 2*x^7 - 2*x^5*y*z0 + x^3*y*z0^3 - x^3*z0^4 + 2*x^6 + x^4*y*z0 - 2*x^4*z0^2 + 2*x^2*y*z0^3 + x^2*z0^4 + 2*x^5 + x^3*y*z0 + 2*x^3*z0^2 - 2*x^2*y*z0 + x^2*z0^2 + x^3 - x^2)/y) * dx, - ((-2*x^31*z0^4 + 2*x^30*z0^4 + 2*x^28*y^2*z0^4 + 2*x^31*z0^2 + x^29*z0^4 - 2*x^27*y^2*z0^4 - 2*x^30*z0^2 - 2*x^28*y^2*z0^2 + 2*x^28*z0^4 - x^26*y^2*z0^4 - x^31 + 2*x^27*y^2*z0^2 - 2*x^27*z0^4 + x^28*y^2 - 2*x^28*z0^2 - x^26*z0^4 - x^29 + 2*x^27*z0^2 - 2*x^25*z0^4 + x^28 + x^26*y^2 + 2*x^24*z0^4 + 2*x^25*z0^2 + x^23*z0^4 + x^26 - 2*x^24*z0^2 + 2*x^22*z0^4 - x^25 - 2*x^21*z0^4 - 2*x^22*z0^2 - x^20*z0^4 - x^23 + 2*x^21*z0^2 - 2*x^19*z0^4 + x^22 + 2*x^18*z0^4 + 2*x^19*z0^2 + x^17*z0^4 + x^20 - 2*x^18*z0^2 + 2*x^16*z0^4 - x^19 - 2*x^15*z0^4 - 2*x^16*z0^2 - x^14*z0^4 - x^17 + 2*x^15*z0^2 - 2*x^13*z0^4 + x^16 + 2*x^12*z0^4 + 2*x^13*z0^2 - x^11*z0^4 + x^14 - 2*x^12*z0^2 + x^10*y*z0^3 - x^10*z0^4 - x^13 - 2*x^9*y*z0^3 - x^10*y*z0 - 2*x^8*y*z0^3 + x^8*z0^4 - 2*x^11 + x^9*y*z0 + 2*x^9*z0^2 - x^7*y*z0^3 + x^7*z0^4 - x^10 - x^8*y*z0 + 2*x^8*z0^2 - 2*x^6*y*z0^3 + 2*x^6*z0^4 - 2*x^9 - 2*x^7*y*z0 - x^7*z0^2 - x^5*y*z0^3 - x^6*y*z0 - x^6*z0^2 - x^4*y*z0^3 + 2*x^4*z0^4 - 2*x^7 - 2*x^5*z0^2 + x^3*z0^4 + x^6 + x^4*y*z0 - x^4*z0^2 - x^2*y*z0^3 + 2*x^2*z0^4 - 2*x^5 - x^3*y*z0 + 2*x^3*z0^2 - x^2*y*z0 - x^2*z0^2 - x^3 - x^2)/y) * dx, - ((2*x^31*z0^4 - 2*x^28*y^2*z0^4 - x^31*z0^2 - x^29*z0^4 + x^30*z0^2 + x^28*y^2*z0^2 - 2*x^28*z0^4 + x^26*y^2*z0^4 - x^29*z0^2 - x^27*y^2*z0^2 - x^30 + x^28*z0^2 + x^26*y^2*z0^2 + x^26*z0^4 + x^27*y^2 - x^27*z0^2 + 2*x^25*z0^4 + x^26*z0^2 + x^27 - x^25*z0^2 - x^23*z0^4 + x^24*z0^2 - 2*x^22*z0^4 - x^23*z0^2 - x^24 + x^22*z0^2 + x^20*z0^4 - x^21*z0^2 + 2*x^19*z0^4 + x^20*z0^2 + x^21 - x^19*z0^2 - x^17*z0^4 + x^18*z0^2 - 2*x^16*z0^4 - x^17*z0^2 - x^18 + x^16*z0^2 + x^14*z0^4 - x^15*z0^2 + 2*x^13*z0^4 + x^14*z0^2 + x^15 - x^13*z0^2 - x^11*z0^4 + x^12*z0^2 - x^10*y*z0^3 - x^11*z0^2 + x^9*y*z0^3 + x^9*z0^4 - x^12 - 2*x^10*y*z0 - 2*x^10*z0^2 + x^8*y*z0^3 + x^8*z0^4 - 2*x^11 - 2*x^7*y*z0^3 + x^7*z0^4 + x^10 - 2*x^8*y*z0 - x^6*y*z0^3 + 2*x^6*z0^4 + x^9 + x^7*y*z0 + x^5*y*z0^3 + 2*x^5*z0^4 + x^8 + x^6*y*z0 + 2*x^6*z0^2 - x^4*y*z0^3 + 2*x^7 - x^5*y*z0 + x^5*z0^2 - 2*x^3*y*z0^3 - 2*x^3*z0^4 + 2*x^4*y*z0 + x^4*z0^2 + x^2*y*z0^3 - 2*x^2*z0^4 - 2*x^3*y*z0 + x^3*z0^2 + 2*x^2*y*z0 - 2*x^2*z0^2 + x^3 + x^2)/y) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(ggg)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7llen[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: len(result) -[?7h[?12l[?25h[?2004l[?7h140 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(result)[?7h[?12l[?25h[?25l[?7lresult[?7h[?12l[?25h[?25l[?7lsage: for a in ggg: -....:  b = a.expansion((-1, 0)) -....:  flag = 1 -....:  for r in result: -....:  if r.expansion((-1, 0)) == b: -....:  flag = 0 -....:  if flag == 1: -....:  result += 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[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7l = de_ham_witt_lft(A[2])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7llen(result)[?7h[?12l[?25h[?25l[?7load('ini.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 -4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 11 1 -5 5 0 -8 ? 0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.branch_points[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^11 -z1^2 - z1 = x - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.branch_points[?7h[?12l[?25h[?25l[?7lbranch_points[?7h[?12l[?25h[?25l[?7lsage: AS.branch_points -[?7h[?12l[?25h[?2004l[?7h[0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 -0 0 0 -1 ? 0 -M, m 3 1 -1 1 0 -2 ? 0 -M, m 5 1 -2 2 0 -4 ? 0 -M, m 7 1 -3 3 0 -5 ? 0 -M, m 9 1 -4 4 0 -7 ? 0 -M, m 11 1 -5 5 0 -8 ? 0 -M, m 13 1 -6 6 0 -10 ? 0 -M, m 15 1 -7 7 0 -11 ? 0 -M, m 3 3 -2 0 1 -2 ? 1 -M, m 5 3 -3 1 1 -4 ? 1 -M, m 7 3 -4 2 1 -5 ? 1 -M, m 9 3 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [5], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :20, in  - -File :344, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :344, in (.0) - -File :131, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :131, in (.0) - -File :124, in residue(self, place) - -File :39, in expansion_at_infty(self, place) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs() - 832 else: - 833 variables.append(gen) ---> 834 return self(*variables) - 835 - 836 def numerical_approx(self, prec=None, digits=None, algorithm=None): - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__() - 447 (-2*x1*x2 + x1 + 1)/(x1 + x2) - 448 """ ---> 449 return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds) - 450 - 451 def _is_atomic(self): - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1083, in sage.rings.laurent_series_ring_element.LaurentSeries._div_() - 1081 try: - 1082 return type(self)(self._parent, --> 1083 self.__u / right.__u, - 1084 self.__n - right.__n) - 1085 except TypeError as msg: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:1091, in sage.rings.power_series_ring_element.PowerSeries._div_() - 1089 raise ZeroDivisionError("Can't divide by something indistinguishable from 0") - 1090 u = denom.valuation_zero_part() --> 1091 inv = ~u # inverse - 1092 - 1093 v = denom.valuation() - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:721, in sage.rings.power_series_poly.PowerSeries_poly.__invert__() - 719 return R(u, -self.valuation()) - 720 ---> 721 return self._parent(self.truncate().inverse_series_trunc(prec), prec=prec) - 722 - 723 def truncate(self, prec=infinity): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__() - 897 return mor._call_(x) - 898 else: ---> 899 return mor._call_with_args(x, args, kwds) - 900 - 901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {})) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:170, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args() - 168 return C._element_constructor(x) - 169 else: ---> 170 return C._element_constructor(x, **kwds) - 171 else: - 172 if len(kwds) == 0: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:700, in PowerSeriesRing_generic._element_constructor_(self, f, prec, check) - 696 if (is_PolynomialRing(S) or is_PowerSeriesRing(S)) and self.base_ring().has_coerce_map_from(S.base_ring()) \ - 697 and self.variable_names()==S.variable_names(): - 698 return True ---> 700 def _element_constructor_(self, f, prec=infinity, check=True): - 701 """ - 702  Coerce object to this power series ring. - 703 - (...) - 793 - 794  """ - 795 if prec is not infinity: - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1 0 z0 0 z1 0 -M, m 3 1 z0 z1 1 z0 1 z1 0 -M, m 5 1 z0 z1 2 z0 2 z1 0 -M, m 7 1 z0 z1 3 z0 3 z1 0 -M, m 9 1 z0 z1 4 z0 4 z1 0 -M, m 11 1 z0 z1 5 z0 5 z1 0 -M, m 13 1 z0 z1 6 z0 6 z1 0 -M, m 15 1 z0 z1 7 z0 7 z1 0 -M, m 3 3 z0 z1 2 z0 0 z1 1 -M, m 5 3 z0 z1 3 z0 1 z1 1 -M, m 7 3 z0 z1 4 z0 2 z1 1 -M, m 9 3 z0 z1 5 z0 3 z1 1 -M, m 11 3 z0 z1 6 z0 4 z1 1 -M, m 13 3 z0 z1 7 z0 5 z1 1 -M, m 15 3 z0 z1 8 z0 6 z1 1 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [6], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :344, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :344, in (.0) - -File :131, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :131, in (.0) - -File :124, in residue(self, place) - -File :39, in expansion_at_infty(self, place) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs() - 832 else: - 833 variables.append(gen) ---> 834 return self(*variables) - 835 - 836 def numerical_approx(self, prec=None, digits=None, algorithm=None): - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__() - 447 (-2*x1*x2 + x1 + 1)/(x1 + x2) - 448 """ ---> 449 return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds) - 450 - 451 def _is_atomic(self): - -File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__() - 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): --> 1739 return coercion_model.bin_op(left, right, truediv) - 1740 - 1741 try: - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op() - 1194 return (action)._act_(x, y) - 1195 else: --> 1196 return (action)._act_(y, x) - 1197 - 1198 # Now coerce to a common parent and do the operation there - -File /ext/sage/9.7/src/sage/categories/action.pyx:407, in sage.categories.action.InverseAction._act_() - 405 if self.S_precomposition is not None: - 406 x = self.S_precomposition(x) ---> 407 return self._action._act_(~g, x) - 408 - 409 def codomain(self): - -File /ext/sage/9.7/src/sage/structure/coerce_actions.pyx:645, in sage.structure.coerce_actions.RightModuleAction._act_() - 643 if self.extended_base is not None: - 644 a = self.extended_base(a) ---> 645 return (a)._lmul_(g) # a * g - 646 - 647 - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:920, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_() - 918 - 919 cpdef _lmul_(self, Element c): ---> 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n) - 921 - 922 def __pow__(_self, r, dummy): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:569, in sage.rings.power_series_poly.PowerSeries_poly._lmul_() - 567 2 + 6*t^4 + O(t^120) - 568 """ ---> 569 return PowerSeries_poly(self._parent, c * self.__f, self._prec, check=False) - 570 - 571 def __lshift__(PowerSeries_poly self, n): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() - 42 ValueError: series has negative valuation - 43 """ ----> 44 R = parent._poly_ring() - 45 if isinstance(f, Element): - 46 if (f)._parent is R: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) - 958 pass - 959 return False ---> 961 def _poly_ring(self): - 962 """ - 963  Return the underlying polynomial ring used to represent elements of - 964  this power series ring. - (...) - 970  Univariate Polynomial Ring in t over Integer Ring - 971  """ - 972 return self.__poly_ring - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -M, m 9 1 z0 z1; z0; z1: 4 4 0 -M, m 11 1 z0 z1; z0; z1: 5 5 0 -M, m 13 1 z0 z1; z0; z1: 6 6 0 -M, m 15 1 z0 z1; z0; z1: 7 7 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -M, m 9 3 z0 z1; z0; z1: 5 3 1 -M, m 11 3 z0 z1; z0; z1: 6 4 1 -M, m 13 3 z0 z1; z0; z1: 7 5 1 -M, m 15 3 z0 z1; z0; z1: 8 6 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -M, m 9 5 z0 z1; z0; z1: 5 3 2 -M, m 11 5 z0 z1; z0; z1: 6 4 2 -M, m 13 5 z0 z1; z0; z1: 7 5 2 -M, m 15 5 z0 z1; z0; z1: 8 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -M, m 9 7 z0 z1; z0; z1: 6 2 3 -M, m 11 7 z0 z1; z0; z1: 7 3 3 -M, m 13 7 z0 z1; z0; z1: 8 4 3 -M, m 15 7 z0 z1; z0; z1: 9 5 3 -M, m 9 9 z0 z1; z0; z1: 6 2 4 -M, m 11 9 z0 z1; z0; z1: 7 3 4 -M, m 13 9 z0 z1; z0; z1: 8 4 4 -M, m 15 9 z0 z1; z0; z1: 9 5 4 -M, m 11 11 z0 z1; z0; z1: 8 2 5 -M, m 13 11 z0 z1; z0; z1: 9 3 5 -M, m 15 11 z0 z1; z0; z1: 10 4 5 -M, m 13 13 z0 z1; z0; z1: 9 3 6 -M, m 15 13 z0 z1; z0; z1: 10 4 6 -I haven't found all forms, only 20 of 21 ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [7], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :318, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -M, m 9 1 z0 z1; z0; z1: 4 4 0 -M, m 11 1 z0 z1; z0; z1: 5 5 0 -M, m 13 1 z0 z1; z0; z1: 6 6 0 -M, m 15 1 z0 z1; z0; z1: 7 7 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -M, m 9 3 z0 z1; z0; z1: 5 3 1 -M, m 11 3 z0 z1; z0; z1: 6 4 1 -M, m 13 3 z0 z1; z0; z1: 7 5 1 -M, m 15 3 z0 z1; z0; z1: 8 6 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -M, m 9 5 z0 z1; z0; z1: 5 3 2 -M, m 11 5 z0 z1; z0; z1: 6 4 2 -M, m 13 5 z0 z1; z0; z1: 7 5 2 -M, m 15 5 z0 z1; z0; z1: 8 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -M, m 9 7 z0 z1; z0; z1: 6 2 3 -M, m 11 7 z0 z1; z0; z1: 7 3 3 -M, m 13 7 z0 z1; z0; z1: 8 4 3 -M, m 15 7 z0 z1; z0; z1: 9 5 3 -M, m 9 9 z0 z1; z0; z1: 6 2 4 -M, m 11 9 z0 z1; z0; z1: 7 3 4 -M, m 13 9 z0 z1; z0; z1: 8 4 4 -M, m 15 9 z0 z1; z0; z1: 9 5 4 -M, m 11 11 z0 z1; z0; z1: 8 2 5 -M, m 13 11 z0 z1; z0; z1: 9 3 5 -M, m 15 11 z0 z1; z0; z1: 10 4 5 -M, m 13 13 z0 z1; z0; z1: 9 3 6 -M, m 15 13 z0 z1; z0; z1: 10 4 6 -M, m 15 15 z0 z1; z0; z1: 11 3 7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -M, m 9 1 z0 z1; z0; z1: 4 4 0 -M, m 11 1 z0 z1; z0; z1: 5 5 0 -M, m 13 1 z0 z1; z0; z1: 6 6 0 -M, m 15 1 z0 z1; z0; z1: 7 7 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -M, m 9 3 z0 z1; z0; z1: 5 3 1 -M, m 11 3 z0 z1; z0; z1: 6 4 1 -M, m 13 3 z0 z1; z0; z1: 7 5 1 -M, m 15 3 z0 z1; z0; z1: 8 6 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -M, m 9 5 z0 z1; z0; z1: 5 3 2 -M, m 11 5 z0 z1; z0; z1: 6 4 2 -M, m 13 5 z0 z1; z0; z1: 7 5 2 -M, m 15 5 z0 z1; z0; z1: 8 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -M, m 9 7 z0 z1; z0; z1: 6 2 3 -M, m 11 7 z0 z1; z0; z1: 7 3 3 -M, m 13 7 z0 z1; z0; z1: 8 4 3 -M, m 15 7 z0 z1; z0; z1: 9 5 3 -M, m 9 9 z0 z1; z0; z1: 6 2 4 -M, m 11 9 z0 z1; z0; z1: 7 3 4 -M, m 13 9 z0 z1; z0; z1: 8 4 4 -M, m 15 9 z0 z1; z0; z1: 9 5 4 -M, m 11 11 z0 z1; z0; z1: 8 2 5 -M, m 13 11 z0 z1; z0; z1: 9 3 5 -M, m 15 11 z0 z1; z0; z1: 10 4 5 -M, m 13 13 z0 z1; z0; z1: 9 3 6 -M, m 15 13 z0 z1; z0; z1: 10 4 6 -M, m 15 15 z0 z1; z0; z1: 11 3 7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in ggg:[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf chang(a):[?7h[?12l[?25h[?25l[?7ldef [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: def aaa(M): -....: [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lreturn[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  return floor(M/2) + ceil(M/4) -....: [?7h[?12l[?25h[?25l[?7lsage: def aaa(M): -....:  return floor(M/2) + ceil(M/4) -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef aaa(M):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ldef [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: def bbb(M): -....: [?7h[?12l[?25h[?25l[?7lreturn floor(M/2) + ceil(M/4)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lreturn[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  return ceil(3*M/4) -....: [?7h[?12l[?25h[?25l[?7lsage: def bbb(M): -....:  return ceil(3*M/4) -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in ggg:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for M in range(20): -....: [?7h[?12l[?25h[?25l[?7lif flag == 1:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:  if M%2 == 1: -....: [?7h[?12l[?25h[?25l[?7laaa(M)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpa(M)[?7h[?12l[?25h[?25l[?7lra(M)[?7h[?12l[?25h[?25l[?7lia(M)[?7h[?12l[?25h[?25l[?7lna(M)[?7h[?12l[?25h[?25l[?7lta(M)[?7h[?12l[?25h[?25l[?7lprint(a(M)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(aaa(M), bbb(M)) -....: [?7h[?12l[?25h[?25l[?7lsage: for M in range(20): -....:  if M%2 == 1: -....:  print(aaa(M), bbb(M)) -....:  -[?7h[?12l[?25h[?2004l1 1 -2 3 -4 4 -5 6 -7 7 -8 9 -10 10 -11 12 -13 13 -14 15 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for M in range(20): -....:  if M%2 == 1: -....:  print(aaa(M), bbb(M))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0):[?7h[?12l[?25h[?25l[?7l40):[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(aaa(M), bbb(M)) -....: [?7h[?12l[?25h[?25l[?7lsage: for M in range(40): -....:  if M%2 == 1: -....:  print(aaa(M), bbb(M)) -....:  -[?7h[?12l[?25h[?2004l1 1 -2 3 -4 4 -5 6 -7 7 -8 9 -10 10 -11 12 -13 13 -14 15 -16 16 -17 18 -19 19 -20 21 -22 22 -23 24 -25 25 -26 27 -28 28 -29 30 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for M in range(40): -....:  if M%2 == 1: -....:  print(aaa(M), bbb(M))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2 - -()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldefbbb(M): -returnceil(3*M/4) - [?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*M/4)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/4)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-)/4)[?7h[?12l[?25h[?25l[?7l3)/4)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7lretur((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4) - [?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7ldef((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l((3*M-3)/4)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef aaa(M): -....:  return floor(M/2) + ceil(M/4)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lload('init.sage') - [?7h[?12l[?25h[?25l[?7lAS.branch_points[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7llen(result)[?7h[?12l[?25h[?25l[?7lresult[?7h[?12l[?25h[?25l[?7llen(result)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l.branch_points[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldef aaa(M): -....:  return floor(M/2) + ceil(M/4)[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l - [?7h[?12l[?25h[?25l[?7lfor M in range(20): -....:  if M%2 == 1: -....:  print(aaa(M), bbb(M))[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l4 - -()[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l -  - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lfor M in range(40): -....:  if M%2 == 1: -....:  print(aaa(M), bbb(M))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2 - -()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldefbbb(M): -returnceil(3*M/4) - [?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(M/4)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-/4)[?7h[?12l[?25h[?25l[?7l2/4)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM-2/4)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*M-2/4)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/4)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() -....: [?7h[?12l[?25h[?25l[?7lsage: def bbb(M): -....:  return ceil((3*M-2)/4) -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def bbb(M): -....:  return ceil((3*M-2)/4)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lforM in range(40): -....:  if M%2 == 1: -....:  print(aaa(M), bbb(M))[?7h[?12l[?25h[?25l[?7l....:  print(aaa(M), bbb(M)) -....: [?7h[?12l[?25h[?25l[?7lsage: for M in range(40): -....:  if M%2 == 1: -....:  print(aaa(M), bbb(M)) -....:  -[?7h[?12l[?25h[?2004l1 1 -2 2 -4 4 -5 5 -7 7 -8 8 -10 10 -11 11 -13 13 -14 14 -16 16 -17 17 -19 19 -20 20 -22 22 -23 23 -25 25 -26 26 -28 28 -29 29 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for M in range(40): -....:  if M%2 == 1: -....:  print(aaa(M), bbb(M))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() b(M)[?7h[?12l[?25h[?25l[?7l()= b(M)[?7h[?12l[?25h[?25l[?7l= b(M)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb(M)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(aaa(M)==bbb(M)) -....: [?7h[?12l[?25h[?25l[?7lsage: for M in range(40): -....:  if M%2 == 1: -....:  print(aaa(M)==bbb(M)) -....:  -[?7h[?12l[?25h[?2004lTrue -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -True -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -M, m 9 1 z0 z1; z0; z1: 4 4 0 -M, m 9 3 z0 z1; z0; z1: 5 3 1 -M, m 9 5 z0 z1; z0; z1: 5 3 2 -M, m 9 7 z0 z1; z0; z1: 6 2 3 -M, m 9 9 z0 z1; z0; z1: 6 2 4 -M, m 11 1 z0 z1; z0; z1: 5 5 0 -M, m 11 3 z0 z1; z0; z1: 6 4 1 -M, m 11 5 z0 z1; z0; z1: 6 4 2 -M, m 11 7 z0 z1; z0; z1: 7 3 3 -M, m 11 9 z0 z1; z0; z1: 7 3 4 -M, m 11 11 z0 z1; z0; z1: 8 2 5 -M, m 13 1 z0 z1; z0; z1: 6 6 0 -M, m 13 3 z0 z1; z0; z1: 7 5 1 -M, m 13 5 z0 z1; z0; z1: 7 5 2 -M, m 13 7 z0 z1; z0; z1: 8 4 3 -M, m 13 9 z0 z1; z0; z1: 8 4 4 -M, m 13 11 z0 z1; z0; z1: 9 3 5 -M, m 13 13 z0 z1; z0; z1: 9 3 6 -M, m 15 1 z0 z1; z0; z1: 7 7 0 -M, m 15 3 z0 z1; z0; z1: 8 6 1 -M, m 15 5 z0 z1; z0; z1: 8 6 2 -M, m 15 7 z0 z1; z0; z1: 9 5 3 -M, m 15 9 z0 z1; z0; z1: 9 5 4 -M, m 15 11 z0 z1; z0; z1: 10 4 5 -M, m 15 13 z0 z1; z0; z1: 10 4 6 -M, m 15 15 z0 z1; z0; z1: 11 3 7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -True False True -M, m 3 1 z0 z1; z0; z1: 1 1 0 -True False True -M, m 3 3 z0 z1; z0; z1: 2 0 1 -False False True -M, m 5 1 z0 z1; z0; z1: 2 2 0 -False False True -M, m 5 3 z0 z1; z0; z1: 3 1 1 -False False True -M, m 5 5 z0 z1; z0; z1: 3 1 2 -False False True -M, m 7 1 z0 z1; z0; z1: 3 3 0 -False False True -M, m 7 3 z0 z1; z0; z1: 4 2 1 -True False True -M, m 7 5 z0 z1; z0; z1: 4 2 2 -False False True -M, m 7 7 z0 z1; z0; z1: 5 1 3 -False False True -M, m 9 1 z0 z1; z0; z1: 4 4 0 -False False True -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [18], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :45, in __init__(self, C, list_of_fcts, branch_points, prec) - -File :196, in artin_schreier_transform(power_series, prec) - -File :12, in new_reverse(power_series, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1829 if x: - 1830 raise ValueError("must not specify %s keyword and positional argument" % name) --> 1831 a = self(kwds[name]) - 1832 del kwds[name] - 1833 try: - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1850 x = x[0] - 1851 --> 1852 return self.__u(*x)*(x[0]**self.__n) - 1853 - 1854 def __pari__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__() - 363 x[0] = a - 364 x = tuple(x) ---> 365 return self.__f(x) - 366 - 367 def _unsafe_mutate(self, i, value): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() - 896 return result - 897 pol._compiled = CompiledPolynomialFunction(pol.list()) ---> 898 return pol._compiled.eval(a) - 899 - 900 def compose_trunc(self, Polynomial other, long n): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval() - 123 cdef object temp - 124 try: ---> 125 pd_eval(self._dag, x, self._coeffs) #see further down - 126 temp = self._dag.value #for an explanation - 127 pd_clean(self._dag) #of these 3 lines - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - - [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (24 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (23 times)] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:508, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: - 507 pd_eval(self.left, vars, coeffs) ---> 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - 510 pd_clean(self.left) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:492, in sage.rings.polynomial.polynomial_compiled.mul_pd.eval() - 490 pd_eval(self.left, vars, coeffs) - 491 pd_eval(self.right, vars, coeffs) ---> 492 self.value = self.left.value * self.right.value - 493 pd_clean(self.left) - 494 pd_clean(self.right) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__() - 1512 cdef int cl = classify_elements(left, right) - 1513 if HAVE_SAME_PARENT(cl): --> 1514 return (left)._mul_(right) - 1515 if BOTH_ARE_ELEMENT(cl): - 1516 return coercion_model.bin_op(left, right, mul) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_() - 911 cdef LaurentSeries right = right_r - 912 return type(self)(self._parent, ---> 913 self.__u * right.__u, - 914 self.__n + right.__n) - 915 - -File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__() - 1512 cdef int cl = classify_elements(left, right) - 1513 if HAVE_SAME_PARENT(cl): --> 1514 return (left)._mul_(right) - 1515 if BOTH_ARE_ELEMENT(cl): - 1516 return coercion_model.bin_op(left, right, mul) - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_() - 538 """ - 539 prec = self._mul_prec(right_r) ---> 540 return PowerSeries_poly(self._parent, - 541 self.__f * (right_r).__f, - 542 prec=prec, - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() - 42 ValueError: series has negative valuation - 43 """ ----> 44 R = parent._poly_ring() - 45 if isinstance(f, Element): - 46 if (f)._parent is R: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) - 958 pass - 959 return False ---> 961 def _poly_ring(self): - 962 """ - 963  Return the underlying polynomial ring used to represent elements of - 964  this power series ring. - (...) - 970  Univariate Polynomial Ring in t over Integer Ring - 971  """ - 972 return self.__poly_ring - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -0 1 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -1 3 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -1 2 1 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -3 6 0 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -2 5 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -2 4 2 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -4 8 0 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -4 7 1 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -3 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -3 5 3 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [19], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :344, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :344, in (.0) - -File :131, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :131, in (.0) - -File :124, in residue(self, place) - -File :39, in expansion_at_infty(self, place) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/structure/element.pyx:830, in sage.structure.element.Element.subs() - 828 if str(gen) in kwds: - 829 variables.append(kwds[str(gen)]) ---> 830 elif in_dict and gen in in_dict: - 831 variables.append(in_dict[gen]) - 832 else: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1112, in sage.structure.element.Element.__richcmp__() - 1110 return (self)._richcmp_(other, op) - 1111 else: --> 1112 return coercion_model.richcmp(self, other, op) - 1113 - 1114 cpdef _richcmp_(left, right, int op): - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp() - 1971 # Coerce to a common parent - 1972 try: --> 1973 x, y = self.canonical_coercion(x, y) - 1974 except (TypeError, NotImplementedError): - 1975 pass - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion() - 1309 x_map, y_map = coercions - 1310 if x_map is not None: --> 1311 x_elt = (x_map)._call_(x) - 1312 else: - 1313 x_elt = x - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) - 636 ring_one = self.ring().one() - 637 try: ---> 638 return self._element_class(self, x, ring_one, coerce=coerce) - 639 except (TypeError, ValueError): - 640 pass - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -0 1 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -2 3 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -1 2 1 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -3 6 0 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -3 5 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -2 4 2 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -5 8 0 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -4 7 1 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -4 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -3 5 3 -M, m 9 1 z0 z1; z0; z1: 4 4 0 -6 11 0 -M, m 9 3 z0 z1; z0; z1: 5 3 1 -6 10 1 -M, m 9 5 z0 z1; z0; z1: 5 3 2 -5 9 2 -M, m 9 7 z0 z1; z0; z1: 6 2 3 -5 8 3 -M, m 9 9 z0 z1; z0; z1: 6 2 4 -4 7 4 -M, m 11 1 z0 z1; z0; z1: 5 5 0 -8 13 0 -M, m 11 3 z0 z1; z0; z1: 6 4 1 -7 12 1 -M, m 11 5 z0 z1; z0; z1: 6 4 2 -7 11 2 -M, m 11 7 z0 z1; z0; z1: 7 3 3 -6 10 3 -M, m 11 9 z0 z1; z0; z1: 7 3 4 -6 9 4 -M, m 11 11 z0 z1; z0; z1: 8 2 5 -5 8 5 -M, m 13 1 z0 z1; z0; z1: 6 6 0 -9 16 0 -M, m 13 3 z0 z1; z0; z1: 7 5 1 -9 15 1 -M, m 13 5 z0 z1; z0; z1: 7 5 2 -8 14 2 -M, m 13 7 z0 z1; z0; z1: 8 4 3 -8 13 3 -M, m 13 9 z0 z1; z0; z1: 8 4 4 -7 12 4 -M, m 13 11 z0 z1; z0; z1: 9 3 5 -7 11 5 -M, m 13 13 z0 z1; z0; z1: 9 3 6 -6 10 6 -M, m 15 1 z0 z1; z0; z1: 7 7 0 -11 18 0 -M, m 15 3 z0 z1; z0; z1: 8 6 1 -10 17 1 -M, m 15 5 z0 z1; z0; z1: 8 6 2 -10 16 2 -M, m 15 7 z0 z1; z0; z1: 9 5 3 -9 15 3 -M, m 15 9 z0 z1; z0; z1: 9 5 4 -9 14 4 -M, m 15 11 z0 z1; z0; z1: 10 4 5 -8 13 5 -M, m 15 13 z0 z1; z0; z1: 10 4 6 -8 12 6 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [20], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :344, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :344, in (.0) - -File :131, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :131, in (.0) - -File :124, in residue(self, place) - -File :39, in expansion_at_infty(self, place) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs() - 832 else: - 833 variables.append(gen) ---> 834 return self(*variables) - 835 - 836 def numerical_approx(self, prec=None, digits=None, algorithm=None): - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__() - 447 (-2*x1*x2 + x1 + 1)/(x1 + x2) - 448 """ ---> 449 return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds) - 450 - 451 def _is_atomic(self): - -File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__() - 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): --> 1739 return coercion_model.bin_op(left, right, truediv) - 1740 - 1741 try: - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() - 1202 self._record_exception() - 1203 else: --> 1204 return PyObject_CallObject(op, xy) - 1205 - 1206 if op is mul: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1083, in sage.rings.laurent_series_ring_element.LaurentSeries._div_() - 1081 try: - 1082 return type(self)(self._parent, --> 1083 self.__u / right.__u, - 1084 self.__n - right.__n) - 1085 except TypeError as msg: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:1091, in sage.rings.power_series_ring_element.PowerSeries._div_() - 1089 raise ZeroDivisionError("Can't divide by something indistinguishable from 0") - 1090 u = denom.valuation_zero_part() --> 1091 inv = ~u # inverse - 1092 - 1093 v = denom.valuation() - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:721, in sage.rings.power_series_poly.PowerSeries_poly.__invert__() - 719 return R(u, -self.valuation()) - 720 ---> 721 return self._parent(self.truncate().inverse_series_trunc(prec), prec=prec) - 722 - 723 def truncate(self, prec=infinity): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1632, in sage.rings.polynomial.polynomial_element.Polynomial.inverse_series_trunc() - 1630 raise ValueError("Impossible inverse modulo") - 1631 --> 1632 cpdef Polynomial inverse_series_trunc(self, long prec): - 1633 r""" - 1634 Return a polynomial approximation of precision ``prec`` of the inverse - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1717, in sage.rings.polynomial.polynomial_element.Polynomial.inverse_series_trunc() - 1715 current = R(first_coeff) - 1716 for next_prec in sage.misc.misc.newton_method_sizes(prec)[1:]: --> 1717 z = current._mul_trunc_(self, next_prec)._mul_trunc_(current, next_prec) - 1718 current = current + current - z - 1719 return current - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1799, in sage.rings.polynomial.polynomial_element.Polynomial._mul_trunc_() - 1797 return self._mul_generic(right) - 1798 --> 1799 cpdef Polynomial _mul_trunc_(self, Polynomial right, long n): - 1800 r""" - 1801 Return the truncated multiplication of two polynomials up to ``n``. - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1838, in sage.rings.polynomial.polynomial_element.Polynomial._mul_trunc_() - 1836 x = self.list(copy=False) - 1837 y = right.list(copy=False) --> 1838 return self._new_generic(do_schoolbook_product(x, y, n)) - 1839 else: - 1840 pol = self.truncate(n) * right.truncate(n) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:248, in sage.rings.polynomial.polynomial_element.Polynomial._new_generic() - 246 del coeffs[n] - 247 n -= 1 ---> 248 return type(self)(self._parent, coeffs, check=False) - 249 - 250 cpdef _add_(self, right): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:151, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__init__() - 149 # not do K.coerce(e) but K(e). - 150 e = K(e) ---> 151 d = parent._modulus.ZZ_pE(list(e.polynomial())) - 152 ZZ_pEX_SetCoeff(self.x, i, d.x) - 153 return - -File /ext/sage/9.7/src/sage/rings/finite_rings/element_givaro.pyx:1514, in sage.rings.finite_rings.element_givaro.FiniteField_givaroElement.polynomial() - 1512 return PolynomialRing(K.prime_subfield(), name)(ret) - 1513 else: --> 1514 return K.polynomial_ring()(ret) - 1515 - 1516 def _magma_init_(self, magma): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:309, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds) - 306 args = (self.base_ring(), self.variable_names(), None, self.is_sparse()) - 307 return unpickle_PolynomialRing, args ---> 309 def _element_constructor_(self, x=None, check=True, is_gen=False, - 310 construct=False, **kwds): - 311 r""" - 312  Convert ``x`` into this univariate polynomial ring, - 313  possibly non-canonically. - (...) - 412  λ^2 - 413  """ - 414 C = self.element_class - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -True False True -M, m 3 1 z0 z1; z0; z1: 1 1 0 -False False True -M, m 3 3 z0 z1; z0; z1: 2 0 1 -False False True -M, m 5 1 z0 z1; z0; z1: 2 2 0 -False False True -M, m 5 3 z0 z1; z0; z1: 3 1 1 -True False True -M, m 5 5 z0 z1; z0; z1: 3 1 2 -False False True -M, m 7 1 z0 z1; z0; z1: 3 3 0 -False False True -M, m 7 3 z0 z1; z0; z1: 4 2 1 -True False True -M, m 7 5 z0 z1; z0; z1: 4 2 2 -True False True -M, m 7 7 z0 z1; z0; z1: 5 1 3 -False False True -M, m 9 1 z0 z1; z0; z1: 4 4 0 -False False True -M, m 9 3 z0 z1; z0; z1: 5 3 1 -False False True -M, m 9 5 z0 z1; z0; z1: 5 3 2 -True False True -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [21], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :38, in __init__(self, C, list_of_fcts, branch_points, prec) - -File :143, in expansion(self, pt, prec) - -File :135, in expansion_at_infty(self, place, prec) - -File :18, in naive_hensel(fct, F, start, prec) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1083, in sage.rings.laurent_series_ring_element.LaurentSeries._div_() - 1081 try: - 1082 return type(self)(self._parent, --> 1083 self.__u / right.__u, - 1084 self.__n - right.__n) - 1085 except TypeError as msg: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:1110, in sage.rings.power_series_ring_element.PowerSeries._div_() - 1108 else: - 1109 num = self --> 1110 return num*inv - 1111 - 1112 def __mod__(self, other): - -File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__() - 1512 cdef int cl = classify_elements(left, right) - 1513 if HAVE_SAME_PARENT(cl): --> 1514 return (left)._mul_(right) - 1515 if BOTH_ARE_ELEMENT(cl): - 1516 return coercion_model.bin_op(left, right, mul) - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_() - 538 """ - 539 prec = self._mul_prec(right_r) ---> 540 return PowerSeries_poly(self._parent, - 541 self.__f * (right_r).__f, - 542 prec=prec, - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() - 42 ValueError: series has negative valuation - 43 """ ----> 44 R = parent._poly_ring() - 45 if isinstance(f, Element): - 46 if (f)._parent is R: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) - 958 pass - 959 return False ---> 961 def _poly_ring(self): - 962 """ - 963  Return the underlying polynomial ring used to represent elements of - 964  this power series ring. - (...) - 970  Univariate Polynomial Ring in t over Integer Ring - 971  """ - 972 return self.__poly_ring - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -0 1 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -2 3 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -1 2 1 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -3 6 0 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -3 5 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -2 4 2 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -5 8 0 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -4 7 1 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -4 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -3 5 3 -M, m 9 1 z0 z1; z0; z1: 4 4 0 -6 11 0 -M, m 9 3 z0 z1; z0; z1: 5 3 1 -6 10 1 -M, m 9 5 z0 z1; z0; z1: 5 3 2 -5 9 2 -M, m 9 7 z0 z1; z0; z1: 6 2 3 -5 8 3 -M, m 9 9 z0 z1; z0; z1: 6 2 4 -4 7 4 -M, m 11 1 z0 z1; z0; z1: 5 5 0 -8 13 0 -M, m 11 3 z0 z1; z0; z1: 6 4 1 -7 12 1 -M, m 11 5 z0 z1; z0; z1: 6 4 2 -7 11 2 -M, m 11 7 z0 z1; z0; z1: 7 3 3 -6 10 3 -M, m 11 9 z0 z1; z0; z1: 7 3 4 -6 9 4 -M, m 11 11 z0 z1; z0; z1: 8 2 5 -5 8 5 -M, m 13 1 z0 z1; z0; z1: 6 6 0 -9 16 0 -M, m 13 3 z0 z1; z0; z1: 7 5 1 -9 15 1 -M, m 13 5 z0 z1; z0; z1: 7 5 2 -8 14 2 -M, m 13 7 z0 z1; z0; z1: 8 4 3 -8 13 3 -M, m 13 9 z0 z1; z0; z1: 8 4 4 -7 12 4 -M, m 13 11 z0 z1; z0; z1: 9 3 5 -7 11 5 -M, m 13 13 z0 z1; z0; z1: 9 3 6 -6 10 6 -M, m 15 1 z0 z1; z0; z1: 7 7 0 -11 18 0 -M, m 15 3 z0 z1; z0; z1: 8 6 1 -10 17 1 -M, m 15 5 z0 z1; z0; z1: 8 6 2 -10 16 2 -M, m 15 7 z0 z1; z0; z1: 9 5 3 -9 15 3 -M, m 15 9 z0 z1; z0; z1: 9 5 4 -9 14 4 -M, m 15 11 z0 z1; z0; z1: 10 4 5 -8 13 5 -M, m 15 13 z0 z1; z0; z1: 10 4 6 -8 12 6 -M, m 15 15 z0 z1; z0; z1: 11 3 7 -7 11 7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -True False True -M, m 3 1 z0 z1; z0; z1: 1 1 0 -True False True -M, m 3 3 z0 z1; z0; z1: 2 0 1 -False False True -M, m 5 1 z0 z1; z0; z1: 2 2 0 -False False True -M, m 5 3 z0 z1; z0; z1: 3 1 1 -False False True -M, m 5 5 z0 z1; z0; z1: 3 1 2 -False False True -M, m 7 1 z0 z1; z0; z1: 3 3 0 -False False True -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [23], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :344, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :344, in (.0) - -File :131, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :131, in (.0) - -File :124, in residue(self, place) - -File :39, in expansion_at_infty(self, place) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs() - 832 else: - 833 variables.append(gen) ---> 834 return self(*variables) - 835 - 836 def numerical_approx(self, prec=None, digits=None, algorithm=None): - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__() - 447 (-2*x1*x2 + x1 + 1)/(x1 + x2) - 448 """ ---> 449 return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds) - 450 - 451 def _is_atomic(self): - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1083, in sage.rings.laurent_series_ring_element.LaurentSeries._div_() - 1081 try: - 1082 return type(self)(self._parent, --> 1083 self.__u / right.__u, - 1084 self.__n - right.__n) - 1085 except TypeError as msg: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:1091, in sage.rings.power_series_ring_element.PowerSeries._div_() - 1089 raise ZeroDivisionError("Can't divide by something indistinguishable from 0") - 1090 u = denom.valuation_zero_part() --> 1091 inv = ~u # inverse - 1092 - 1093 v = denom.valuation() - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:721, in sage.rings.power_series_poly.PowerSeries_poly.__invert__() - 719 return R(u, -self.valuation()) - 720 ---> 721 return self._parent(self.truncate().inverse_series_trunc(prec), prec=prec) - 722 - 723 def truncate(self, prec=infinity): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__() - 897 return mor._call_(x) - 898 else: ---> 899 return mor._call_with_args(x, args, kwds) - 900 - 901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {})) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:170, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args() - 168 return C._element_constructor(x) - 169 else: ---> 170 return C._element_constructor(x, **kwds) - 171 else: - 172 if len(kwds) == 0: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:700, in PowerSeriesRing_generic._element_constructor_(self, f, prec, check) - 696 if (is_PolynomialRing(S) or is_PowerSeriesRing(S)) and self.base_ring().has_coerce_map_from(S.base_ring()) \ - 697 and self.variable_names()==S.variable_names(): - 698 return True ---> 700 def _element_constructor_(self, f, prec=infinity, check=True): - 701 """ - 702  Coerce object to this power series ring. - 703 - (...) - 793 - 794  """ - 795 if prec is not infinity: - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -0 1 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -1 3 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -1 2 1 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -1 6 0 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -2 5 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -2 4 2 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -2 8 0 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -2 7 1 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -3 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -3 5 3 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [24], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :45, in __init__(self, C, list_of_fcts, branch_points, prec) - -File :196, in artin_schreier_transform(power_series, prec) - -File :12, in new_reverse(power_series, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1829 if x: - 1830 raise ValueError("must not specify %s keyword and positional argument" % name) --> 1831 a = self(kwds[name]) - 1832 del kwds[name] - 1833 try: - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1850 x = x[0] - 1851 --> 1852 return self.__u(*x)*(x[0]**self.__n) - 1853 - 1854 def __pari__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__() - 363 x[0] = a - 364 x = tuple(x) ---> 365 return self.__f(x) - 366 - 367 def _unsafe_mutate(self, i, value): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() - 896 return result - 897 pol._compiled = CompiledPolynomialFunction(pol.list()) ---> 898 return pol._compiled.eval(a) - 899 - 900 def compose_trunc(self, Polynomial other, long n): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval() - 123 cdef object temp - 124 try: ---> 125 pd_eval(self._dag, x, self._coeffs) #see further down - 126 temp = self._dag.value #for an explanation - 127 pd_clean(self._dag) #of these 3 lines - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - - [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (7 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (6 times)] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) ---> 509 self.value = self.left.value * self.right.value + coeffs[self.index] - 510 pd_clean(self.left) - 511 pd_clean(self.right) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__() - 1231 # Left and right are Sage elements => use coercion model - 1232 if BOTH_ARE_ELEMENT(cl): --> 1233 return coercion_model.bin_op(left, right, add) - 1234 - 1235 cdef long value - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op() - 1198 # Now coerce to a common parent and do the operation there - 1199 try: --> 1200 xy = self.canonical_coercion(x, y) - 1201 except TypeError: - 1202 self._record_exception() - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion() - 1313 x_elt = x - 1314 if y_map is not None: --> 1315 y_elt = (y_map)._call_(y) - 1316 else: - 1317 y_elt = y - -File /ext/sage/9.7/src/sage/categories/morphism.pyx:601, in sage.categories.morphism.SetMorphism._call_() - 599 3 - 600 """ ---> 601 return self._function(x) - 602 - 603 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:919, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_() - 917 return type(self)(self._parent, self.__u._rmul_(c), self.__n) - 918 ---> 919 cpdef _lmul_(self, Element c): - 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n) - 921 - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:920, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_() - 918 - 919 cpdef _lmul_(self, Element c): ---> 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n) - 921 - 922 def __pow__(_self, r, dummy): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:569, in sage.rings.power_series_poly.PowerSeries_poly._lmul_() - 567 2 + 6*t^4 + O(t^120) - 568 """ ---> 569 return PowerSeries_poly(self._parent, c * self.__f, self._prec, check=False) - 570 - 571 def __lshift__(PowerSeries_poly self, n): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() - 42 ValueError: series has negative valuation - 43 """ ----> 44 R = parent._poly_ring() - 45 if isinstance(f, Element): - 46 if (f)._parent is R: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) - 958 pass - 959 return False ---> 961 def _poly_ring(self): - 962 """ - 963  Return the underlying polynomial ring used to represent elements of - 964  this power series ring. - (...) - 970  Univariate Polynomial Ring in t over Integer Ring - 971  """ - 972 return self.__poly_ring - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -True False True -M, m 3 1 z0 z1; z0; z1: 1 1 0 -True False True -M, m 3 3 z0 z1; z0; z1: 2 0 1 -False False True -M, m 5 1 z0 z1; z0; z1: 2 2 0 -True False True -M, m 5 3 z0 z1; z0; z1: 3 1 1 -False False True -M, m 5 5 z0 z1; z0; z1: 3 1 2 -False False True -M, m 7 1 z0 z1; z0; z1: 3 3 0 -True False True -M, m 7 3 z0 z1; z0; z1: 4 2 1 -False False True -M, m 7 5 z0 z1; z0; z1: 4 2 2 -False False True -M, m 7 7 z0 z1; z0; z1: 5 1 3 -False False True -M, m 9 1 z0 z1; z0; z1: 4 4 0 -True False True -M, m 9 3 z0 z1; z0; z1: 5 3 1 -False False True -M, m 9 5 z0 z1; z0; z1: 5 3 2 -False False True -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [25], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :318, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :139, in holomorphic_differentials_basis(self, threshold) - -File :425, in holomorphic_combinations(S) - -File :67, in __add__(self, other) - -File :13, in __init__(self, C, g) - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -True False True -M, m 3 1 z0 z1; z0; z1: 1 1 0 -False False True -M, m 3 3 z0 z1; z0; z1: 2 0 1 -False False True -M, m 5 1 z0 z1; z0; z1: 2 2 0 -True False True -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [26], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :45, in __init__(self, C, list_of_fcts, branch_points, prec) - -File :196, in artin_schreier_transform(power_series, prec) - -File :12, in new_reverse(power_series, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1829 if x: - 1830 raise ValueError("must not specify %s keyword and positional argument" % name) --> 1831 a = self(kwds[name]) - 1832 del kwds[name] - 1833 try: - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1850 x = x[0] - 1851 --> 1852 return self.__u(*x)*(x[0]**self.__n) - 1853 - 1854 def __pari__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__() - 363 x[0] = a - 364 x = tuple(x) ---> 365 return self.__f(x) - 366 - 367 def _unsafe_mutate(self, i, value): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() - 896 return result - 897 pol._compiled = CompiledPolynomialFunction(pol.list()) ---> 898 return pol._compiled.eval(a) - 899 - 900 def compose_trunc(self, Polynomial other, long n): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval() - 123 cdef object temp - 124 try: ---> 125 pd_eval(self._dag, x, self._coeffs) #see further down - 126 temp = self._dag.value #for an explanation - 127 pd_clean(self._dag) #of these 3 lines - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - - [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (19 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (18 times)] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) ---> 509 self.value = self.left.value * self.right.value + coeffs[self.index] - 510 pd_clean(self.left) - 511 pd_clean(self.right) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__() - 1231 # Left and right are Sage elements => use coercion model - 1232 if BOTH_ARE_ELEMENT(cl): --> 1233 return coercion_model.bin_op(left, right, add) - 1234 - 1235 cdef long value - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op() - 1198 # Now coerce to a common parent and do the operation there - 1199 try: --> 1200 xy = self.canonical_coercion(x, y) - 1201 except TypeError: - 1202 self._record_exception() - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion() - 1313 x_elt = x - 1314 if y_map is not None: --> 1315 y_elt = (y_map)._call_(y) - 1316 else: - 1317 y_elt = y - -File /ext/sage/9.7/src/sage/categories/morphism.pyx:601, in sage.categories.morphism.SetMorphism._call_() - 599 3 - 600 """ ---> 601 return self._function(x) - 602 - 603 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:919, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_() - 917 return type(self)(self._parent, self.__u._rmul_(c), self.__n) - 918 ---> 919 cpdef _lmul_(self, Element c): - 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n) - 921 - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:920, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_() - 918 - 919 cpdef _lmul_(self, Element c): ---> 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n) - 921 - 922 def __pow__(_self, r, dummy): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:569, in sage.rings.power_series_poly.PowerSeries_poly._lmul_() - 567 2 + 6*t^4 + O(t^120) - 568 """ ---> 569 return PowerSeries_poly(self._parent, c * self.__f, self._prec, check=False) - 570 - 571 def __lshift__(PowerSeries_poly self, n): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() - 42 ValueError: series has negative valuation - 43 """ ----> 44 R = parent._poly_ring() - 45 if isinstance(f, Element): - 46 if (f)._parent is R: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) - 958 pass - 959 return False ---> 961 def _poly_ring(self): - 962 """ - 963  Return the underlying polynomial ring used to represent elements of - 964  this power series ring. - (...) - 970  Univariate Polynomial Ring in t over Integer Ring - 971  """ - 972 return self.__poly_ring - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -True False True -M, m 3 1 z0 z1; z0; z1: 1 1 0 -True False True -M, m 3 3 z0 z1; z0; z1: 2 0 1 -False False True -M, m 5 1 z0 z1; z0; z1: 2 2 0 -False False True -M, m 5 3 z0 z1; z0; z1: 3 1 1 -False False True -M, m 5 5 z0 z1; z0; z1: 3 1 2 -False False True -M, m 7 1 z0 z1; z0; z1: 3 3 0 -False False True -M, m 7 3 z0 z1; z0; z1: 4 2 1 -False False True -M, m 7 5 z0 z1; z0; z1: 4 2 2 -False False True -M, m 7 7 z0 z1; z0; z1: 5 1 3 -False False True -M, m 9 1 z0 z1; z0; z1: 4 4 0 -False False True -M, m 9 3 z0 z1; z0; z1: 5 3 1 -False False True -M, m 9 5 z0 z1; z0; z1: 5 3 2 -False False True -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [27], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :344, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :344, in (.0) - -File :131, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :131, in (.0) - -File :124, in residue(self, place) - -File :39, in expansion_at_infty(self, place) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs() - 832 else: - 833 variables.append(gen) ---> 834 return self(*variables) - 835 - 836 def numerical_approx(self, prec=None, digits=None, algorithm=None): - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__() - 447 (-2*x1*x2 + x1 + 1)/(x1 + x2) - 448 """ ---> 449 return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds) - 450 - 451 def _is_atomic(self): - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1083, in sage.rings.laurent_series_ring_element.LaurentSeries._div_() - 1081 try: - 1082 return type(self)(self._parent, --> 1083 self.__u / right.__u, - 1084 self.__n - right.__n) - 1085 except TypeError as msg: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:1091, in sage.rings.power_series_ring_element.PowerSeries._div_() - 1089 raise ZeroDivisionError("Can't divide by something indistinguishable from 0") - 1090 u = denom.valuation_zero_part() --> 1091 inv = ~u # inverse - 1092 - 1093 v = denom.valuation() - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:721, in sage.rings.power_series_poly.PowerSeries_poly.__invert__() - 719 return R(u, -self.valuation()) - 720 ---> 721 return self._parent(self.truncate().inverse_series_trunc(prec), prec=prec) - 722 - 723 def truncate(self, prec=infinity): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__() - 897 return mor._call_(x) - 898 else: ---> 899 return mor._call_with_args(x, args, kwds) - 900 - 901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {})) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:170, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args() - 168 return C._element_constructor(x) - 169 else: ---> 170 return C._element_constructor(x, **kwds) - 171 else: - 172 if len(kwds) == 0: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:700, in PowerSeriesRing_generic._element_constructor_(self, f, prec, check) - 696 if (is_PolynomialRing(S) or is_PowerSeriesRing(S)) and self.base_ring().has_coerce_map_from(S.base_ring()) \ - 697 and self.variable_names()==S.variable_names(): - 698 return True ---> 700 def _element_constructor_(self, f, prec=infinity, check=True): - 701 """ - 702  Coerce object to this power series ring. - 703 - (...) - 793 - 794  """ - 795 if prec is not infinity: - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -0 1 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -1 3 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -1 2 1 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -1 6 0 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -2 5 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -1 4 2 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -2 8 0 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -2 7 1 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -2 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -2 5 3 -M, m 9 1 z0 z1; z0; z1: 4 4 0 -2 11 0 -M, m 9 3 z0 z1; z0; z1: 5 3 1 -3 10 1 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [28], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :12, in  - -File :45, in __init__(self, C, list_of_fcts, branch_points, prec) - -File :196, in artin_schreier_transform(power_series, prec) - -File :12, in new_reverse(power_series, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1829 if x: - 1830 raise ValueError("must not specify %s keyword and positional argument" % name) --> 1831 a = self(kwds[name]) - 1832 del kwds[name] - 1833 try: - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1850 x = x[0] - 1851 --> 1852 return self.__u(*x)*(x[0]**self.__n) - 1853 - 1854 def __pari__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__() - 363 x[0] = a - 364 x = tuple(x) ---> 365 return self.__f(x) - 366 - 367 def _unsafe_mutate(self, i, value): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() - 896 return result - 897 pol._compiled = CompiledPolynomialFunction(pol.list()) ---> 898 return pol._compiled.eval(a) - 899 - 900 def compose_trunc(self, Polynomial other, long n): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval() - 123 cdef object temp - 124 try: ---> 125 pd_eval(self._dag, x, self._coeffs) #see further down - 126 temp = self._dag.value #for an explanation - 127 pd_clean(self._dag) #of these 3 lines - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - - [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (23 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (22 times)] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) ---> 509 self.value = self.left.value * self.right.value + coeffs[self.index] - 510 pd_clean(self.left) - 511 pd_clean(self.right) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__() - 1231 # Left and right are Sage elements => use coercion model - 1232 if BOTH_ARE_ELEMENT(cl): --> 1233 return coercion_model.bin_op(left, right, add) - 1234 - 1235 cdef long value - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op() - 1198 # Now coerce to a common parent and do the operation there - 1199 try: --> 1200 xy = self.canonical_coercion(x, y) - 1201 except TypeError: - 1202 self._record_exception() - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion() - 1313 x_elt = x - 1314 if y_map is not None: --> 1315 y_elt = (y_map)._call_(y) - 1316 else: - 1317 y_elt = y - -File /ext/sage/9.7/src/sage/categories/morphism.pyx:601, in sage.categories.morphism.SetMorphism._call_() - 599 3 - 600 """ ---> 601 return self._function(x) - 602 - 603 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:919, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_() - 917 return type(self)(self._parent, self.__u._rmul_(c), self.__n) - 918 ---> 919 cpdef _lmul_(self, Element c): - 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n) - 921 - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:920, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_() - 918 - 919 cpdef _lmul_(self, Element c): ---> 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n) - 921 - 922 def __pow__(_self, r, dummy): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:569, in sage.rings.power_series_poly.PowerSeries_poly._lmul_() - 567 2 + 6*t^4 + O(t^120) - 568 """ ---> 569 return PowerSeries_poly(self._parent, c * self.__f, self._prec, check=False) - 570 - 571 def __lshift__(PowerSeries_poly self, n): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() - 42 ValueError: series has negative valuation - 43 """ ----> 44 R = parent._poly_ring() - 45 if isinstance(f, Element): - 46 if (f)._parent is R: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) - 958 pass - 959 return False ---> 961 def _poly_ring(self): - 962 """ - 963  Return the underlying polynomial ring used to represent elements of - 964  this power series ring. - (...) - 970  Univariate Polynomial Ring in t over Integer Ring - 971  """ - 972 return self.__poly_ring - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -0 1 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -2 3 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -1 2 1 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -2 6 0 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -2 5 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -1 4 2 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -4 8 0 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -3 7 1 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -3 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -2 5 3 -M, m 9 1 z0 z1; z0; z1: 4 4 0 -4 11 0 -M, m 9 3 z0 z1; z0; z1: 5 3 1 -4 10 1 -M, m 9 5 z0 z1; z0; z1: 5 3 2 -3 9 2 -M, m 9 7 z0 z1; z0; z1: 6 2 3 -3 8 3 -M, m 9 9 z0 z1; z0; z1: 6 2 4 -2 7 4 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [29], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :318, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :135, in holomorphic_differentials_basis(self, threshold) - -File :10, in __init__(self, C, g) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds) - 629 except KeyError: - 630 raise TypeError("you must specify the names of the variables") ---> 632 names = normalize_names(n, names) - 634 # At this point, we have only handled the "names" keyword if it was - 635 # needed. Since we know the variable names, it would logically be - 636 # an error to specify an additional "names" keyword. However, - (...) - 639 # and we allow this for historical reasons. However, the names - 640 # must be consistent! - 641 if "names" in kwds: - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -0 1 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -1 3 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -2 2 1 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -1 6 0 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -3 5 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -3 4 2 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -2 8 0 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -3 7 1 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [30], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :344, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :344, in (.0) - -File :131, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :131, in (.0) - -File :124, in residue(self, place) - -File :39, in expansion_at_infty(self, place) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs() - 832 else: - 833 variables.append(gen) ---> 834 return self(*variables) - 835 - 836 def numerical_approx(self, prec=None, digits=None, algorithm=None): - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__() - 447 (-2*x1*x2 + x1 + 1)/(x1 + x2) - 448 """ ---> 449 return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds) - 450 - 451 def _is_atomic(self): - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1083, in sage.rings.laurent_series_ring_element.LaurentSeries._div_() - 1081 try: - 1082 return type(self)(self._parent, --> 1083 self.__u / right.__u, - 1084 self.__n - right.__n) - 1085 except TypeError as msg: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:1091, in sage.rings.power_series_ring_element.PowerSeries._div_() - 1089 raise ZeroDivisionError("Can't divide by something indistinguishable from 0") - 1090 u = denom.valuation_zero_part() --> 1091 inv = ~u # inverse - 1092 - 1093 v = denom.valuation() - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:721, in sage.rings.power_series_poly.PowerSeries_poly.__invert__() - 719 return R(u, -self.valuation()) - 720 ---> 721 return self._parent(self.truncate().inverse_series_trunc(prec), prec=prec) - 722 - 723 def truncate(self, prec=infinity): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__() - 897 return mor._call_(x) - 898 else: ---> 899 return mor._call_with_args(x, args, kwds) - 900 - 901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {})) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:170, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args() - 168 return C._element_constructor(x) - 169 else: ---> 170 return C._element_constructor(x, **kwds) - 171 else: - 172 if len(kwds) == 0: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:700, in PowerSeriesRing_generic._element_constructor_(self, f, prec, check) - 696 if (is_PolynomialRing(S) or is_PowerSeriesRing(S)) and self.base_ring().has_coerce_map_from(S.base_ring()) \ - 697 and self.variable_names()==S.variable_names(): - 698 return True ---> 700 def _element_constructor_(self, f, prec=infinity, check=True): - 701 """ - 702  Coerce object to this power series ring. - 703 - (...) - 793 - 794  """ - 795 if prec is not infinity: - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -0 1 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -3 3 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -2 2 1 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -4 6 0 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -4 5 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -3 4 2 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -7 8 0 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -6 7 1 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -6 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -5 5 3 -M, m 9 1 z0 z1; z0; z1: 4 4 0 -8 11 0 -M, m 9 3 z0 z1; z0; z1: 5 3 1 -8 10 1 -M, m 9 5 z0 z1; z0; z1: 5 3 2 -7 9 2 -M, m 9 7 z0 z1; z0; z1: 6 2 3 -7 8 3 -M, m 9 9 z0 z1; z0; z1: 6 2 4 -6 7 4 -M, m 11 1 z0 z1; z0; z1: 5 5 0 -11 13 0 -M, m 11 3 z0 z1; z0; z1: 6 4 1 -10 12 1 -M, m 11 5 z0 z1; z0; z1: 6 4 2 -10 11 2 -M, m 11 7 z0 z1; z0; z1: 7 3 3 -9 10 3 -M, m 11 9 z0 z1; z0; z1: 7 3 4 -9 9 4 -M, m 11 11 z0 z1; z0; z1: 8 2 5 -8 8 5 -M, m 13 1 z0 z1; z0; z1: 6 6 0 -12 16 0 -M, m 13 3 z0 z1; z0; z1: 7 5 1 -12 15 1 -M, m 13 5 z0 z1; z0; z1: 7 5 2 -11 14 2 -M, m 13 7 z0 z1; z0; z1: 8 4 3 -11 13 3 -M, m 13 9 z0 z1; z0; z1: 8 4 4 -10 12 4 -M, m 13 11 z0 z1; z0; z1: 9 3 5 -10 11 5 -M, m 13 13 z0 z1; z0; z1: 9 3 6 -9 10 6 -M, m 15 1 z0 z1; z0; z1: 7 7 0 -15 18 0 -M, m 15 3 z0 z1; z0; z1: 8 6 1 -14 17 1 -M, m 15 5 z0 z1; z0; z1: 8 6 2 -14 16 2 -M, m 15 7 z0 z1; z0; z1: 9 5 3 -13 15 3 -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [31], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :344, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :344, in (.0) - -File :131, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :131, in (.0) - -File :124, in residue(self, place) - -File :39, in expansion_at_infty(self, place) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs() - 832 else: - 833 variables.append(gen) ---> 834 return self(*variables) - 835 - 836 def numerical_approx(self, prec=None, digits=None, algorithm=None): - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__() - 447 (-2*x1*x2 + x1 + 1)/(x1 + x2) - 448 """ ---> 449 return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds) - 450 - 451 def _is_atomic(self): - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1083, in sage.rings.laurent_series_ring_element.LaurentSeries._div_() - 1081 try: - 1082 return type(self)(self._parent, --> 1083 self.__u / right.__u, - 1084 self.__n - right.__n) - 1085 except TypeError as msg: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:1091, in sage.rings.power_series_ring_element.PowerSeries._div_() - 1089 raise ZeroDivisionError("Can't divide by something indistinguishable from 0") - 1090 u = denom.valuation_zero_part() --> 1091 inv = ~u # inverse - 1092 - 1093 v = denom.valuation() - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:721, in sage.rings.power_series_poly.PowerSeries_poly.__invert__() - 719 return R(u, -self.valuation()) - 720 ---> 721 return self._parent(self.truncate().inverse_series_trunc(prec), prec=prec) - 722 - 723 def truncate(self, prec=infinity): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__() - 897 return mor._call_(x) - 898 else: ---> 899 return mor._call_with_args(x, args, kwds) - 900 - 901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {})) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:170, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args() - 168 return C._element_constructor(x) - 169 else: ---> 170 return C._element_constructor(x, **kwds) - 171 else: - 172 if len(kwds) == 0: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:700, in PowerSeriesRing_generic._element_constructor_(self, f, prec, check) - 696 if (is_PolynomialRing(S) or is_PowerSeriesRing(S)) and self.base_ring().has_coerce_map_from(S.base_ring()) \ - 697 and self.variable_names()==S.variable_names(): - 698 return True ---> 700 def _element_constructor_(self, f, prec=infinity, check=True): - 701 """ - 702  Coerce object to this power series ring. - 703 - (...) - 793 - 794  """ - 795 if prec is not infinity: - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -True False True -M, m 3 1 z0 z1; z0; z1: 1 1 0 -True False True -M, m 3 3 z0 z1; z0; z1: 2 0 1 -True False True -M, m 5 1 z0 z1; z0; z1: 2 2 0 -True False True -M, m 5 3 z0 z1; z0; z1: 3 1 1 -False False True -M, m 5 5 z0 z1; z0; z1: 3 1 2 -True False True -M, m 7 1 z0 z1; z0; z1: 3 3 0 -True False True -M, m 7 3 z0 z1; z0; z1: 4 2 1 -True False True -M, m 7 5 z0 z1; z0; z1: 4 2 2 -True False True -M, m 7 7 z0 z1; z0; z1: 5 1 3 -True False True -M, m 9 1 z0 z1; z0; z1: 4 4 0 -True False True -M, m 9 3 z0 z1; z0; z1: 5 3 1 -False False True -M, m 9 5 z0 z1; z0; z1: 5 3 2 -True False True -M, m 9 7 z0 z1; z0; z1: 6 2 3 -False False True -M, m 9 9 z0 z1; z0; z1: 6 2 4 -True False True -M, m 11 1 z0 z1; z0; z1: 5 5 0 -True False True -M, m 11 3 z0 z1; z0; z1: 6 4 1 -True False True -M, m 11 5 z0 z1; z0; z1: 6 4 2 -True False True -M, m 11 7 z0 z1; z0; z1: 7 3 3 -True False True -M, m 11 9 z0 z1; z0; z1: 7 3 4 -True False True -M, m 11 11 z0 z1; z0; z1: 8 2 5 -True False True -M, m 13 1 z0 z1; z0; z1: 6 6 0 -True False True -M, m 13 3 z0 z1; z0; z1: 7 5 1 -False False True -M, m 13 5 z0 z1; z0; z1: 7 5 2 -True False True -M, m 13 7 z0 z1; z0; z1: 8 4 3 -False False True -M, m 13 9 z0 z1; z0; z1: 8 4 4 -True False True -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [32], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :19, in  - -File :344, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :344, in (.0) - -File :131, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :131, in (.0) - -File :124, in residue(self, place) - -File :39, in expansion_at_infty(self, place) - -File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() - 941 5 - 942 """ ---> 943 return self.subs(in_dict,**kwds) - 944 - 945 cpdef _act_on_(self, x, bint self_on_left): - -File /ext/sage/9.7/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs() - 832 else: - 833 variables.append(gen) ---> 834 return self(*variables) - 835 - 836 def numerical_approx(self, prec=None, digits=None, algorithm=None): - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__() - 447 (-2*x1*x2 + x1 + 1)/(x1 + x2) - 448 """ ---> 449 return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds) - 450 - 451 def _is_atomic(self): - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1083, in sage.rings.laurent_series_ring_element.LaurentSeries._div_() - 1081 try: - 1082 return type(self)(self._parent, --> 1083 self.__u / right.__u, - 1084 self.__n - right.__n) - 1085 except TypeError as msg: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() - 1735 cdef int cl = classify_elements(left, right) - 1736 if HAVE_SAME_PARENT(cl): --> 1737 return (left)._div_(right) - 1738 if BOTH_ARE_ELEMENT(cl): - 1739 return coercion_model.bin_op(left, right, truediv) - -File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:1091, in sage.rings.power_series_ring_element.PowerSeries._div_() - 1089 raise ZeroDivisionError("Can't divide by something indistinguishable from 0") - 1090 u = denom.valuation_zero_part() --> 1091 inv = ~u # inverse - 1092 - 1093 v = denom.valuation() - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:721, in sage.rings.power_series_poly.PowerSeries_poly.__invert__() - 719 return R(u, -self.valuation()) - 720 ---> 721 return self._parent(self.truncate().inverse_series_trunc(prec), prec=prec) - 722 - 723 def truncate(self, prec=infinity): - -File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__() - 897 return mor._call_(x) - 898 else: ---> 899 return mor._call_with_args(x, args, kwds) - 900 - 901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {})) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:170, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args() - 168 return C._element_constructor(x) - 169 else: ---> 170 return C._element_constructor(x, **kwds) - 171 else: - 172 if len(kwds) == 0: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:700, in PowerSeriesRing_generic._element_constructor_(self, f, prec, check) - 696 if (is_PolynomialRing(S) or is_PowerSeriesRing(S)) and self.base_ring().has_coerce_map_from(S.base_ring()) \ - 697 and self.variable_names()==S.variable_names(): - 698 return True ---> 700 def _element_constructor_(self, f, prec=infinity, check=True): - 701 """ - 702  Coerce object to this power series ring. - 703 - (...) - 793 - 794  """ - 795 if prec is not infinity: - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lM, m 1 1 z0 z1; z0; z1: 0 0 0 -0 1 0 -M, m 3 1 z0 z1; z0; z1: 1 1 0 -1 3 0 -M, m 3 3 z0 z1; z0; z1: 2 0 1 -2 2 1 -M, m 5 1 z0 z1; z0; z1: 2 2 0 -2 6 0 -M, m 5 3 z0 z1; z0; z1: 3 1 1 -2 5 1 -M, m 5 5 z0 z1; z0; z1: 3 1 2 -3 4 2 -M, m 7 1 z0 z1; z0; z1: 3 3 0 -3 8 0 -M, m 7 3 z0 z1; z0; z1: 4 2 1 -4 7 1 -M, m 7 5 z0 z1; z0; z1: 4 2 2 -4 6 2 -M, m 7 7 z0 z1; z0; z1: 5 1 3 -5 5 3 -M, m 9 1 z0 z1; z0; z1: 4 4 0 -4 11 0 -M, m 9 3 z0 z1; z0; z1: 5 3 1 -4 10 1 -M, m 9 5 z0 z1; z0; z1: 5 3 2 -5 9 2 -M, m 9 7 z0 z1; z0; z1: 6 2 3 -5 8 3 -M, m 9 9 z0 z1; z0; z1: 6 2 4 -6 7 4 -M, m 11 1 z0 z1; z0; z1: 5 5 0 -5 13 0 -M, m 11 3 z0 z1; z0; z1: 6 4 1 -6 12 1 -M, m 11 5 z0 z1; z0; z1: 6 4 2 -6 11 2 -M, m 11 7 z0 z1; z0; z1: 7 3 3 -7 10 3 -M, m 11 9 z0 z1; z0; z1: 7 3 4 -7 9 4 -M, m 11 11 z0 z1; z0; z1: 8 2 5 -8 8 5 -M, m 13 1 z0 z1; z0; z1: 6 6 0 -6 16 0 -M, m 13 3 z0 z1; z0; z1: 7 5 1 -6 15 1 -M, m 13 5 z0 z1; z0; z1: 7 5 2 -7 14 2 -M, m 13 7 z0 z1; z0; z1: 8 4 3 -7 13 3 -M, m 13 9 z0 z1; z0; z1: 8 4 4 -8 12 4 -M, m 13 11 z0 z1; z0; z1: 9 3 5 -8 11 5 -M, m 13 13 z0 z1; z0; z1: 9 3 6 -9 10 6 -M, m 15 1 z0 z1; z0; z1: 7 7 0 -7 18 0 -M, m 15 3 z0 z1; z0; z1: 8 6 1 -8 17 1 -M, m 15 5 z0 z1; z0; z1: 8 6 2 -8 16 2 -M, m 15 7 z0 z1; z0; z1: 9 5 3 -9 15 3 -M, m 15 9 z0 z1; z0; z1: 9 5 4 -9 14 4 -M, m 15 11 z0 z1; z0; z1: 10 4 5 -10 13 5 -M, m 15 13 z0 z1; z0; z1: 10 4 6 -10 12 6 -M, m 15 15 z0 z1; z0; z1: 11 3 7 -11 11 7 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l3 5 2 3 -3 9 4 5 -7 9 5 6 -3 13 6 7 -7 13 7 8 -11 13 8 9 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l3 5 2 3 -3 9 4 5 -7 9 5 6 -3 13 6 7 -7 13 7 8 -11 13 8 9 -3 17 8 9 -7 17 9 10 -11 17 10 11 -15 17 11 12 -3 21 10 11 -7 21 11 12 -11 21 12 13 -15 21 13 14 -19 21 14 15 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l3 3 1 2 -3 7 3 4 -7 7 4 5 -3 11 5 6 -7 11 6 7 -11 11 7 8 -3 15 7 8 -7 15 8 9 -11 15 9 10 -15 15 10 11 -3 19 9 10 -7 19 10 11 -11 19 11 12 -15 19 12 13 -19 19 13 14 -3 23 11 12 -7 23 12 13 -11 23 13 14 -15 23 14 15 -19 23 15 16 -23 23 16 17 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l3 5 2 3 -3 9 4 5 -7 9 5 6 -3 13 6 7 -7 13 7 8 -11 13 8 9 -3 17 8 9 -7 17 9 10 -11 17 10 11 -15 17 11 12 -3 21 10 11 -7 21 11 12 -11 21 12 13 -15 21 13 14 -19 21 14 15 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTrue True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -True True -^C^C -KeyboardInterrupt - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004lTrue True -True True -False True -True True -False True -True True -True True -False True -True True -False True -True True -False True -True True -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [2], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :18, in  - -File :45, in __init__(self, C, list_of_fcts, branch_points, prec) - -File :196, in artin_schreier_transform(power_series, prec) - -File :12, in new_reverse(power_series, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1829 if x: - 1830 raise ValueError("must not specify %s keyword and positional argument" % name) --> 1831 a = self(kwds[name]) - 1832 del kwds[name] - 1833 try: - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1850 x = x[0] - 1851 --> 1852 return self.__u(*x)*(x[0]**self.__n) - 1853 - 1854 def __pari__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__() - 363 x[0] = a - 364 x = tuple(x) ---> 365 return self.__f(x) - 366 - 367 def _unsafe_mutate(self, i, value): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() - 896 return result - 897 pol._compiled = CompiledPolynomialFunction(pol.list()) ---> 898 return pol._compiled.eval(a) - 899 - 900 def compose_trunc(self, Polynomial other, long n): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval() - 123 cdef object temp - 124 try: ---> 125 pd_eval(self._dag, x, self._coeffs) #see further down - 126 temp = self._dag.value #for an explanation - 127 pd_clean(self._dag) #of these 3 lines - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - - [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (8 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (7 times)] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) ---> 509 self.value = self.left.value * self.right.value + coeffs[self.index] - 510 pd_clean(self.left) - 511 pd_clean(self.right) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__() - 1231 # Left and right are Sage elements => use coercion model - 1232 if BOTH_ARE_ELEMENT(cl): --> 1233 return coercion_model.bin_op(left, right, add) - 1234 - 1235 cdef long value - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op() - 1198 # Now coerce to a common parent and do the operation there - 1199 try: --> 1200 xy = self.canonical_coercion(x, y) - 1201 except TypeError: - 1202 self._record_exception() - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion() - 1313 x_elt = x - 1314 if y_map is not None: --> 1315 y_elt = (y_map)._call_(y) - 1316 else: - 1317 y_elt = y - -File /ext/sage/9.7/src/sage/categories/morphism.pyx:601, in sage.categories.morphism.SetMorphism._call_() - 599 3 - 600 """ ---> 601 return self._function(x) - 602 - 603 cpdef Element _call_with_args(self, x, args=(), kwds={}): - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:919, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_() - 917 return type(self)(self._parent, self.__u._rmul_(c), self.__n) - 918 ---> 919 cpdef _lmul_(self, Element c): - 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n) - 921 - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:920, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_() - 918 - 919 cpdef _lmul_(self, Element c): ---> 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n) - 921 - 922 def __pow__(_self, r, dummy): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:569, in sage.rings.power_series_poly.PowerSeries_poly._lmul_() - 567 2 + 6*t^4 + O(t^120) - 568 """ ---> 569 return PowerSeries_poly(self._parent, c * self.__f, self._prec, check=False) - 570 - 571 def __lshift__(PowerSeries_poly self, n): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() - 42 ValueError: series has negative valuation - 43 """ ----> 44 R = parent._poly_ring() - 45 if isinstance(f, Element): - 46 if (f)._parent is R: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) - 958 pass - 959 return False ---> 961 def _poly_ring(self): - 962 """ - 963  Return the underlying polynomial ring used to represent elements of - 964  this power series ring. - (...) - 970  Univariate Polynomial Ring in t over Integer Ring - 971  """ - 972 return self.__poly_ring - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 True True -3 1 True True -3 3 False True -5 1 True True -5 3 False True -5 5 True True -7 1 True True -7 3 False True -7 5 True True -7 7 False True -9 1 True True -9 3 False True -9 5 True True -9 7 False True -9 9 True True -11 1 True True -11 3 False True -11 5 True True -11 7 False True -11 9 True True -11 11 False True -13 1 True True -13 3 False True -13 5 True True -13 7 False True -13 9 True True -13 11 False True -13 13 True True -15 1 True True -15 3 False True -15 5 True True -15 7 False True -15 9 True True -15 11 False True -15 13 True True -15 15 False True -17 1 True True -17 3 False True -17 5 True True -17 7 False True -17 9 True True -17 11 False True -17 13 True True -17 15 False True -17 17 True True -19 1 True True -19 3 False True -19 5 True True -19 7 False True -19 9 True True -^C^C -KeyboardInterrupt - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l1 1 0 0 -3 1 1 1 -3 3 1 1 -5 1 2 2 -5 3 4 2 -5 5 3 3 -7 1 3 3 -7 3 3 3 -7 5 4 4 -7 7 4 4 -9 1 4 4 -9 3 6 4 -9 5 5 5 -9 7 7 5 -9 9 6 6 -11 1 5 5 -11 3 5 5 -11 5 6 6 -11 7 6 6 -11 9 7 7 -11 11 7 7 -13 1 6 6 -13 3 8 6 -13 5 7 7 -13 7 9 7 -13 9 8 8 -13 11 10 8 -13 13 9 9 -15 1 7 7 -15 3 7 7 -15 5 8 8 -15 7 8 8 -15 9 9 9 -15 11 9 9 -15 13 10 10 -15 15 10 10 -17 1 8 8 -17 3 10 8 -17 5 9 9 -17 7 11 9 -17 9 10 10 -17 11 12 10 -17 13 11 11 -17 15 13 11 -17 17 12 12 -19 1 9 9 -19 3 9 9 -19 5 10 10 -19 7 10 10 -19 9 11 11 -19 11 11 11 -19 13 12 12 -19 15 12 12 -19 17 13 13 -19 19 13 13 -21 1 10 10 -21 3 12 10 -21 5 11 11 -21 7 13 11 -21 9 12 12 -21 11 14 12 -21 13 13 13 -21 15 15 13 -21 17 14 14 -21 19 16 14 -21 21 15 15 -23 1 11 11 -23 3 11 11 -23 5 12 12 -23 7 12 12 -23 9 13 13 -23 11 13 13 -23 13 14 14 -23 15 14 14 -23 17 15 15 -23 19 15 15 -23 21 16 16 -23 23 16 16 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l5 3 4 2 -9 3 6 4 -9 7 7 5 -13 3 8 6 -13 7 9 7 -13 11 10 8 -17 3 10 8 -17 7 11 9 -17 11 12 10 -17 15 13 11 -21 3 12 10 -21 7 13 11 -21 11 14 12 -21 15 15 13 -21 19 16 14 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.branch_points[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^19 -z1^2 - z1 = x^11 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.branch_points[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() -[?7h[?12l[?25h[?2004l[?7h23 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l13 -1 + 1[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: 18 + 5 -[?7h[?12l[?25h[?2004l[?7h23 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS -[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: -z0^2 - z0 = x^19 -z1^2 - z1 = x^11 - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lz_series[?7h[?12l[?25h[?25l[?7l[0]/AS.x[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.z[0].valuation() -[?7h[?12l[?25h[?2004l[?7h-22 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0].valuation()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.expnsion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004lI haven't found all forms, only 18 of 23 ---------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [11], in () -----> 1 AS.de_rham_basis() - -File :389, in de_rham_basis(self, threshold) - -File :147, in holomorphic_differentials_basis(self, threshold) - -NameError: name 'holomorphic_differentials_basis' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7las_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [12], in () -----> 1 C - -NameError: name 'C' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: P1 -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y/C.x], prec = 200, branch_points = [(-1, 0), (1, 0)])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(C.x)^7, (C.x)^5]) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [14], in () -----> 1 AS = as_cover(P1, [(C.x)**Integer(7), (C.x)**Integer(5)]) - -NameError: name 'C' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(C.x)^7, (C.x)^5])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(C.x)^7, (C.x)^5])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x)^5])[?7h[?12l[?25h[?25l[?7lP.x)^5])[?7h[?12l[?25h[?25l[?7l1.x)^5])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x)^7, (P1.x)^5])[?7h[?12l[?25h[?25l[?7lP.x)^7, (P1.x)^5])[?7h[?12l[?25h[?25l[?7l1.x)^7, (P1.x)^5])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^7, (P1.x)^5]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^7, (P1.x)^5])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004lIncrease precision. -Increase precision. ---------------------------------------------------------------------------- -IndexError Traceback (most recent call last) -Input In [16], in () -----> 1 AS.de_rham_basis() - -File :391, in de_rham_basis(self, threshold) - -File :344, in cohomology_of_structure_sheaf_basis(self, threshold) - -File :344, in (.0) - -File :131, in serre_duality_pairing(self, fct) - -File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) - 583 return expression.sum(*args, **kwds) - 584 elif max(len(args),len(kwds)) <= 1: ---> 585 return sum(expression, *args, **kwds) - 586 else: - 587 from sage.symbolic.ring import SR - -File :131, in (.0) - -File :124, in residue(self, place) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:618, in sage.rings.laurent_series_ring_element.LaurentSeries.residue() - 616 Integer Ring - 617 """ ---> 618 return self[-1] - 619 - 620 def exponents(self): - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() - 542 return type(self)(self._parent, f, self.__n) - 543 ---> 544 return self.__u[i - self.__n] - 545 - 546 def __iter__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() - 451 return self.base_ring().zero() - 452 else: ---> 453 raise IndexError("coefficient not known") - 454 return self.__f[n] - 455 - -IndexError: coefficient not known -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^7, (P1.x)^5])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^7, (P1.x)^5], prec = 200) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^7, (P1.x)^5], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), - ( (z1) * dx, 0 ), - ( (z0) * dx, 0 ), - ( (x) * dx, 0 ), - ( (x*z1) * dx, 0 ), - ( (x^2*z1 + x*z0) * dx, 0 ), - ( (x^2) * dx, 0 ), - ( (x^3) * dx, 0 ), - ( (0) * dx, z1/x ), - ( (x^5) * dx, z0/x ), - ( (x^5*z1 + x^4 + x^3*z0) * dx, z0*z1/x ), - ( (x^2) * dx, z1/x^2 ), - ( (x^4) * dx, z0/x^2 ), - ( (x^4*z1 + x^2*z0) * dx, z0*z1/x^2 ), - ( (x^3*z1 + x^2*z1) * dx, z0*z1/x^3 ), - ( (x^2*z1 + z0) * dx, z0*z1/x^4 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^7, (P1.x)^5], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, (P1.x)^5], prec = 20)[?7h[?12l[?25h[?25l[?7l1, (P1.x)^5], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l3], prec = 20)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^1, (P1.x)^3], prec = 200) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^1, (P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), - ( (z0) * dx, 0 ), - ( (x) * dx, z1/x ), - ( (x*z0) * dx, z0*z1/x )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^1, (P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, (P1.x)^3], prec = 20)[?7h[?12l[?25h[?25l[?7l3, (P1.x)^3], prec = 20)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^3, (P1.x)^3], prec = 200) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/structure/element.pyx:1971, in sage.structure.element.Element._mod_() - 1970 try: --> 1971 python_op = (self)._mod_ - 1972 except AttributeError: - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - -AttributeError: 'InfinityRing_class_with_category' object has no attribute '__custom_name' - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [21], in () -----> 1 AS = as_cover(P1, [(P1.x)**Integer(3), (P1.x)**Integer(3)], prec = Integer(200)) - -File :45, in __init__(self, C, list_of_fcts, branch_points, prec) - -File :185, in artin_schreier_transform(power_series, prec) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1940, in sage.structure.element.Element.__mod__() - 1938 return (left)._mod_(right) - 1939 if BOTH_ARE_ELEMENT(cl): --> 1940 return coercion_model.bin_op(left, right, mod) - 1941 - 1942 try: - -File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() - 1202 self._record_exception() - 1203 else: --> 1204 return PyObject_CallObject(op, xy) - 1205 - 1206 if op is mul: - -File /ext/sage/9.7/src/sage/structure/element.pyx:1938, in sage.structure.element.Element.__mod__() - 1936 cdef int cl = classify_elements(left, right) - 1937 if HAVE_SAME_PARENT(cl): --> 1938 return (left)._mod_(right) - 1939 if BOTH_ARE_ELEMENT(cl): - 1940 return coercion_model.bin_op(left, right, mod) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1973, in sage.structure.element.Element._mod_() - 1971 python_op = (self)._mod_ - 1972 except AttributeError: --> 1973 raise bin_op_exception('%', self, other) - 1974 else: - 1975 return python_op(other) - -TypeError: unsupported operand parent(s) for %: 'The Infinity Ring' and 'The Infinity Ring' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF(x, y, z, L) = x/(z^2*x + 2) + y/(x^2*y + 2) + z/(y^2*z + 2) - 1 - L*x*y*z[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, (P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF(x, y, z, L) = x/(z^2*x + 2) + y/(x^2*y + 2) + z/(y^2*z + 2) - 1 - L*x*y*z[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: F = GF(4) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF = GF(4)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l')[?7h[?12l[?25h[?25l[?7la')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: F = GF(4, 'a') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las_cover.holomorphic_differentials_basis2 = holomorphic_differentials_basis2[?7h[?12l[?25h[?25l[?7l = de_ham_witt_lft(A[2])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: a = F.gens()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = F.gens()[0][?7h[?12l[?25h[?25l[?7lFGF(4, 'a')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, (P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^3, (P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lF = GF(4)[?7h[?12l[?25h[?25l[?7l, 'a')[?7h[?12l[?25h[?25l[?7laF.gens()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l. = PolynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(F) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(F)[?7h[?12l[?25h[?25l[?7la = F.gens()[0][?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(F)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: P1 = superelliptic(1, x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2441, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__() - 2440 try: --> 2441 right = Integer(right) - 2442 except TypeError: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__() - 657 if otmp is not None: ---> 658 set_from_Integer(self, otmp(the_integer_ring)) - 659 return - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1390, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion() - 1389 if self.degree() > 0: --> 1390 raise TypeError("cannot convert nonconstant polynomial") - 1391 return R(self.get_coeff_c(0)) - -TypeError: cannot convert nonconstant polynomial - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [26], in () -----> 1 P1 = superelliptic(Integer(1), x) - -File :20, in __init__(self, f, m) - -File :14, in __init__(self, C, g) - -File :223, in reduction(C, g) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2443, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__() - 2441 right = Integer(right) - 2442 except TypeError: --> 2443 raise TypeError("non-integral exponents not supported") - 2444 - 2445 d = self.degree() - -TypeError: non-integral exponents not supported -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1 = superelliptic(1, x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: P1 = superelliptic(x, 1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1 = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1x[?7h[?12l[?25h[?25l[?7lRx. = PoynomalRing(F)[?7h[?12l[?25h[?25l[?7la = F.gens()[0][?7h[?12l[?25h[?25l[?7lFGF(4, 'a')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, (P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7la(P1.x)^3], prec = 20)[?7h[?12l[?25h[?25l[?7l*(P1.x)^3], prec = 20)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372: -******************************************************************************** -Denominators of fraction field elements are sometimes dropped without warning. -This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. -******************************************************************************** -[?7h[( (1) * dx, 0 ), - ( ((a + 1)*z0 + z1) * dx, 0 ), - ( (x) * dx, 0 ), - ( (0) * dx, z1/x ), - ( (a*x*z0 + x*z1) * dx, z0*z1/x ), - ( (a*z0 + z1) * dx, z0*z1/x^2 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0].valuton()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0].valuation()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: AS.z[1]/AS.x^2 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [30], in () -----> 1 AS.z[Integer(1)]/AS.x**Integer(2) - -KeyError: 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x)^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.z[1]/(AS.x)^2 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [31], in () -----> 1 AS.z[Integer(1)]/(AS.x)**Integer(2) - -KeyError: 1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7lsage: AS.z -[?7h[?12l[?25h[?2004l[?7h{0: z1} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l5 3 4 2 -9 3 6 4 -9 7 7 5 -13 3 8 6 -13 7 9 7 -13 11 10 8 -17 3 10 8 -17 7 11 9 -17 11 12 10 -17 15 13 11 -21 3 12 10 -21 7 13 11 -21 11 14 12 -21 15 15 13 -21 19 16 14 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.z[?7h[?12l[?25h[?25l[?7l[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7lAS.x^2[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lP1superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1x[?7h[?12l[?25h[?25l[?7lRx. = PoynomalRing(F)[?7h[?12l[?25h[?25l[?7la = F.gens()[0][?7h[?12l[?25h[?25l[?7lFGF(4, 'a')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l, 'a')[?7h[?12l[?25h[?25l[?7laF.gens()[0][?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(F)[?7h[?12l[?25h[?25l[?7lP1 = supereliptc(1, x)[?7h[?12l[?25h[?25l[?7lsage: P1 = superelliptic(1, x) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2441, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__() - 2440 try: --> 2441 right = Integer(right) - 2442 except TypeError: - -File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__() - 657 if otmp is not None: ---> 658 set_from_Integer(self, otmp(the_integer_ring)) - 659 return - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1390, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion() - 1389 if self.degree() > 0: --> 1390 raise TypeError("cannot convert nonconstant polynomial") - 1391 return R(self.get_coeff_c(0)) - -TypeError: cannot convert nonconstant polynomial - -During handling of the above exception, another exception occurred: - -TypeError Traceback (most recent call last) -Input In [34], in () -----> 1 P1 = superelliptic(Integer(1), x) - -File :20, in __init__(self, f, m) - -File :14, in __init__(self, C, g) - -File :223, in reduction(C, g) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2443, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__() - 2441 right = Integer(right) - 2442 except TypeError: --> 2443 raise TypeError("non-integral exponents not supported") - 2444 - 2445 d = self.degree() - -TypeError: non-integral exponents not supported -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1 = superelliptic(1, x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: P1 = superelliptic(x, 1) -[?7h[?12l[?25h[?2004l'[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1 = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1x[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.z[?7h[?12l[?25h[?25l[?7l[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7lAS.x^2[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lP1superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1x[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.z[?7h[?12l[?25h[?25l[?7l[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7lsage: AS.z[1]/(AS.x)^2 -[?7h[?12l[?25h[?2004l[?7hz1/x^2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/(AS.x)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lio[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/(AS.x)^2).valuation() -[?7h[?12l[?25h[?2004l[?7h2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), - ( ((a + 1)*z0 + z1) * dx, 0 ), - ( (x) * dx, 0 ), - ( (0) * dx, z1/x ), - ( (a*x*z0 + x*z1) * dx, z0*z1/x ), - ( (a*z0 + z1) * dx, z0*z1/x^2 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lggg = [a for a in lll if a.form != 0][?7h[?12l[?25h[?25l[?7lroup_actin_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lction_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices_dR(AS) -[?7h[?12l[?25h[?2004l[?7h[ -[ 1 a + 1 0 0 0 a] [1 1 0 0 0 1] -[ 0 1 0 0 0 0] [0 1 0 0 0 0] -[ 0 0 1 0 a 0] [0 0 1 0 1 0] -[ 0 0 0 1 1 0] [0 0 0 1 a 0] -[ 0 0 0 0 1 0] [0 0 0 0 1 0] -[ 0 0 0 0 0 1], [0 0 0 0 0 1] -] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lminimize(F, [4,3,2,1], algorithm='ncg', avextol=10^(-30) , maxiter =10000 )[?7h[?12l[?25h[?25l[?7lagmathis(A, B)[?7h[?12l[?25h[?25l[?7lgmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) -[?7h[?12l[?25h[?2004l[?7h[ -RModule of dimension 3 over GF(2^2), -RModule of dimension 3 over GF(2^2) -] -{ -[ 1 a^2 a] -[ 0 1 0] -[ 0 0 1], -[ 1 1 0] -[ 0 1 0] -[ 0 0 1] -} -{ -[ 1 0 1] -[ 0 1 a] -[ 0 0 1], -[ 1 0 a] -[ 0 1 1] -[ 0 0 1] -} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) -[?7h[?12l[?25h[?2004l[?7h[ -RModule of dimension 3 over GF(2^2), -RModule of dimension 3 over GF(2^2) -] -{ -[ 1 0 a^2] -[ 0 1 1] -[ 0 0 1], -[ 1 0 a] -[ 0 1 a] -[ 0 0 1] -} -{ -[ 1 1 a] -[ 0 1 0] -[ 0 0 1], -[ 1 a^2 a^2] -[ 0 1 0] -[ 0 0 1] -} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) -[?7h[?12l[?25h[?2004l[?7h[ -RModule of dimension 3 over GF(2^2), -RModule of dimension 3 over GF(2^2) -] -{ -[ 1 0 a^2] -[ 0 1 1] -[ 0 0 1], -[ 1 0 a] -[ 0 1 a] -[ 0 0 1] -} -{ -[ 1 a^2 1] -[ 0 1 0] -[ 0 0 1], -[ 1 1 1] -[ 0 1 0] -[ 0 0 1] -} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/(AS.x)^2).valuation()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l3.[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l6))^3.kernel()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (A - identity_matrix(6))^3.kernel() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [45], in () -----> 1 (A - identity_matrix(Integer(6)))**Integer(3).kernel() - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'kernel' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - identity_matrix(6))^3.kernel()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3).kernel()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((A - identity_matrix(6))^3).kernel()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((A - identity_matrix(6))^3).kernel() -[?7h[?12l[?25h[?2004l[?7hVector space of degree 6 and dimension 6 over Finite Field in a of size 2^2 -Basis matrix: -[1 0 0 0 0 0] -[0 1 0 0 0 0] -[0 0 1 0 0 0] -[0 0 0 1 0 0] -[0 0 0 0 1 0] -[0 0 0 0 0 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((A - identity_matrix(6))^3).kernel()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).kernel()[?7h[?12l[?25h[?25l[?7l2).kernel()[?7h[?12l[?25h[?25l[?7lsage: ((A - identity_matrix(6))^2).kernel() -[?7h[?12l[?25h[?2004l[?7hVector space of degree 6 and dimension 6 over Finite Field in a of size 2^2 -Basis matrix: -[1 0 0 0 0 0] -[0 1 0 0 0 0] -[0 0 1 0 0 0] -[0 0 0 1 0 0] -[0 0 0 0 1 0] -[0 0 0 0 0 1] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) -[?7h[?12l[?25h[?2004l[?7h[ -RModule of dimension 3 over GF(2^2), -RModule of dimension 3 over GF(2^2) -] -{ -[ 1 a^2 a] -[ 0 1 0] -[ 0 0 1], -[ 1 1 a] -[ 0 1 0] -[ 0 0 1] -} -{ -[ 1 0 a^2] -[ 0 1 1] -[ 0 0 1], -[ 1 0 a] -[ 0 1 a] -[ 0 0 1] -} -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....: ^I^Ifor v2 in product(*pr): -....: ^I^I if A*v2 == v2 and B*v2 == v2: -....: ^I^I^I for v3 in product(*pr): -....: ^I^I^I^I if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....: ^I^I^I^I^I print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7lsage: import itertools -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....: ^I^Ifor v2 in product(*pr): -....: ^I^I if A*v2 == v2 and B*v2 == v2: -....: ^I^I^I for v3 in product(*pr): -....: ^I^I^I^I if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....: ^I^I^I^I^I print(v1, v2, v3) -[?7h[?12l[?25h[?2004l Input In [49] - for v2 in product(*pr): - ^ -TabError: inconsistent use of tabs and spaces in indentation - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....: ^I^Ifor v2 in product(*pr): -....: ^I^I if A*v2 == v2 and B*v2 == v2: -....: ^I^I^I for v3 in product(*pr): -....: ^I^I^I^I if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....: ^I^I^I^I^I print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7lprint(v1, 23)[?7h[?12l[?25h[?25l[?7l p -rint(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l p r -int(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l pr i -nt(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l pri n -t(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l prin t -(v1, v2, v3)[?7h[?12l[?25h[?25l[?7lprint ( -v1, v2, v3)[?7h[?12l[?25h[?25l[?7l print( v -1, v2, v3)[?7h[?12l[?25h[?25l[?7lprint(v 1 -, v2, v3)[?7h[?12l[?25h[?25l[?7l print(v1 , - v2, v3)[?7h[?12l[?25h[?25l[?7l print(v1,  -v2, v3)[?7h[?12l[?25h[?25l[?7l print(v1, v -2, v3)[?7h[?12l[?25h[?25l[?7l print(v1, v 2 -, v3)[?7h[?12l[?25h[?7h[?2004l -[1]+ Stopped sage -]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l5 3 4 2 -9 3 6 4 -9 7 7 5 -13 3 8 6 -13 7 9 7 -13 11 10 8 -17 3 10 8 -17 7 11 9 -17 11 12 10 -17 15 13 11 -21 3 12 10 -21 7 13 11 -21 11 14 12 -21 15 15 13 -21 19 16 14 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: import itertools -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....: ^I^Ifor v2 in product(*pr): -....: ^I^I if A*v2 == v2 and B*v2 == v2: -....: ^I^I^I for v3 in product(*pr): -....: ^I^I^I^I if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....: ^I^I^I^I^I print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lmagmathis(A, B) -  -  -  -  -  -  -  - [?7h[?12l[?25h[?25l[?7l((A - identity_matrix(6))^2).kernel()[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lA - identity_matrix(6)^3.kernel()[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lgroup_actionmarices_dR(AS)[?7h[?12l[?25h[?25l[?7lAS.derham_basis()[?7h[?12l[?25h[?25l[?7l(AS.z[1]/(AS.x)^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.z[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lP1superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1x[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.z[?7h[?12l[?25h[?25l[?7l[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7lAS.x^2[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lP1superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1x[?7h[?12l[?25h[?25l[?7lRx. = PoynomalRing(F)[?7h[?12l[?25h[?25l[?7la = F.gens()[0][?7h[?12l[?25h[?25l[?7lFGF(4, 'a')[?7h[?12l[?25h[?25l[?7lsage: F = GF(4, 'a') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - - - - - [?7h[?12l[?25h[?25l[?7lF = GF(4, 'a')[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7limport itertools -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....: ^I^Ifor v2 in product(*pr): -....: ^I^I if A*v2 == v2 and B*v2 == v2: -....: ^I^I^I for v3 in product(*pr): -....: ^I^I^I^I if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....: ^I^I^I^I^I print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lmagmathis(A, B) -  -  -  -  -  -  -  - [?7h[?12l[?25h[?25l[?7l((A - identity_matrix(6))^2).kernel()[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lA - identity_matrix(6)^3.kernel()[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lgroup_actionmarices_dR(AS)[?7h[?12l[?25h[?25l[?7lAS.derham_basis()[?7h[?12l[?25h[?25l[?7l(AS.z[1]/(AS.x)^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.z[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lP1superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1x[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.z[?7h[?12l[?25h[?25l[?7l[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7lAS.x^2[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lP1superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1x[?7h[?12l[?25h[?25l[?7lRx. = PoynomalRing(F)[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(F) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - - - - - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(F)[?7h[?12l[?25h[?25l[?7lF = GF(4, 'a')[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7limport itertools -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....: ^I^Ifor v2 in product(*pr): -....: ^I^I if A*v2 == v2 and B*v2 == v2: -....: ^I^I^I for v3 in product(*pr): -....: ^I^I^I^I if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....: ^I^I^I^I^I print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lmagmathis(A, B) -  -  -  -  -  -  -  - [?7h[?12l[?25h[?25l[?7l((A - identity_matrix(6))^2).kernel()[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lA - identity_matrix(6)^3.kernel()[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lgroup_actionmarices_dR(AS)[?7h[?12l[?25h[?25l[?7lAS.derham_basis()[?7h[?12l[?25h[?25l[?7l(AS.z[1]/(AS.x)^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.z[1]/(AS.x)^2[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [4], in () -----> 1 AS = as_cover(P1, [(P1.x)**Integer(3), a*(P1.x)**Integer(3)], prec = Integer(200)) - -NameError: name 'P1' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1 = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7lsage: P1 = superelliptic(x, 1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1 = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7lASas_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [6], in () -----> 1 AS = as_cover(P1, [(P1.x)**Integer(3), a*(P1.x)**Integer(3)], prec = Integer(200)) - -NameError: name 'a' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = F.gens()[0][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgens()[0][?7h[?12l[?25h[?25l[?7lsage: a = F.gens()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = F.gens()[0][?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7l,B= grup_action_matrices_dRAS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS) -[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372: -******************************************************************************** -Denominators of fraction field elements are sometimes dropped without warning. -This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. -******************************************************************************** -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: A, B -[?7h[?12l[?25h[?2004l[?7h( -[ 1 a + 1 0 0 0 a] [1 1 0 0 0 1] -[ 0 1 0 0 0 0] [0 1 0 0 0 0] -[ 0 0 1 0 a 0] [0 0 1 0 1 0] -[ 0 0 0 1 1 0] [0 0 0 1 a 0] -[ 0 0 0 0 1 0] [0 0 0 0 1 0] -[ 0 0 0 0 0 1], [0 0 0 0 0 1] -) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....:  for v2 in product(*pr): -....:  if A*v2 == v2 and B*v2 == v2: -....:  for v3 in product(*pr): -....:  if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a -....: *v1: -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: import itertools -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....:  for v2 in product(*pr): -....:  if A*v2 == v2 and B*v2 == v2: -....:  for v3 in product(*pr): -....:  if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: import itertools -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....:  for v2 in product(*pr): -....:  if A*v2 == v2 and B*v2 == v2: -....:  for v3 in product(*pr): -....:  if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7l....:  - [?7h[?12l[?25h[?25l[?7lsage: import itertools -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....:  for v2 in product(*pr): -....:  if A*v2 == v2 and B*v2 == v2: -....:  for v3 in product(*pr): -....:  if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [11], in () - 1 import itertools - 2 pr = [F for _ in range(Integer(6))] -----> 3 for v1 in product(*pr): - 4 if A*v1 == v1 and B*v1 == v1: - 5 for v2 in product(*pr): - -File /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds) - 637 from .misc_c import prod as c_prod - 638 if hasattr(expression, 'prod'): ---> 639 return expression.prod(*args, **kwds) - 640 elif len(args) <= 1: - 641 return c_prod(expression, *args) - -TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 6 were given -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools.product as product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....:  for v2 in product(*pr): -....:  if A*v2 == v2 and B*v2 == v2: -....:  for v3 in product(*pr): -....:  if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7lsage: import itertools.product as product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....:  for v2 in product(*pr): -....:  if A*v2 == v2 and B*v2 == v2: -....:  for v3 in product(*pr): -....:  if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -ModuleNotFoundError Traceback (most recent call last) -Input In [12], in () -----> 1 import itertools.product as product - 2 pr = [F for _ in range(Integer(6))] - 3 for v1 in product(*pr): - -ModuleNotFoundError: No module named 'itertools.product'; 'itertools' is not a package -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....:  for v2 in product(*pr): -....:  if A*v2 == v2 and B*v2 == v2: -....:  for v3 in product(*pr): -....:  if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*v1 == v1 and B*v1 == v1: -....:  for v2 in product(*pr): -....:  if A*v2 == v2 and B*v2 == v2: -....:  for v3 in product(*pr): -....:  if A*v3 == v3 + v2 + a^2*v1 and B*v3 == v3 + a*v2 + a*v1: -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [13], in () - 2 pr = [F for _ in range(Integer(6))] - 3 for v1 in product(*pr): -----> 4 if A*v1 == v1 and B*v1 == v1: - 5 for v2 in product(*pr): - 6 if A*v2 == v2 and B*v2 == v2: - -TypeError: can't multiply sequence by non-int of type 'sage.matrix.matrix_gf2e_dense.Matrix_gf2e_dense' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a.f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lvar('x, y, z, L')[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: v1 -[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: A*v1 -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [15], in () -----> 1 A*v1 - -TypeError: can't multiply sequence by non-int of type 'sage.matrix.matrix_gf2e_dense.Matrix_gf2e_dense' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA*v1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1[?7h[?12l[?25h[?25l[?7lev1[?7h[?12l[?25h[?25l[?7lcv1[?7h[?12l[?25h[?25l[?7ltv1[?7h[?12l[?25h[?25l[?7lov1[?7h[?12l[?25h[?25l[?7lrv1[?7h[?12l[?25h[?25l[?7l(v1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A*vector(v1) -[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + A*vector(v2) + A*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + A*vector(v2) + A*vector(v1): -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + A*vector(v2) + A*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*vector(v2) + A*vector(v1):[?7h[?12l[?25h[?25l[?7la*vector(v2) + A*vector(v1):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*vector(v1):[?7h[?12l[?25h[?25l[?7la*vector(v1):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - -forv3in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() - -forv3in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() - for v3 in product(*pr): - ifA*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -  print(v1, v2, v3) - [?7h[?12l[?25h[?25l[?7l() -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  print(v1, v2) -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  print(v1, v2) -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[] -[?7h[?12l[?25h[?25l[?7l - -ifA*vector(v1) == v1 and B*vector(v1) == v1: -forv2in product(*pr): -ifA*vector(v2) == v2 and B*vector(v2) == v2: -print(v1,v2) -forv3in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() - -ifA*vector(v1) == v1 and B*vector(v1) == v1: -forv2in product(*pr): -ifA*vector(v2) == v2 and B*vector(v2) == v2: -print(v1,v2) -forv3in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() - if A*vector(v1) == v1 and B*vector(v1) == v1: -  for v2 in product(*pr): - ifA*vector(v2) == v2 and B*vector(v2) == v2: -  print(v1, v2) -for v3 inproduct(*pr): - ifA*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -  print(v1, v2, v3) - [?7h[?12l[?25h[?25l[?7l() -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  print(v1) -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  print(v1, v2) -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l(0, 0, 0, 0, 0, 0) -(0, 0, 0, 0, 0, a) -(0, 0, 0, 0, 0, a + 1) -(0, 0, 0, 0, 0, 1) -(0, 0, 0, 0, a, 0) -(0, 0, 0, 0, a, a) -(0, 0, 0, 0, a, a + 1) -(0, 0, 0, 0, a, 1) -(0, 0, 0, 0, a + 1, 0) -(0, 0, 0, 0, a + 1, a) -(0, 0, 0, 0, a + 1, a + 1) -(0, 0, 0, 0, a + 1, 1) -(0, 0, 0, 0, 1, 0) -(0, 0, 0, 0, 1, a) -(0, 0, 0, 0, 1, a + 1) -(0, 0, 0, 0, 1, 1) -(0, 0, 0, a, 0, 0) -(0, 0, 0, a, 0, a) -(0, 0, 0, a, 0, a + 1) -(0, 0, 0, a, 0, 1) -(0, 0, 0, a, a, 0) -(0, 0, 0, a, a, a) -(0, 0, 0, a, a, a + 1) -(0, 0, 0, a, a, 1) -(0, 0, 0, a, a + 1, 0) -(0, 0, 0, a, a + 1, a) -(0, 0, 0, a, a + 1, a + 1) -(0, 0, 0, a, a + 1, 1) -(0, 0, 0, a, 1, 0) -(0, 0, 0, a, 1, a) -(0, 0, 0, a, 1, a + 1) -(0, 0, 0, a, 1, 1) -(0, 0, 0, a + 1, 0, 0) -(0, 0, 0, a + 1, 0, a) -(0, 0, 0, a + 1, 0, a + 1) -(0, 0, 0, a + 1, 0, 1) -(0, 0, 0, a + 1, a, 0) -(0, 0, 0, a + 1, a, a) -(0, 0, 0, a + 1, a, a + 1) -(0, 0, 0, a + 1, a, 1) -(0, 0, 0, a + 1, a + 1, 0) -(0, 0, 0, a + 1, a + 1, a) -(0, 0, 0, a + 1, a + 1, a + 1) -(0, 0, 0, a + 1, a + 1, 1) -(0, 0, 0, a + 1, 1, 0) -(0, 0, 0, a + 1, 1, a) -(0, 0, 0, a + 1, 1, a + 1) -(0, 0, 0, a + 1, 1, 1) -(0, 0, 0, 1, 0, 0) -(0, 0, 0, 1, 0, a) -(0, 0, 0, 1, 0, a + 1) -(0, 0, 0, 1, 0, 1) -(0, 0, 0, 1, a, 0) -(0, 0, 0, 1, a, a) -(0, 0, 0, 1, a, a + 1) -(0, 0, 0, 1, a, 1) -(0, 0, 0, 1, a + 1, 0) -(0, 0, 0, 1, a + 1, a) -(0, 0, 0, 1, a + 1, a + 1) -(0, 0, 0, 1, a + 1, 1) -(0, 0, 0, 1, 1, 0) -(0, 0, 0, 1, 1, a) -(0, 0, 0, 1, 1, a + 1) -(0, 0, 0, 1, 1, 1) -(0, 0, a, 0, 0, 0) -(0, 0, a, 0, 0, a) -(0, 0, a, 0, 0, a + 1) -(0, 0, a, 0, 0, 1) -(0, 0, a, 0, a, 0) -(0, 0, a, 0, a, a) -(0, 0, a, 0, a, a + 1) -(0, 0, a, 0, a, 1) -(0, 0, a, 0, a + 1, 0) -(0, 0, a, 0, a + 1, a) -(0, 0, a, 0, a + 1, a + 1) -(0, 0, a, 0, a + 1, 1) -(0, 0, a, 0, 1, 0) -(0, 0, a, 0, 1, a) -(0, 0, a, 0, 1, a + 1) -(0, 0, a, 0, 1, 1) -(0, 0, a, a, 0, 0) -(0, 0, a, a, 0, a) -(0, 0, a, a, 0, a + 1) -(0, 0, a, a, 0, 1) -(0, 0, a, a, a, 0) -(0, 0, a, a, a, a) -(0, 0, a, a, a, a + 1) -(0, 0, a, a, a, 1) -(0, 0, a, a, a + 1, 0) -(0, 0, a, a, a + 1, a) -(0, 0, a, a, a + 1, a + 1) -(0, 0, a, a, a + 1, 1) -(0, 0, a, a, 1, 0) -(0, 0, a, a, 1, a) -(0, 0, a, a, 1, a + 1) -(0, 0, a, a, 1, 1) -(0, 0, a, a + 1, 0, 0) -(0, 0, a, a + 1, 0, a) -(0, 0, a, a + 1, 0, a + 1) -(0, 0, a, a + 1, 0, 1) -(0, 0, a, a + 1, a, 0) -(0, 0, a, a + 1, a, a) -(0, 0, a, a + 1, a, a + 1) -(0, 0, a, a + 1, a, 1) -(0, 0, a, a + 1, a + 1, 0) -(0, 0, a, a + 1, a + 1, a) -(0, 0, a, a + 1, a + 1, a + 1) -(0, 0, a, a + 1, a + 1, 1) -(0, 0, a, a + 1, 1, 0) -(0, 0, a, a + 1, 1, a) -(0, 0, a, a + 1, 1, a + 1) -(0, 0, a, a + 1, 1, 1) -(0, 0, a, 1, 0, 0) -(0, 0, a, 1, 0, a) -(0, 0, a, 1, 0, a + 1) -(0, 0, a, 1, 0, 1) -(0, 0, a, 1, a, 0) -(0, 0, a, 1, a, a) -(0, 0, a, 1, a, a + 1) -(0, 0, a, 1, a, 1) -(0, 0, a, 1, a + 1, 0) -(0, 0, a, 1, a + 1, a) -(0, 0, a, 1, a + 1, a + 1) -(0, 0, a, 1, a + 1, 1) -(0, 0, a, 1, 1, 0) -(0, 0, a, 1, 1, a) -(0, 0, a, 1, 1, a + 1) -(0, 0, a, 1, 1, 1) -(0, 0, a + 1, 0, 0, 0) -(0, 0, a + 1, 0, 0, a) -(0, 0, a + 1, 0, 0, a + 1) -(0, 0, a + 1, 0, 0, 1) -(0, 0, a + 1, 0, a, 0) -(0, 0, a + 1, 0, a, a) -(0, 0, a + 1, 0, a, a + 1) -(0, 0, a + 1, 0, a, 1) -(0, 0, a + 1, 0, a + 1, 0) -(0, 0, a + 1, 0, a + 1, a) -(0, 0, a + 1, 0, a + 1, a + 1) -(0, 0, a + 1, 0, a + 1, 1) -(0, 0, a + 1, 0, 1, 0) -(0, 0, a + 1, 0, 1, a) -(0, 0, a + 1, 0, 1, a + 1) -(0, 0, a + 1, 0, 1, 1) -(0, 0, a + 1, a, 0, 0) -(0, 0, a + 1, a, 0, a) -(0, 0, a + 1, a, 0, a + 1) -(0, 0, a + 1, a, 0, 1) -(0, 0, a + 1, a, a, 0) -(0, 0, a + 1, a, a, a) -(0, 0, a + 1, a, a, a + 1) -(0, 0, a + 1, a, a, 1) -(0, 0, a + 1, a, a + 1, 0) -(0, 0, a + 1, a, a + 1, a) -(0, 0, a + 1, a, a + 1, a + 1) -(0, 0, a + 1, a, a + 1, 1) -(0, 0, a + 1, a, 1, 0) -(0, 0, a + 1, a, 1, a) -(0, 0, a + 1, a, 1, a + 1) -(0, 0, a + 1, a, 1, 1) -(0, 0, a + 1, a + 1, 0, 0) -(0, 0, a + 1, a + 1, 0, a) -(0, 0, a + 1, a + 1, 0, a + 1) -(0, 0, a + 1, a + 1, 0, 1) -(0, 0, a + 1, a + 1, a, 0) -(0, 0, a + 1, a + 1, a, a) -(0, 0, a + 1, a + 1, a, a + 1) -(0, 0, a + 1, a + 1, a, 1) -(0, 0, a + 1, a + 1, a + 1, 0) -(0, 0, a + 1, a + 1, a + 1, a) -(0, 0, a + 1, a + 1, a + 1, a + 1) -(0, 0, a + 1, a + 1, a + 1, 1) -(0, 0, a + 1, a + 1, 1, 0) -(0, 0, a + 1, a + 1, 1, a) -(0, 0, a + 1, a + 1, 1, a + 1) -(0, 0, a + 1, a + 1, 1, 1) -(0, 0, a + 1, 1, 0, 0) -(0, 0, a + 1, 1, 0, a) -(0, 0, a + 1, 1, 0, a + 1) -(0, 0, a + 1, 1, 0, 1) -(0, 0, a + 1, 1, a, 0) -(0, 0, a + 1, 1, a, a) -(0, 0, a + 1, 1, a, a + 1) -(0, 0, a + 1, 1, a, 1) -(0, 0, a + 1, 1, a + 1, 0) -(0, 0, a + 1, 1, a + 1, a) -(0, 0, a + 1, 1, a + 1, a + 1) -(0, 0, a + 1, 1, a + 1, 1) -(0, 0, a + 1, 1, 1, 0) -(0, 0, a + 1, 1, 1, a) -(0, 0, a + 1, 1, 1, a + 1) -(0, 0, a + 1, 1, 1, 1) -(0, 0, 1, 0, 0, 0) -(0, 0, 1, 0, 0, a) -(0, 0, 1, 0, 0, a + 1) -(0, 0, 1, 0, 0, 1) -(0, 0, 1, 0, a, 0) -(0, 0, 1, 0, a, a) -(0, 0, 1, 0, a, a + 1) -(0, 0, 1, 0, a, 1) -(0, 0, 1, 0, a + 1, 0) -(0, 0, 1, 0, a + 1, a) -(0, 0, 1, 0, a + 1, a + 1) -(0, 0, 1, 0, a + 1, 1) -(0, 0, 1, 0, 1, 0) -(0, 0, 1, 0, 1, a) -(0, 0, 1, 0, 1, a + 1) -(0, 0, 1, 0, 1, 1) -(0, 0, 1, a, 0, 0) -(0, 0, 1, a, 0, a) -(0, 0, 1, a, 0, a + 1) -(0, 0, 1, a, 0, 1) -(0, 0, 1, a, a, 0) -(0, 0, 1, a, a, a) -(0, 0, 1, a, a, a + 1) -(0, 0, 1, a, a, 1) -(0, 0, 1, a, a + 1, 0) -(0, 0, 1, a, a + 1, a) -(0, 0, 1, a, a + 1, a + 1) -(0, 0, 1, a, a + 1, 1) -(0, 0, 1, a, 1, 0) -(0, 0, 1, a, 1, a) -(0, 0, 1, a, 1, a + 1) -(0, 0, 1, a, 1, 1) -(0, 0, 1, a + 1, 0, 0) -(0, 0, 1, a + 1, 0, a) -(0, 0, 1, a + 1, 0, a + 1) -(0, 0, 1, a + 1, 0, 1) -(0, 0, 1, a + 1, a, 0) -(0, 0, 1, a + 1, a, a) -(0, 0, 1, a + 1, a, a + 1) -(0, 0, 1, a + 1, a, 1) -(0, 0, 1, a + 1, a + 1, 0) -(0, 0, 1, a + 1, a + 1, a) -(0, 0, 1, a + 1, a + 1, a + 1) -(0, 0, 1, a + 1, a + 1, 1) -(0, 0, 1, a + 1, 1, 0) -(0, 0, 1, a + 1, 1, a) -(0, 0, 1, a + 1, 1, a + 1) -(0, 0, 1, a + 1, 1, 1) -(0, 0, 1, 1, 0, 0) -(0, 0, 1, 1, 0, a) -(0, 0, 1, 1, 0, a + 1) -(0, 0, 1, 1, 0, 1) -(0, 0, 1, 1, a, 0) -(0, 0, 1, 1, a, a) -(0, 0, 1, 1, a, a + 1) -(0, 0, 1, 1, a, 1) -(0, 0, 1, 1, a + 1, 0) -(0, 0, 1, 1, a + 1, a) -(0, 0, 1, 1, a + 1, a + 1) -(0, 0, 1, 1, a + 1, 1) -(0, 0, 1, 1, 1, 0) -(0, 0, 1, 1, 1, a) -(0, 0, 1, 1, 1, a + 1) -(0, 0, 1, 1, 1, 1) -(0, a, 0, 0, 0, 0) -(0, a, 0, 0, 0, a) -(0, a, 0, 0, 0, a + 1) -(0, a, 0, 0, 0, 1) -(0, a, 0, 0, a, 0) -(0, a, 0, 0, a, a) -(0, a, 0, 0, a, a + 1) -(0, a, 0, 0, a, 1) -(0, a, 0, 0, a + 1, 0) -(0, a, 0, 0, a + 1, a) -(0, a, 0, 0, a + 1, a + 1) -(0, a, 0, 0, a + 1, 1) -(0, a, 0, 0, 1, 0) -(0, a, 0, 0, 1, a) -(0, a, 0, 0, 1, a + 1) -(0, a, 0, 0, 1, 1) -(0, a, 0, a, 0, 0) -(0, a, 0, a, 0, a) -(0, a, 0, a, 0, a + 1) -(0, a, 0, a, 0, 1) -(0, a, 0, a, a, 0) -(0, a, 0, a, a, a) -(0, a, 0, a, a, a + 1) -(0, a, 0, a, a, 1) -(0, a, 0, a, a + 1, 0) -(0, a, 0, a, a + 1, a) -(0, a, 0, a, a + 1, a + 1) -(0, a, 0, a, a + 1, 1) -(0, a, 0, a, 1, 0) -(0, a, 0, a, 1, a) -(0, a, 0, a, 1, a + 1) -(0, a, 0, a, 1, 1) -(0, a, 0, a + 1, 0, 0) -(0, a, 0, a + 1, 0, a) -(0, a, 0, a + 1, 0, a + 1) -(0, a, 0, a + 1, 0, 1) -(0, a, 0, a + 1, a, 0) -(0, a, 0, a + 1, a, a) -(0, a, 0, a + 1, a, a + 1) -(0, a, 0, a + 1, a, 1) -(0, a, 0, a + 1, a + 1, 0) -(0, a, 0, a + 1, a + 1, a) -(0, a, 0, a + 1, a + 1, a + 1) -(0, a, 0, a + 1, a + 1, 1) -(0, a, 0, a + 1, 1, 0) -(0, a, 0, a + 1, 1, a) -(0, a, 0, a + 1, 1, a + 1) -(0, a, 0, a + 1, 1, 1) -(0, a, 0, 1, 0, 0) -(0, a, 0, 1, 0, a) -(0, a, 0, 1, 0, a + 1) -(0, a, 0, 1, 0, 1) -(0, a, 0, 1, a, 0) -(0, a, 0, 1, a, a) -(0, a, 0, 1, a, a + 1) -(0, a, 0, 1, a, 1) -(0, a, 0, 1, a + 1, 0) -(0, a, 0, 1, a + 1, a) -(0, a, 0, 1, a + 1, a + 1) -(0, a, 0, 1, a + 1, 1) -(0, a, 0, 1, 1, 0) -(0, a, 0, 1, 1, a) -(0, a, 0, 1, 1, a + 1) -(0, a, 0, 1, 1, 1) -(0, a, a, 0, 0, 0) -(0, a, a, 0, 0, a) -(0, a, a, 0, 0, a + 1) -(0, a, a, 0, 0, 1) -(0, a, a, 0, a, 0) -(0, a, a, 0, a, a) -(0, a, a, 0, a, a + 1) -(0, a, a, 0, a, 1) -(0, a, a, 0, a + 1, 0) -(0, a, a, 0, a + 1, a) -(0, a, a, 0, a + 1, a + 1) -(0, a, a, 0, a + 1, 1) -(0, a, a, 0, 1, 0) -(0, a, a, 0, 1, a) -(0, a, a, 0, 1, a + 1) -(0, a, a, 0, 1, 1) -(0, a, a, a, 0, 0) -(0, a, a, a, 0, a) -(0, a, a, a, 0, a + 1) -(0, a, a, a, 0, 1) -(0, a, a, a, a, 0) -(0, a, a, a, a, a) -(0, a, a, a, a, a + 1) -(0, a, a, a, a, 1) -(0, a, a, a, a + 1, 0) -(0, a, a, a, a + 1, a) -(0, a, a, a, a + 1, a + 1) -(0, a, a, a, a + 1, 1) -(0, a, a, a, 1, 0) -(0, a, a, a, 1, a) -(0, a, a, a, 1, a + 1) -(0, a, a, a, 1, 1) -(0, a, a, a + 1, 0, 0) -(0, a, a, a + 1, 0, a) -(0, a, a, a + 1, 0, a + 1) -(0, a, a, a + 1, 0, 1) -(0, a, a, a + 1, a, 0) -(0, a, a, a + 1, a, a) -(0, a, a, a + 1, a, a + 1) -(0, a, a, a 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a, a + 1, a, 0, 0) -(0, a, a + 1, a, 0, a) -(0, a, a + 1, a, 0, a + 1) -(0, a, a + 1, a, 0, 1) -(0, a, a + 1, a, a, 0) -(0, a, a + 1, a, a, a) -(0, a, a + 1, a, a, a + 1) -(0, a, a + 1, a, a, 1) -(0, a, a + 1, a, a + 1, 0) -(0, a, a + 1, a, a + 1, a) -(0, a, a + 1, a, a + 1, a + 1) -(0, a, a + 1, a, a + 1, 1) -(0, a, a + 1, a, 1, 0) -(0, a, a + 1, a, 1, a) -(0, a, a + 1, a, 1, a + 1) -(0, a, a + 1, a, 1, 1) -(0, a, a + 1, a + 1, 0, 0) -(0, a, a + 1, a + 1, 0, a) -(0, a, a + 1, a + 1, 0, a + 1) -(0, a, a + 1, a + 1, 0, 1) -(0, a, a + 1, a + 1, a, 0) -(0, a, a + 1, a + 1, a, a) -(0, a, a + 1, a + 1, a, a + 1) -(0, a, a + 1, a + 1, a, 1) -(0, a, a + 1, a + 1, a + 1, 0) -(0, a, a + 1, a + 1, a + 1, a) -(0, a, a + 1, a + 1, a + 1, a + 1) -(0, a, a + 1, a + 1, a + 1, 1) -(0, a, a + 1, a + 1, 1, 0) -(0, a, a + 1, a + 1, 1, a) -(0, a, a + 1, a + 1, 1, a + 1) -(0, a, a + 1, a + 1, 1, 1) -(0, a, a + 1, 1, 0, 0) -(0, a, a + 1, 1, 0, a) -(0, a, a + 1, 1, 0, a + 1) -(0, a, a + 1, 1, 0, 1) -(0, a, a 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0, 0, a + 1) -(0, 1, 0, 0, 0, 1) -(0, 1, 0, 0, a, 0) -(0, 1, 0, 0, a, a) -(0, 1, 0, 0, a, a + 1) -(0, 1, 0, 0, a, 1) -(0, 1, 0, 0, a + 1, 0) -(0, 1, 0, 0, a + 1, a) -(0, 1, 0, 0, a + 1, a + 1) -(0, 1, 0, 0, a + 1, 1) -(0, 1, 0, 0, 1, 0) -(0, 1, 0, 0, 1, a) -(0, 1, 0, 0, 1, a + 1) -(0, 1, 0, 0, 1, 1) -(0, 1, 0, a, 0, 0) -(0, 1, 0, a, 0, a) -(0, 1, 0, a, 0, a + 1) -(0, 1, 0, a, 0, 1) -(0, 1, 0, a, a, 0) -(0, 1, 0, a, a, a) -(0, 1, 0, a, a, a + 1) -(0, 1, 0, a, a, 1) -(0, 1, 0, a, a + 1, 0) -(0, 1, 0, a, a + 1, a) -(0, 1, 0, a, a + 1, a + 1) -(0, 1, 0, a, a + 1, 1) -(0, 1, 0, a, 1, 0) -(0, 1, 0, a, 1, a) -(0, 1, 0, a, 1, a + 1) -(0, 1, 0, a, 1, 1) -(0, 1, 0, a + 1, 0, 0) -(0, 1, 0, a + 1, 0, a) -(0, 1, 0, a + 1, 0, a + 1) -(0, 1, 0, a + 1, 0, 1) -(0, 1, 0, a + 1, a, 0) -(0, 1, 0, a + 1, a, a) -(0, 1, 0, a + 1, a, a + 1) -(0, 1, 0, a + 1, a, 1) -(0, 1, 0, a + 1, a + 1, 0) -(0, 1, 0, a + 1, a + 1, a) -(0, 1, 0, a + 1, a + 1, a + 1) -(0, 1, 0, a + 1, a + 1, 1) -(0, 1, 0, a + 1, 1, 0) -(0, 1, 0, a + 1, 1, a) -(0, 1, 0, a + 1, 1, a + 1) -(0, 1, 0, a + 1, 1, 1) -(0, 1, 0, 1, 0, 0) -(0, 1, 0, 1, 0, a) -(0, 1, 0, 1, 0, a + 1) -(0, 1, 0, 1, 0, 1) -(0, 1, 0, 1, a, 0) -(0, 1, 0, 1, a, a) -(0, 1, 0, 1, a, a + 1) -(0, 1, 0, 1, a, 1) -(0, 1, 0, 1, a + 1, 0) -(0, 1, 0, 1, a + 1, a) -(0, 1, 0, 1, a + 1, a + 1) -(0, 1, 0, 1, a + 1, 1) -(0, 1, 0, 1, 1, 0) -(0, 1, 0, 1, 1, a) -(0, 1, 0, 1, 1, a + 1) -(0, 1, 0, 1, 1, 1) -(0, 1, a, 0, 0, 0) -(0, 1, a, 0, 0, a) -(0, 1, a, 0, 0, a + 1) -(0, 1, a, 0, 0, 1) -(0, 1, a, 0, a, 0) -(0, 1, a, 0, a, a) -(0, 1, a, 0, a, a + 1) -(0, 1, a, 0, a, 1) -(0, 1, a, 0, a + 1, 0) -(0, 1, a, 0, a + 1, a) -(0, 1, a, 0, a + 1, a + 1) -(0, 1, a, 0, a + 1, 1) -(0, 1, a, 0, 1, 0) -(0, 1, a, 0, 1, a) -(0, 1, a, 0, 1, a + 1) -(0, 1, a, 0, 1, 1) -(0, 1, a, a, 0, 0) -(0, 1, a, a, 0, a) -(0, 1, a, a, 0, a + 1) -(0, 1, a, a, 0, 1) -(0, 1, a, a, a, 0) -(0, 1, a, a, a, a) -(0, 1, a, a, a, a + 1) -(0, 1, a, a, a, 1) -(0, 1, a, a, a + 1, 0) -(0, 1, a, a, a + 1, a) -(0, 1, a, a, a + 1, a + 1) -(0, 1, a, a, a + 1, 1) -(0, 1, a, a, 1, 0) -(0, 1, a, a, 1, a) -(0, 1, a, a, 1, a + 1) -(0, 1, a, a, 1, 1) -(0, 1, a, a + 1, 0, 0) -(0, 1, a, a + 1, 0, a) -(0, 1, a, a + 1, 0, a + 1) -(0, 1, a, a + 1, 0, 1) -(0, 1, a, a + 1, a, 0) -(0, 1, a, a + 1, a, a) -(0, 1, a, a + 1, a, a + 1) -(0, 1, a, a + 1, a, 1) -(0, 1, a, a + 1, a + 1, 0) -(0, 1, a, a + 1, a + 1, a) -(0, 1, a, a + 1, a + 1, a + 1) -(0, 1, a, a + 1, a + 1, 1) -(0, 1, a, a + 1, 1, 0) -(0, 1, a, a + 1, 1, a) -(0, 1, a, a + 1, 1, a + 1) -(0, 1, a, a + 1, 1, 1) -(0, 1, a, 1, 0, 0) -(0, 1, a, 1, 0, a) -(0, 1, a, 1, 0, a + 1) -(0, 1, a, 1, 0, 1) -(0, 1, a, 1, a, 0) -(0, 1, a, 1, a, a) -(0, 1, a, 1, a, a + 1) -(0, 1, a, 1, a, 1) -(0, 1, a, 1, a + 1, 0) -(0, 1, a, 1, a + 1, a) -(0, 1, a, 1, a + 1, a + 1) -(0, 1, a, 1, a + 1, 1) -(0, 1, a, 1, 1, 0) -(0, 1, a, 1, 1, a) -(0, 1, a, 1, 1, a + 1) -(0, 1, a, 1, 1, 1) -(0, 1, a + 1, 0, 0, 0) -(0, 1, a + 1, 0, 0, a) -(0, 1, a + 1, 0, 0, a + 1) -(0, 1, a + 1, 0, 0, 1) -(0, 1, a + 1, 0, a, 0) -(0, 1, a + 1, 0, a, a) -(0, 1, a + 1, 0, a, a + 1) -(0, 1, a + 1, 0, a, 1) -(0, 1, a + 1, 0, a + 1, 0) -(0, 1, a + 1, 0, a + 1, a) -(0, 1, a + 1, 0, a + 1, a + 1) -(0, 1, a + 1, 0, a + 1, 1) -(0, 1, a + 1, 0, 1, 0) -(0, 1, a + 1, 0, 1, a) -(0, 1, a + 1, 0, 1, a + 1) -(0, 1, a + 1, 0, 1, 1) -(0, 1, a + 1, a, 0, 0) -(0, 1, a + 1, a, 0, a) -(0, 1, a + 1, a, 0, a + 1) -(0, 1, a + 1, a, 0, 1) -(0, 1, a + 1, a, a, 0) -(0, 1, a + 1, a, a, a) -(0, 1, a + 1, a, a, a + 1) -(0, 1, a + 1, a, a, 1) -(0, 1, a + 1, a, a + 1, 0) -(0, 1, a + 1, a, a + 1, a) -(0, 1, a + 1, a, a + 1, a + 1) -(0, 1, a + 1, a, a + 1, 1) -(0, 1, a + 1, a, 1, 0) -(0, 1, a + 1, a, 1, a) -(0, 1, a + 1, a, 1, a + 1) -(0, 1, a + 1, a, 1, 1) -(0, 1, a + 1, a + 1, 0, 0) -(0, 1, a + 1, a + 1, 0, a) -(0, 1, a + 1, a + 1, 0, a + 1) -(0, 1, a + 1, a + 1, 0, 1) -(0, 1, a + 1, a + 1, a, 0) -(0, 1, a + 1, a + 1, a, a) -(0, 1, a + 1, a + 1, a, a + 1) -(0, 1, a + 1, a + 1, a, 1) -(0, 1, a + 1, a + 1, a + 1, 0) -(0, 1, a + 1, a + 1, a + 1, a) -(0, 1, a + 1, a + 1, a + 1, a + 1) -(0, 1, a + 1, a + 1, a + 1, 1) -(0, 1, a + 1, a + 1, 1, 0) -(0, 1, a + 1, a + 1, 1, a) -(0, 1, a + 1, a + 1, 1, a + 1) -(0, 1, a + 1, a + 1, 1, 1) -(0, 1, a + 1, 1, 0, 0) -(0, 1, a + 1, 1, 0, a) -(0, 1, a + 1, 1, 0, a + 1) -(0, 1, a + 1, 1, 0, 1) -(0, 1, a + 1, 1, a, 0) -(0, 1, a + 1, 1, a, a) -(0, 1, a + 1, 1, a, a + 1) -(0, 1, a + 1, 1, a, 1) -(0, 1, a + 1, 1, a + 1, 0) -(0, 1, a + 1, 1, a + 1, a) -(0, 1, a + 1, 1, a + 1, a + 1) -(0, 1, a + 1, 1, a + 1, 1) -(0, 1, a + 1, 1, 1, 0) -(0, 1, a + 1, 1, 1, a) -(0, 1, a + 1, 1, 1, a + 1) -(0, 1, a + 1, 1, 1, 1) -(0, 1, 1, 0, 0, 0) -(0, 1, 1, 0, 0, a) -(0, 1, 1, 0, 0, a + 1) -(0, 1, 1, 0, 0, 1) -(0, 1, 1, 0, a, 0) -(0, 1, 1, 0, a, a) -(0, 1, 1, 0, a, a + 1) -(0, 1, 1, 0, a, 1) -(0, 1, 1, 0, a + 1, 0) -(0, 1, 1, 0, a + 1, a) -(0, 1, 1, 0, a + 1, a + 1) -(0, 1, 1, 0, a + 1, 1) -(0, 1, 1, 0, 1, 0) -(0, 1, 1, 0, 1, a) -(0, 1, 1, 0, 1, a + 1) -(0, 1, 1, 0, 1, 1) -(0, 1, 1, a, 0, 0) -(0, 1, 1, a, 0, a) -(0, 1, 1, a, 0, a + 1) -(0, 1, 1, a, 0, 1) -(0, 1, 1, a, a, 0) -(0, 1, 1, a, a, a) -(0, 1, 1, a, a, a + 1) -(0, 1, 1, a, a, 1) -(0, 1, 1, a, a + 1, 0) -(0, 1, 1, a, a + 1, a) -(0, 1, 1, a, a + 1, a + 1) -(0, 1, 1, a, a + 1, 1) -(0, 1, 1, a, 1, 0) -(0, 1, 1, a, 1, a) -(0, 1, 1, a, 1, a + 1) -(0, 1, 1, a, 1, 1) -(0, 1, 1, a + 1, 0, 0) -(0, 1, 1, a + 1, 0, a) -(0, 1, 1, a + 1, 0, a + 1) -(0, 1, 1, a + 1, 0, 1) -(0, 1, 1, a + 1, a, 0) -(0, 1, 1, a + 1, a, a) -(0, 1, 1, a + 1, a, a + 1) -(0, 1, 1, a + 1, a, 1) -(0, 1, 1, a + 1, a + 1, 0) -(0, 1, 1, a + 1, a + 1, a) -(0, 1, 1, a + 1, a + 1, a + 1) -(0, 1, 1, a + 1, a + 1, 1) -(0, 1, 1, a + 1, 1, 0) -(0, 1, 1, a + 1, 1, a) -(0, 1, 1, a + 1, 1, a + 1) -(0, 1, 1, a + 1, 1, 1) -(0, 1, 1, 1, 0, 0) -(0, 1, 1, 1, 0, a) -(0, 1, 1, 1, 0, a + 1) -(0, 1, 1, 1, 0, 1) -(0, 1, 1, 1, a, 0) -(0, 1, 1, 1, a, a) -(0, 1, 1, 1, a, a + 1) -(0, 1, 1, 1, a, 1) -(0, 1, 1, 1, a + 1, 0) -(0, 1, 1, 1, a + 1, a) -(0, 1, 1, 1, a + 1, a + 1) -(0, 1, 1, 1, a + 1, 1) -(0, 1, 1, 1, 1, 0) -(0, 1, 1, 1, 1, a) -(0, 1, 1, 1, 1, a + 1) -(0, 1, 1, 1, 1, 1) -(a, 0, 0, 0, 0, 0) -(a, 0, 0, 0, 0, a) -(a, 0, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 1) -(a, 0, 0, 0, a, 0) -(a, 0, 0, 0, a, a) -(a, 0, 0, 0, a, a + 1) -(a, 0, 0, 0, a, 1) -(a, 0, 0, 0, a + 1, 0) -(a, 0, 0, 0, a + 1, a) -(a, 0, 0, 0, a + 1, a + 1) -(a, 0, 0, 0, a + 1, 1) -(a, 0, 0, 0, 1, 0) -(a, 0, 0, 0, 1, a) -(a, 0, 0, 0, 1, a + 1) -(a, 0, 0, 0, 1, 1) -(a, 0, 0, a, 0, 0) -(a, 0, 0, a, 0, a) -(a, 0, 0, a, 0, a + 1) -(a, 0, 0, a, 0, 1) -(a, 0, 0, a, a, 0) -(a, 0, 0, a, a, a) -(a, 0, 0, a, a, a + 1) -(a, 0, 0, a, a, 1) -(a, 0, 0, a, a + 1, 0) -(a, 0, 0, a, a + 1, a) -(a, 0, 0, a, a + 1, a + 1) -(a, 0, 0, a, a + 1, 1) -(a, 0, 0, a, 1, 0) -(a, 0, 0, a, 1, a) -(a, 0, 0, a, 1, a + 1) -(a, 0, 0, a, 1, 1) -(a, 0, 0, a + 1, 0, 0) -(a, 0, 0, a + 1, 0, a) -(a, 0, 0, a + 1, 0, a + 1) -(a, 0, 0, a + 1, 0, 1) -(a, 0, 0, a + 1, a, 0) -(a, 0, 0, a + 1, a, a) -(a, 0, 0, a + 1, a, a + 1) -(a, 0, 0, a + 1, a, 1) -(a, 0, 0, a + 1, a + 1, 0) -(a, 0, 0, a + 1, a + 1, a) -(a, 0, 0, a + 1, a + 1, a + 1) -(a, 0, 0, a + 1, a + 1, 1) -(a, 0, 0, a + 1, 1, 0) -(a, 0, 0, a + 1, 1, a) -(a, 0, 0, a + 1, 1, a + 1) -(a, 0, 0, a + 1, 1, 1) -(a, 0, 0, 1, 0, 0) -(a, 0, 0, 1, 0, a) -(a, 0, 0, 1, 0, a + 1) -(a, 0, 0, 1, 0, 1) -(a, 0, 0, 1, a, 0) -(a, 0, 0, 1, a, a) -(a, 0, 0, 1, a, a + 1) -(a, 0, 0, 1, a, 1) -(a, 0, 0, 1, a + 1, 0) -(a, 0, 0, 1, a + 1, a) -(a, 0, 0, 1, a + 1, a + 1) -(a, 0, 0, 1, a + 1, 1) -(a, 0, 0, 1, 1, 0) -(a, 0, 0, 1, 1, a) -(a, 0, 0, 1, 1, a + 1) -(a, 0, 0, 1, 1, 1) -(a, 0, a, 0, 0, 0) -(a, 0, a, 0, 0, a) -(a, 0, a, 0, 0, a + 1) -(a, 0, a, 0, 0, 1) -(a, 0, a, 0, a, 0) -(a, 0, a, 0, a, a) -(a, 0, a, 0, a, a + 1) -(a, 0, a, 0, a, 1) -(a, 0, a, 0, a + 1, 0) -(a, 0, a, 0, a + 1, a) -(a, 0, a, 0, a + 1, a + 1) -(a, 0, a, 0, a + 1, 1) -(a, 0, a, 0, 1, 0) -(a, 0, a, 0, 1, a) -(a, 0, a, 0, 1, a + 1) -(a, 0, a, 0, 1, 1) -(a, 0, a, a, 0, 0) -(a, 0, a, a, 0, a) -(a, 0, a, a, 0, a + 1) -(a, 0, a, a, 0, 1) -(a, 0, a, a, a, 0) -(a, 0, a, a, a, a) -(a, 0, a, a, a, a + 1) -(a, 0, a, a, a, 1) -(a, 0, a, a, a + 1, 0) -(a, 0, a, a, a + 1, a) -(a, 0, a, a, a + 1, a + 1) -(a, 0, a, a, a + 1, 1) -(a, 0, a, a, 1, 0) -(a, 0, a, a, 1, a) -(a, 0, a, a, 1, a + 1) -(a, 0, a, a, 1, 1) -(a, 0, a, a + 1, 0, 0) -(a, 0, a, a + 1, 0, a) -(a, 0, a, a + 1, 0, a + 1) -(a, 0, a, a + 1, 0, 1) -(a, 0, a, a + 1, a, 0) -(a, 0, a, a + 1, a, a) -(a, 0, a, a + 1, a, a + 1) -(a, 0, a, a + 1, a, 1) -(a, 0, a, a + 1, a + 1, 0) -(a, 0, a, a + 1, a + 1, a) -(a, 0, a, a + 1, a + 1, a + 1) -(a, 0, a, a + 1, a + 1, 1) -(a, 0, a, a + 1, 1, 0) -(a, 0, a, a + 1, 1, a) -(a, 0, a, a + 1, 1, a + 1) -(a, 0, a, a + 1, 1, 1) -(a, 0, a, 1, 0, 0) -(a, 0, a, 1, 0, a) -(a, 0, a, 1, 0, a + 1) -(a, 0, a, 1, 0, 1) -(a, 0, a, 1, a, 0) -(a, 0, a, 1, a, a) -(a, 0, a, 1, a, a + 1) -(a, 0, a, 1, a, 1) -(a, 0, a, 1, a + 1, 0) -(a, 0, a, 1, a + 1, a) -(a, 0, a, 1, a + 1, a + 1) -(a, 0, a, 1, a + 1, 1) -(a, 0, a, 1, 1, 0) -(a, 0, a, 1, 1, a) -(a, 0, a, 1, 1, a + 1) -(a, 0, a, 1, 1, 1) -(a, 0, a + 1, 0, 0, 0) -(a, 0, a + 1, 0, 0, a) -(a, 0, a + 1, 0, 0, a + 1) -(a, 0, a + 1, 0, 0, 1) -(a, 0, a + 1, 0, a, 0) -(a, 0, a + 1, 0, a, a) -(a, 0, a + 1, 0, a, a + 1) -(a, 0, a + 1, 0, a, 1) -(a, 0, a + 1, 0, a + 1, 0) -(a, 0, a + 1, 0, a + 1, a) -(a, 0, a + 1, 0, a + 1, a + 1) -(a, 0, a + 1, 0, a + 1, 1) -(a, 0, a + 1, 0, 1, 0) -(a, 0, a + 1, 0, 1, a) -(a, 0, a + 1, 0, 1, a + 1) -(a, 0, a + 1, 0, 1, 1) -(a, 0, a + 1, a, 0, 0) -(a, 0, a + 1, a, 0, a) -(a, 0, a + 1, a, 0, a + 1) -(a, 0, a + 1, a, 0, 1) -(a, 0, a + 1, a, a, 0) -(a, 0, a + 1, a, a, a) -(a, 0, a + 1, a, a, a + 1) -(a, 0, a + 1, a, a, 1) -(a, 0, a + 1, a, a + 1, 0) -(a, 0, a + 1, a, a + 1, a) -(a, 0, a + 1, a, a + 1, a + 1) -(a, 0, a + 1, a, a + 1, 1) -(a, 0, a + 1, a, 1, 0) -(a, 0, a + 1, a, 1, a) -(a, 0, a + 1, a, 1, a + 1) -(a, 0, a + 1, a, 1, 1) -(a, 0, a + 1, a + 1, 0, 0) -(a, 0, a + 1, a + 1, 0, a) -(a, 0, a + 1, a + 1, 0, a + 1) -(a, 0, a + 1, a + 1, 0, 1) -(a, 0, a + 1, a + 1, a, 0) -(a, 0, a + 1, a + 1, a, a) -(a, 0, a + 1, a + 1, a, a + 1) -(a, 0, a + 1, a + 1, a, 1) -(a, 0, a + 1, a + 1, a + 1, 0) -(a, 0, a + 1, a + 1, a + 1, a) -(a, 0, a + 1, a + 1, a + 1, a + 1) -(a, 0, a + 1, a + 1, a + 1, 1) -(a, 0, a + 1, a + 1, 1, 0) -(a, 0, a + 1, a + 1, 1, a) -(a, 0, a + 1, a + 1, 1, a + 1) -(a, 0, a + 1, a + 1, 1, 1) -(a, 0, a + 1, 1, 0, 0) -(a, 0, a + 1, 1, 0, a) -(a, 0, a + 1, 1, 0, a + 1) -(a, 0, a + 1, 1, 0, 1) -(a, 0, a + 1, 1, a, 0) -(a, 0, a + 1, 1, a, a) -(a, 0, a + 1, 1, a, a + 1) -(a, 0, a + 1, 1, a, 1) -(a, 0, a + 1, 1, a + 1, 0) -(a, 0, a + 1, 1, a + 1, a) -(a, 0, a + 1, 1, a + 1, a + 1) -(a, 0, a + 1, 1, a + 1, 1) -(a, 0, a + 1, 1, 1, 0) -(a, 0, a + 1, 1, 1, a) -(a, 0, a + 1, 1, 1, a + 1) -(a, 0, a + 1, 1, 1, 1) -(a, 0, 1, 0, 0, 0) -(a, 0, 1, 0, 0, a) -(a, 0, 1, 0, 0, a + 1) -(a, 0, 1, 0, 0, 1) -(a, 0, 1, 0, a, 0) -(a, 0, 1, 0, a, a) -(a, 0, 1, 0, a, a + 1) -(a, 0, 1, 0, a, 1) -(a, 0, 1, 0, a + 1, 0) -(a, 0, 1, 0, a + 1, a) -(a, 0, 1, 0, a + 1, a + 1) -(a, 0, 1, 0, a + 1, 1) -(a, 0, 1, 0, 1, 0) -(a, 0, 1, 0, 1, a) -(a, 0, 1, 0, 1, a + 1) -(a, 0, 1, 0, 1, 1) -(a, 0, 1, a, 0, 0) -(a, 0, 1, a, 0, a) -(a, 0, 1, a, 0, a + 1) -(a, 0, 1, a, 0, 1) -(a, 0, 1, a, a, 0) -(a, 0, 1, a, a, a) -(a, 0, 1, a, a, a + 1) -(a, 0, 1, a, a, 1) -(a, 0, 1, a, a + 1, 0) -(a, 0, 1, a, a + 1, a) -(a, 0, 1, a, a + 1, a + 1) -(a, 0, 1, a, a + 1, 1) -(a, 0, 1, a, 1, 0) -(a, 0, 1, a, 1, a) -(a, 0, 1, a, 1, a + 1) -(a, 0, 1, a, 1, 1) -(a, 0, 1, a + 1, 0, 0) -(a, 0, 1, a + 1, 0, a) -(a, 0, 1, a + 1, 0, a + 1) -(a, 0, 1, a + 1, 0, 1) -(a, 0, 1, a + 1, a, 0) -(a, 0, 1, a + 1, a, a) -(a, 0, 1, a + 1, a, a + 1) -(a, 0, 1, a + 1, a, 1) -(a, 0, 1, a + 1, a + 1, 0) -(a, 0, 1, a + 1, a + 1, a) -(a, 0, 1, a + 1, a + 1, a + 1) -(a, 0, 1, a + 1, a + 1, 1) -(a, 0, 1, a + 1, 1, 0) -(a, 0, 1, a + 1, 1, a) -(a, 0, 1, a + 1, 1, a + 1) -(a, 0, 1, a + 1, 1, 1) -(a, 0, 1, 1, 0, 0) -(a, 0, 1, 1, 0, a) -(a, 0, 1, 1, 0, a + 1) -(a, 0, 1, 1, 0, 1) -(a, 0, 1, 1, a, 0) -(a, 0, 1, 1, a, a) -(a, 0, 1, 1, a, a + 1) -(a, 0, 1, 1, a, 1) -(a, 0, 1, 1, a + 1, 0) -(a, 0, 1, 1, a + 1, a) -(a, 0, 1, 1, a + 1, a + 1) -(a, 0, 1, 1, a + 1, 1) -(a, 0, 1, 1, 1, 0) -(a, 0, 1, 1, 1, a) -(a, 0, 1, 1, 1, a + 1) -(a, 0, 1, 1, 1, 1) -(a, a, 0, 0, 0, 0) -(a, a, 0, 0, 0, a) -(a, a, 0, 0, 0, a + 1) -(a, a, 0, 0, 0, 1) -(a, a, 0, 0, a, 0) -(a, a, 0, 0, a, a) -(a, a, 0, 0, a, a + 1) -(a, a, 0, 0, a, 1) -(a, a, 0, 0, a + 1, 0) -(a, a, 0, 0, a + 1, a) -(a, a, 0, 0, a + 1, a + 1) -(a, a, 0, 0, a + 1, 1) -(a, a, 0, 0, 1, 0) -(a, a, 0, 0, 1, a) -(a, a, 0, 0, 1, a + 1) -(a, a, 0, 0, 1, 1) -(a, a, 0, a, 0, 0) -(a, a, 0, a, 0, a) -(a, a, 0, a, 0, a + 1) -(a, a, 0, a, 0, 1) -(a, a, 0, a, a, 0) -(a, a, 0, a, a, a) -(a, a, 0, a, a, a + 1) -(a, a, 0, a, a, 1) -(a, a, 0, a, a + 1, 0) -(a, a, 0, a, a + 1, a) -(a, a, 0, a, a + 1, a + 1) -(a, a, 0, a, a + 1, 1) -(a, a, 0, a, 1, 0) -(a, a, 0, a, 1, a) -(a, a, 0, a, 1, a + 1) -(a, a, 0, a, 1, 1) -(a, a, 0, a + 1, 0, 0) -(a, a, 0, a + 1, 0, a) -(a, a, 0, a + 1, 0, a + 1) -(a, a, 0, a + 1, 0, 1) -(a, a, 0, a + 1, a, 0) -(a, a, 0, a + 1, a, a) -(a, a, 0, a + 1, a, a + 1) -(a, a, 0, a + 1, a, 1) -(a, a, 0, a + 1, a + 1, 0) -(a, a, 0, a + 1, a + 1, a) -(a, a, 0, a + 1, a + 1, a + 1) -(a, a, 0, a + 1, a + 1, 1) -(a, a, 0, a + 1, 1, 0) -(a, a, 0, a + 1, 1, a) -(a, a, 0, a + 1, 1, a + 1) -(a, a, 0, a + 1, 1, 1) -(a, a, 0, 1, 0, 0) -(a, a, 0, 1, 0, a) -(a, a, 0, 1, 0, a + 1) -(a, a, 0, 1, 0, 1) -(a, a, 0, 1, a, 0) -(a, a, 0, 1, a, a) -(a, a, 0, 1, a, a + 1) -(a, a, 0, 1, a, 1) -(a, a, 0, 1, a + 1, 0) -(a, a, 0, 1, a + 1, a) -(a, a, 0, 1, a + 1, a + 1) -(a, a, 0, 1, a + 1, 1) -(a, a, 0, 1, 1, 0) -(a, a, 0, 1, 1, a) -(a, a, 0, 1, 1, a + 1) -(a, a, 0, 1, 1, 1) -(a, a, a, 0, 0, 0) -(a, a, a, 0, 0, a) -(a, a, a, 0, 0, a + 1) -(a, a, a, 0, 0, 1) -(a, a, a, 0, a, 0) -(a, a, a, 0, a, a) -(a, a, a, 0, a, a + 1) -(a, a, a, 0, a, 1) -(a, a, a, 0, a + 1, 0) -(a, a, a, 0, a + 1, a) -(a, a, a, 0, a + 1, a + 1) -(a, a, a, 0, a + 1, 1) -(a, a, a, 0, 1, 0) -(a, a, a, 0, 1, a) -(a, a, a, 0, 1, a + 1) -(a, a, a, 0, 1, 1) -(a, a, a, a, 0, 0) -(a, a, a, a, 0, a) -(a, a, a, a, 0, a + 1) -(a, a, a, a, 0, 1) -(a, a, a, a, a, 0) -(a, a, a, a, a, a) -(a, a, a, a, a, a + 1) -(a, a, a, a, a, 1) -(a, a, a, a, a + 1, 0) -(a, a, a, a, a + 1, a) -(a, a, a, a, a + 1, a + 1) -(a, a, a, a, a + 1, 1) -(a, a, a, a, 1, 0) -(a, a, a, a, 1, a) -(a, a, a, a, 1, a + 1) -(a, a, a, a, 1, 1) -(a, a, a, a + 1, 0, 0) -(a, a, a, a + 1, 0, a) -(a, a, a, a + 1, 0, a + 1) -(a, a, a, a + 1, 0, 1) -(a, a, a, a + 1, a, 0) -(a, a, a, a + 1, a, a) -(a, a, a, a + 1, a, a + 1) -(a, a, a, a + 1, a, 1) -(a, a, a, a + 1, a + 1, 0) -(a, a, a, a + 1, a + 1, a) -(a, a, a, a + 1, a + 1, a + 1) -(a, a, a, a + 1, a + 1, 1) -(a, a, a, a + 1, 1, 0) -(a, a, a, a + 1, 1, a) -(a, a, a, a + 1, 1, a + 1) -(a, a, a, a + 1, 1, 1) -(a, a, a, 1, 0, 0) -(a, a, a, 1, 0, a) -(a, a, a, 1, 0, a + 1) -(a, a, a, 1, 0, 1) -(a, a, a, 1, a, 0) -(a, a, a, 1, a, a) -(a, a, a, 1, a, a + 1) -(a, a, a, 1, a, 1) -(a, a, a, 1, a + 1, 0) -(a, a, a, 1, a + 1, a) -(a, a, a, 1, a + 1, a + 1) -(a, a, a, 1, a + 1, 1) -(a, a, a, 1, 1, 0) -(a, a, a, 1, 1, a) -(a, a, a, 1, 1, a + 1) -(a, a, a, 1, 1, 1) -(a, a, a + 1, 0, 0, 0) -(a, a, a + 1, 0, 0, a) -(a, a, a + 1, 0, 0, a + 1) -(a, a, a + 1, 0, 0, 1) -(a, a, a + 1, 0, a, 0) -(a, a, a + 1, 0, a, a) -(a, a, a + 1, 0, a, a + 1) -(a, a, a + 1, 0, a, 1) -(a, a, a + 1, 0, a + 1, 0) -(a, a, a + 1, 0, a + 1, a) -(a, a, a + 1, 0, a + 1, a + 1) -(a, a, a + 1, 0, a + 1, 1) -(a, a, a + 1, 0, 1, 0) -(a, a, a + 1, 0, 1, a) -(a, a, a + 1, 0, 1, a + 1) -(a, a, a + 1, 0, 1, 1) -(a, a, a + 1, a, 0, 0) -(a, a, a + 1, a, 0, a) -(a, a, a + 1, a, 0, a + 1) -(a, a, a + 1, a, 0, 1) -(a, a, a + 1, a, a, 0) -(a, a, a + 1, a, a, a) -(a, a, a + 1, a, a, a + 1) -(a, a, a + 1, a, a, 1) -(a, a, a + 1, a, a + 1, 0) -(a, a, a + 1, a, a + 1, a) -(a, a, a + 1, a, a + 1, a + 1) -(a, a, a + 1, a, a + 1, 1) -(a, a, a + 1, a, 1, 0) -(a, a, a + 1, a, 1, a) -(a, a, a + 1, a, 1, a + 1) -(a, a, a + 1, a, 1, 1) -(a, a, a + 1, a + 1, 0, 0) -(a, a, a + 1, a + 1, 0, a) -(a, a, a + 1, a + 1, 0, a + 1) -(a, a, a + 1, a + 1, 0, 1) -(a, a, a + 1, a + 1, a, 0) -(a, a, a + 1, a + 1, a, a) -(a, a, a + 1, a + 1, a, a + 1) -(a, a, a + 1, a + 1, a, 1) -(a, a, a + 1, a + 1, a + 1, 0) -(a, a, a + 1, a + 1, a + 1, a) -(a, a, a + 1, a + 1, a + 1, a + 1) -(a, a, a + 1, a + 1, a + 1, 1) -(a, a, a + 1, a + 1, 1, 0) -(a, a, a + 1, a + 1, 1, a) -(a, a, a + 1, a + 1, 1, a + 1) -(a, a, a + 1, a + 1, 1, 1) -(a, a, a + 1, 1, 0, 0) -(a, a, a + 1, 1, 0, a) -(a, a, a + 1, 1, 0, a + 1) -(a, a, a + 1, 1, 0, 1) -(a, a, a + 1, 1, a, 0) -(a, a, a + 1, 1, a, a) -(a, a, a + 1, 1, a, a + 1) -(a, a, a + 1, 1, a, 1) -(a, a, a + 1, 1, a + 1, 0) -(a, a, a + 1, 1, a + 1, a) -(a, a, a + 1, 1, a + 1, a + 1) -(a, a, a + 1, 1, a + 1, 1) -(a, a, a + 1, 1, 1, 0) -(a, a, a + 1, 1, 1, a) -(a, a, a + 1, 1, 1, a + 1) -(a, a, a + 1, 1, 1, 1) -(a, a, 1, 0, 0, 0) -(a, a, 1, 0, 0, a) -(a, a, 1, 0, 0, a + 1) -(a, a, 1, 0, 0, 1) -(a, a, 1, 0, a, 0) -(a, a, 1, 0, a, a) -(a, a, 1, 0, a, a + 1) -(a, a, 1, 0, a, 1) -(a, a, 1, 0, a + 1, 0) -(a, a, 1, 0, a + 1, a) -(a, a, 1, 0, a + 1, a + 1) -(a, a, 1, 0, a + 1, 1) -(a, a, 1, 0, 1, 0) -(a, a, 1, 0, 1, a) -(a, a, 1, 0, 1, a + 1) -(a, a, 1, 0, 1, 1) -(a, a, 1, a, 0, 0) -(a, a, 1, a, 0, a) -(a, a, 1, a, 0, a + 1) -(a, a, 1, a, 0, 1) -(a, a, 1, a, a, 0) -(a, a, 1, a, a, a) -(a, a, 1, a, a, a + 1) -(a, a, 1, a, a, 1) -(a, a, 1, a, a + 1, 0) -(a, a, 1, a, a + 1, a) -(a, a, 1, a, a + 1, a + 1) -(a, a, 1, a, a + 1, 1) -(a, a, 1, a, 1, 0) -(a, a, 1, a, 1, a) -(a, a, 1, a, 1, a + 1) -(a, a, 1, a, 1, 1) -(a, a, 1, a + 1, 0, 0) -(a, a, 1, a + 1, 0, a) -(a, a, 1, a + 1, 0, a + 1) -(a, a, 1, a + 1, 0, 1) -(a, a, 1, a + 1, a, 0) -(a, a, 1, a + 1, a, a) -(a, a, 1, a + 1, a, a + 1) -(a, a, 1, a + 1, a, 1) -(a, a, 1, a + 1, a + 1, 0) -(a, a, 1, a + 1, a + 1, a) -(a, a, 1, a + 1, a + 1, a + 1) -(a, a, 1, a + 1, a + 1, 1) -(a, a, 1, a + 1, 1, 0) -(a, a, 1, a + 1, 1, a) -(a, a, 1, a + 1, 1, a + 1) -(a, a, 1, a + 1, 1, 1) -(a, a, 1, 1, 0, 0) -(a, a, 1, 1, 0, a) -(a, a, 1, 1, 0, a + 1) -(a, a, 1, 1, 0, 1) -(a, a, 1, 1, a, 0) -(a, a, 1, 1, a, a) -(a, a, 1, 1, a, a + 1) -(a, a, 1, 1, a, 1) -(a, a, 1, 1, a + 1, 0) -(a, a, 1, 1, a + 1, a) -(a, a, 1, 1, a + 1, a + 1) -(a, a, 1, 1, a + 1, 1) -(a, a, 1, 1, 1, 0) -(a, a, 1, 1, 1, a) -(a, a, 1, 1, 1, a + 1) -(a, a, 1, 1, 1, 1) -(a, a + 1, 0, 0, 0, 0) -(a, a + 1, 0, 0, 0, a) -(a, a + 1, 0, 0, 0, a + 1) -(a, a + 1, 0, 0, 0, 1) -(a, a + 1, 0, 0, a, 0) -(a, a + 1, 0, 0, a, a) -(a, a + 1, 0, 0, a, a + 1) -(a, a + 1, 0, 0, a, 1) -(a, a + 1, 0, 0, a + 1, 0) -(a, a + 1, 0, 0, a + 1, a) -(a, a + 1, 0, 0, a + 1, a + 1) -(a, a + 1, 0, 0, a + 1, 1) -(a, a + 1, 0, 0, 1, 0) -(a, a + 1, 0, 0, 1, a) -(a, a + 1, 0, 0, 1, a + 1) -(a, a + 1, 0, 0, 1, 1) -(a, a + 1, 0, a, 0, 0) -(a, a + 1, 0, a, 0, a) -(a, a + 1, 0, a, 0, a + 1) -(a, a + 1, 0, a, 0, 1) -(a, a + 1, 0, a, a, 0) -(a, a + 1, 0, a, a, a) -(a, a + 1, 0, a, a, a + 1) -(a, a + 1, 0, a, a, 1) -(a, a + 1, 0, a, a + 1, 0) -(a, a + 1, 0, a, a + 1, a) -(a, a + 1, 0, a, a + 1, a + 1) -(a, a + 1, 0, a, a + 1, 1) -(a, a + 1, 0, a, 1, 0) -(a, a + 1, 0, a, 1, a) -(a, a + 1, 0, a, 1, a + 1) -(a, a + 1, 0, a, 1, 1) -(a, a + 1, 0, a + 1, 0, 0) -(a, a + 1, 0, a + 1, 0, a) -(a, a + 1, 0, a + 1, 0, a + 1) -(a, a + 1, 0, a + 1, 0, 1) -(a, a + 1, 0, a + 1, a, 0) -(a, a + 1, 0, a + 1, a, a) -(a, a + 1, 0, a + 1, a, a + 1) -(a, a + 1, 0, a + 1, a, 1) -(a, a + 1, 0, a + 1, a + 1, 0) -(a, a + 1, 0, a + 1, a + 1, a) -(a, a + 1, 0, a + 1, a + 1, a + 1) -(a, a + 1, 0, a + 1, a + 1, 1) -(a, a + 1, 0, a + 1, 1, 0) -(a, a + 1, 0, a + 1, 1, a) -(a, a + 1, 0, a + 1, 1, a + 1) -(a, a + 1, 0, a + 1, 1, 1) -(a, a + 1, 0, 1, 0, 0) -(a, a + 1, 0, 1, 0, a) -(a, a + 1, 0, 1, 0, a + 1) -(a, a + 1, 0, 1, 0, 1) -(a, a + 1, 0, 1, a, 0) -(a, a + 1, 0, 1, a, a) -(a, a + 1, 0, 1, a, a + 1) -(a, a + 1, 0, 1, a, 1) -(a, a + 1, 0, 1, a + 1, 0) -(a, a + 1, 0, 1, a + 1, a) -(a, a + 1, 0, 1, a + 1, a + 1) -(a, a + 1, 0, 1, a + 1, 1) -(a, a + 1, 0, 1, 1, 0) -(a, a + 1, 0, 1, 1, a) -(a, a + 1, 0, 1, 1, a + 1) -(a, a + 1, 0, 1, 1, 1) -(a, a + 1, a, 0, 0, 0) -(a, a + 1, a, 0, 0, a) -(a, a + 1, a, 0, 0, a + 1) -(a, a + 1, a, 0, 0, 1) -(a, a + 1, a, 0, a, 0) -(a, a + 1, a, 0, a, a) -(a, a + 1, a, 0, a, a + 1) -(a, a + 1, a, 0, a, 1) -(a, a + 1, a, 0, a + 1, 0) -(a, a + 1, a, 0, a + 1, a) -(a, a + 1, a, 0, a + 1, a + 1) -(a, a + 1, a, 0, a + 1, 1) -(a, a + 1, a, 0, 1, 0) -(a, a + 1, a, 0, 1, a) -(a, a + 1, a, 0, 1, a + 1) -(a, a + 1, a, 0, 1, 1) -(a, a + 1, a, a, 0, 0) -(a, a + 1, a, a, 0, a) -(a, a + 1, a, a, 0, a + 1) -(a, a + 1, a, a, 0, 1) -(a, a + 1, a, a, a, 0) -(a, a + 1, a, a, a, a) -(a, a + 1, a, a, a, a + 1) -(a, a + 1, a, a, a, 1) -(a, a + 1, a, a, a + 1, 0) -(a, a + 1, a, a, a + 1, a) -(a, a + 1, a, a, a + 1, a + 1) -(a, a + 1, a, a, a + 1, 1) -(a, a + 1, a, a, 1, 0) -(a, a + 1, a, a, 1, a) -(a, a + 1, a, a, 1, a + 1) -(a, a + 1, a, a, 1, 1) -(a, a + 1, a, a + 1, 0, 0) -(a, a + 1, a, a + 1, 0, a) -(a, a + 1, a, a + 1, 0, a + 1) -(a, a + 1, a, a + 1, 0, 1) -(a, a + 1, a, a + 1, a, 0) -(a, a + 1, a, a + 1, a, a) -(a, a + 1, a, a + 1, a, a + 1) -(a, a + 1, a, a + 1, a, 1) -(a, a + 1, a, a + 1, a + 1, 0) -(a, a + 1, a, a + 1, a + 1, a) -(a, a + 1, a, a + 1, a + 1, a + 1) -(a, a + 1, a, a + 1, a + 1, 1) -(a, a + 1, a, a + 1, 1, 0) -(a, a + 1, a, a + 1, 1, a) -(a, a + 1, a, a + 1, 1, a + 1) -(a, a + 1, a, a + 1, 1, 1) -(a, a + 1, a, 1, 0, 0) -(a, a + 1, a, 1, 0, a) -(a, a + 1, a, 1, 0, a + 1) -(a, a + 1, a, 1, 0, 1) -(a, a + 1, a, 1, a, 0) -(a, a + 1, a, 1, a, a) -(a, a + 1, a, 1, a, a + 1) -(a, a + 1, a, 1, a, 1) -(a, a + 1, a, 1, a + 1, 0) -(a, a + 1, a, 1, a + 1, a) -(a, a + 1, a, 1, a + 1, a + 1) -(a, a + 1, a, 1, a + 1, 1) -(a, a + 1, a, 1, 1, 0) -(a, a + 1, a, 1, 1, a) -(a, a + 1, a, 1, 1, a + 1) -(a, a + 1, a, 1, 1, 1) -(a, a + 1, a + 1, 0, 0, 0) -(a, a + 1, a + 1, 0, 0, a) -(a, a + 1, a + 1, 0, 0, a + 1) -(a, a + 1, a + 1, 0, 0, 1) -(a, a + 1, a + 1, 0, a, 0) -(a, a + 1, a + 1, 0, a, a) -(a, a + 1, a + 1, 0, a, a + 1) -(a, a + 1, a + 1, 0, a, 1) -(a, a + 1, a + 1, 0, a + 1, 0) -(a, a + 1, a + 1, 0, a + 1, a) -(a, a + 1, a + 1, 0, a + 1, a + 1) -(a, a + 1, a + 1, 0, a + 1, 1) -(a, a + 1, a + 1, 0, 1, 0) -(a, a + 1, a + 1, 0, 1, a) -(a, a + 1, a + 1, 0, 1, a + 1) -(a, a + 1, a + 1, 0, 1, 1) -(a, a + 1, a + 1, a, 0, 0) -(a, a + 1, a + 1, a, 0, a) -(a, a + 1, a + 1, a, 0, a + 1) -(a, a + 1, a + 1, a, 0, 1) -(a, a + 1, a + 1, a, a, 0) -(a, a + 1, a + 1, a, a, a) -(a, a + 1, a + 1, a, a, a + 1) -(a, a + 1, a + 1, a, a, 1) -(a, a + 1, a + 1, a, a + 1, 0) -(a, a + 1, a + 1, a, a + 1, a) -(a, a + 1, a + 1, a, a + 1, a + 1) -(a, a + 1, a + 1, a, a + 1, 1) -(a, a + 1, a + 1, a, 1, 0) -(a, a + 1, a + 1, a, 1, a) -(a, a + 1, a + 1, a, 1, a + 1) -(a, a + 1, a + 1, a, 1, 1) -(a, a + 1, a + 1, a + 1, 0, 0) -(a, a + 1, a + 1, a + 1, 0, a) -(a, a + 1, a + 1, a + 1, 0, a + 1) -(a, a + 1, a + 1, a + 1, 0, 1) -(a, a + 1, a + 1, a + 1, a, 0) -(a, a + 1, a + 1, a + 1, a, a) -(a, a + 1, a + 1, a + 1, a, a + 1) -(a, a + 1, a + 1, a + 1, a, 1) -(a, a + 1, a + 1, a + 1, a + 1, 0) -(a, a + 1, a + 1, a + 1, a + 1, a) -(a, a + 1, a + 1, a + 1, a + 1, a + 1) -(a, a + 1, a + 1, a + 1, a + 1, 1) -(a, a + 1, a + 1, a + 1, 1, 0) -(a, a + 1, a + 1, a + 1, 1, a) -(a, a + 1, a + 1, a + 1, 1, a + 1) -(a, a + 1, a + 1, a + 1, 1, 1) -(a, a + 1, a + 1, 1, 0, 0) -(a, a + 1, a + 1, 1, 0, a) -(a, a + 1, a + 1, 1, 0, a + 1) -(a, a + 1, a + 1, 1, 0, 1) -(a, a + 1, a + 1, 1, a, 0) -(a, a + 1, a + 1, 1, a, a) -(a, a + 1, a + 1, 1, a, a + 1) -(a, a + 1, a + 1, 1, a, 1) -(a, a + 1, a + 1, 1, a + 1, 0) -(a, a + 1, a + 1, 1, a + 1, a) -(a, a + 1, a + 1, 1, a + 1, a + 1) -(a, a + 1, a + 1, 1, a + 1, 1) -(a, a + 1, a + 1, 1, 1, 0) -(a, a + 1, a + 1, 1, 1, a) -(a, a + 1, a + 1, 1, 1, a + 1) -(a, a + 1, a + 1, 1, 1, 1) -(a, a + 1, 1, 0, 0, 0) -(a, a + 1, 1, 0, 0, a) -(a, a + 1, 1, 0, 0, a + 1) -(a, a + 1, 1, 0, 0, 1) -(a, a + 1, 1, 0, a, 0) -(a, a + 1, 1, 0, a, a) -(a, a + 1, 1, 0, a, a + 1) -(a, a + 1, 1, 0, a, 1) -(a, a + 1, 1, 0, a + 1, 0) -(a, a + 1, 1, 0, a + 1, a) -(a, a + 1, 1, 0, a + 1, a + 1) -(a, a + 1, 1, 0, a + 1, 1) -(a, a + 1, 1, 0, 1, 0) -(a, a + 1, 1, 0, 1, a) -(a, a + 1, 1, 0, 1, a + 1) -(a, a + 1, 1, 0, 1, 1) -(a, a + 1, 1, a, 0, 0) -(a, a + 1, 1, a, 0, a) -(a, a + 1, 1, a, 0, a + 1) -(a, a + 1, 1, a, 0, 1) -(a, a + 1, 1, a, a, 0) -(a, a + 1, 1, a, a, a) -(a, a + 1, 1, a, a, a + 1) -(a, a + 1, 1, a, a, 1) -(a, a + 1, 1, a, a + 1, 0) -(a, a + 1, 1, a, a + 1, a) -(a, a + 1, 1, a, a + 1, a + 1) -(a, a + 1, 1, a, a + 1, 1) -(a, a + 1, 1, a, 1, 0) -(a, a + 1, 1, a, 1, a) -(a, a + 1, 1, a, 1, a + 1) -(a, a + 1, 1, a, 1, 1) -(a, a + 1, 1, a + 1, 0, 0) -(a, a + 1, 1, a + 1, 0, a) -(a, a + 1, 1, a + 1, 0, a + 1) -(a, a + 1, 1, a + 1, 0, 1) -(a, a + 1, 1, a + 1, a, 0) -(a, a + 1, 1, a + 1, a, a) -(a, a + 1, 1, a + 1, a, a + 1) -(a, a + 1, 1, a + 1, a, 1) -(a, a + 1, 1, a + 1, a + 1, 0) -(a, a + 1, 1, a + 1, a + 1, a) -(a, a + 1, 1, a + 1, a + 1, a + 1) -(a, a + 1, 1, a + 1, a + 1, 1) -(a, a + 1, 1, a + 1, 1, 0) -(a, a + 1, 1, a + 1, 1, a) -(a, a + 1, 1, a + 1, 1, a + 1) -(a, a + 1, 1, a + 1, 1, 1) -(a, a + 1, 1, 1, 0, 0) -(a, a + 1, 1, 1, 0, a) -(a, a + 1, 1, 1, 0, a + 1) -(a, a + 1, 1, 1, 0, 1) -(a, a + 1, 1, 1, a, 0) -(a, a + 1, 1, 1, a, a) -(a, a + 1, 1, 1, a, a + 1) -(a, a + 1, 1, 1, a, 1) -(a, a + 1, 1, 1, a + 1, 0) -(a, a + 1, 1, 1, a + 1, a) -(a, a + 1, 1, 1, a + 1, a + 1) -(a, a + 1, 1, 1, a + 1, 1) -(a, a + 1, 1, 1, 1, 0) -(a, a + 1, 1, 1, 1, a) -(a, a + 1, 1, 1, 1, a + 1) -(a, a + 1, 1, 1, 1, 1) -(a, 1, 0, 0, 0, 0) -(a, 1, 0, 0, 0, a) -(a, 1, 0, 0, 0, a + 1) -(a, 1, 0, 0, 0, 1) -(a, 1, 0, 0, a, 0) -(a, 1, 0, 0, a, a) -(a, 1, 0, 0, a, a + 1) -(a, 1, 0, 0, a, 1) -(a, 1, 0, 0, a + 1, 0) -(a, 1, 0, 0, a + 1, a) -(a, 1, 0, 0, a + 1, a + 1) -(a, 1, 0, 0, a + 1, 1) -(a, 1, 0, 0, 1, 0) -(a, 1, 0, 0, 1, a) -(a, 1, 0, 0, 1, a + 1) -(a, 1, 0, 0, 1, 1) -(a, 1, 0, a, 0, 0) -(a, 1, 0, a, 0, a) -(a, 1, 0, a, 0, a + 1) -(a, 1, 0, a, 0, 1) -(a, 1, 0, a, a, 0) -(a, 1, 0, a, a, a) -(a, 1, 0, a, a, a + 1) -(a, 1, 0, a, a, 1) -(a, 1, 0, a, a + 1, 0) -(a, 1, 0, a, a + 1, a) -(a, 1, 0, a, a + 1, a + 1) -(a, 1, 0, a, a + 1, 1) -(a, 1, 0, a, 1, 0) -(a, 1, 0, a, 1, a) -(a, 1, 0, a, 1, a + 1) -(a, 1, 0, a, 1, 1) -(a, 1, 0, a + 1, 0, 0) -(a, 1, 0, a + 1, 0, a) -(a, 1, 0, a + 1, 0, a + 1) -(a, 1, 0, a + 1, 0, 1) -(a, 1, 0, a + 1, a, 0) -(a, 1, 0, a + 1, a, a) -(a, 1, 0, a + 1, a, a + 1) -(a, 1, 0, a + 1, a, 1) -(a, 1, 0, a + 1, a + 1, 0) -(a, 1, 0, a + 1, a + 1, a) -(a, 1, 0, a + 1, a + 1, a + 1) -(a, 1, 0, a + 1, a + 1, 1) -(a, 1, 0, a + 1, 1, 0) -(a, 1, 0, a + 1, 1, a) -(a, 1, 0, a + 1, 1, a + 1) -(a, 1, 0, a + 1, 1, 1) -(a, 1, 0, 1, 0, 0) -(a, 1, 0, 1, 0, a) -(a, 1, 0, 1, 0, a + 1) -(a, 1, 0, 1, 0, 1) -(a, 1, 0, 1, a, 0) -(a, 1, 0, 1, a, a) -(a, 1, 0, 1, a, a + 1) -(a, 1, 0, 1, a, 1) -(a, 1, 0, 1, a + 1, 0) -(a, 1, 0, 1, a + 1, a) -(a, 1, 0, 1, a + 1, a + 1) -(a, 1, 0, 1, a + 1, 1) -(a, 1, 0, 1, 1, 0) -(a, 1, 0, 1, 1, a) -(a, 1, 0, 1, 1, a + 1) -(a, 1, 0, 1, 1, 1) -(a, 1, a, 0, 0, 0) -(a, 1, a, 0, 0, a) -(a, 1, a, 0, 0, a + 1) -(a, 1, a, 0, 0, 1) -(a, 1, a, 0, a, 0) -(a, 1, a, 0, a, a) -(a, 1, a, 0, a, a + 1) -(a, 1, a, 0, a, 1) -(a, 1, a, 0, a + 1, 0) -(a, 1, a, 0, a + 1, a) -(a, 1, a, 0, a + 1, a + 1) -(a, 1, a, 0, a + 1, 1) -(a, 1, a, 0, 1, 0) -(a, 1, a, 0, 1, a) -(a, 1, a, 0, 1, a + 1) -(a, 1, a, 0, 1, 1) -(a, 1, a, a, 0, 0) -(a, 1, a, a, 0, a) -(a, 1, a, a, 0, a + 1) -(a, 1, a, a, 0, 1) -(a, 1, a, a, a, 0) -(a, 1, a, a, a, a) -(a, 1, a, a, a, a + 1) -(a, 1, a, a, a, 1) -(a, 1, a, a, a + 1, 0) -(a, 1, a, a, a + 1, a) -(a, 1, a, a, a + 1, a + 1) -(a, 1, a, a, a + 1, 1) -(a, 1, a, a, 1, 0) -(a, 1, a, a, 1, a) -(a, 1, a, a, 1, a + 1) -(a, 1, a, a, 1, 1) -(a, 1, a, a + 1, 0, 0) -(a, 1, a, a + 1, 0, a) -(a, 1, a, a + 1, 0, a + 1) -(a, 1, a, a + 1, 0, 1) -(a, 1, a, a + 1, a, 0) -(a, 1, a, a + 1, a, a) -(a, 1, a, a + 1, a, a + 1) -(a, 1, a, a + 1, a, 1) -(a, 1, a, a + 1, a + 1, 0) -(a, 1, a, a + 1, a + 1, a) -(a, 1, a, a + 1, a + 1, a + 1) -(a, 1, a, a + 1, a + 1, 1) -(a, 1, a, a + 1, 1, 0) -(a, 1, a, a + 1, 1, a) -(a, 1, a, a + 1, 1, a + 1) -(a, 1, a, a + 1, 1, 1) -(a, 1, a, 1, 0, 0) -(a, 1, a, 1, 0, a) -(a, 1, a, 1, 0, a + 1) -(a, 1, a, 1, 0, 1) -(a, 1, a, 1, a, 0) -(a, 1, a, 1, a, a) -(a, 1, a, 1, a, a + 1) -(a, 1, a, 1, a, 1) -(a, 1, a, 1, a + 1, 0) -(a, 1, a, 1, a + 1, a) -(a, 1, a, 1, a + 1, a + 1) -(a, 1, a, 1, a + 1, 1) -(a, 1, a, 1, 1, 0) -(a, 1, a, 1, 1, a) -(a, 1, a, 1, 1, a + 1) -(a, 1, a, 1, 1, 1) -(a, 1, a + 1, 0, 0, 0) -(a, 1, a + 1, 0, 0, a) -(a, 1, a + 1, 0, 0, a + 1) -(a, 1, a + 1, 0, 0, 1) -(a, 1, a + 1, 0, a, 0) -(a, 1, a + 1, 0, a, a) -(a, 1, a + 1, 0, a, a + 1) -(a, 1, a + 1, 0, a, 1) -(a, 1, a + 1, 0, a + 1, 0) -(a, 1, a + 1, 0, a + 1, a) -(a, 1, a + 1, 0, a + 1, a + 1) -(a, 1, a + 1, 0, a + 1, 1) -(a, 1, a + 1, 0, 1, 0) -(a, 1, a + 1, 0, 1, a) -(a, 1, a + 1, 0, 1, a + 1) -(a, 1, a + 1, 0, 1, 1) -(a, 1, a + 1, a, 0, 0) -(a, 1, a + 1, a, 0, a) -(a, 1, a + 1, a, 0, a + 1) -(a, 1, a + 1, a, 0, 1) -(a, 1, a + 1, a, a, 0) -(a, 1, a + 1, a, a, a) -(a, 1, a + 1, a, a, a + 1) -(a, 1, a + 1, a, a, 1) -(a, 1, a + 1, a, a + 1, 0) -(a, 1, a + 1, a, a + 1, a) -(a, 1, a + 1, a, a + 1, a + 1) -(a, 1, a + 1, a, a + 1, 1) -(a, 1, a + 1, a, 1, 0) -(a, 1, a + 1, a, 1, a) -(a, 1, a + 1, a, 1, a + 1) -(a, 1, a + 1, a, 1, 1) -(a, 1, a + 1, a + 1, 0, 0) -(a, 1, a + 1, a + 1, 0, a) -(a, 1, a + 1, a + 1, 0, a + 1) -(a, 1, a + 1, a + 1, 0, 1) -(a, 1, a + 1, a + 1, a, 0) -(a, 1, a + 1, a + 1, a, a) -(a, 1, a + 1, a + 1, a, a + 1) -(a, 1, a + 1, a + 1, a, 1) -(a, 1, a + 1, a + 1, a + 1, 0) -(a, 1, a + 1, a + 1, a + 1, a) -(a, 1, a + 1, a + 1, a + 1, a + 1) -(a, 1, a + 1, a + 1, a + 1, 1) -(a, 1, a + 1, a + 1, 1, 0) -(a, 1, a + 1, a + 1, 1, a) -(a, 1, a + 1, a + 1, 1, a + 1) -(a, 1, a + 1, a + 1, 1, 1) -(a, 1, a + 1, 1, 0, 0) -(a, 1, a + 1, 1, 0, a) -(a, 1, a + 1, 1, 0, a + 1) -(a, 1, a + 1, 1, 0, 1) -(a, 1, a + 1, 1, a, 0) -(a, 1, a + 1, 1, a, a) -(a, 1, a + 1, 1, a, a + 1) -(a, 1, a + 1, 1, a, 1) -(a, 1, a + 1, 1, a + 1, 0) -(a, 1, a + 1, 1, a + 1, a) -(a, 1, a + 1, 1, a + 1, a + 1) -(a, 1, a + 1, 1, a + 1, 1) -(a, 1, a + 1, 1, 1, 0) -(a, 1, a + 1, 1, 1, a) -(a, 1, a + 1, 1, 1, a + 1) -(a, 1, a + 1, 1, 1, 1) -(a, 1, 1, 0, 0, 0) -(a, 1, 1, 0, 0, a) -(a, 1, 1, 0, 0, a + 1) -(a, 1, 1, 0, 0, 1) -(a, 1, 1, 0, a, 0) -(a, 1, 1, 0, a, a) -(a, 1, 1, 0, a, a + 1) -(a, 1, 1, 0, a, 1) -(a, 1, 1, 0, a + 1, 0) -(a, 1, 1, 0, a + 1, a) -(a, 1, 1, 0, a + 1, a + 1) -(a, 1, 1, 0, a + 1, 1) -(a, 1, 1, 0, 1, 0) -(a, 1, 1, 0, 1, a) -(a, 1, 1, 0, 1, a + 1) -(a, 1, 1, 0, 1, 1) -(a, 1, 1, a, 0, 0) -(a, 1, 1, a, 0, a) -(a, 1, 1, a, 0, a + 1) -(a, 1, 1, a, 0, 1) -(a, 1, 1, a, a, 0) -(a, 1, 1, a, a, a) -(a, 1, 1, a, a, a + 1) -(a, 1, 1, a, a, 1) -(a, 1, 1, a, a + 1, 0) -(a, 1, 1, a, a + 1, a) -(a, 1, 1, a, a + 1, a + 1) -(a, 1, 1, a, a + 1, 1) -(a, 1, 1, a, 1, 0) -(a, 1, 1, a, 1, a) -(a, 1, 1, a, 1, a + 1) -(a, 1, 1, a, 1, 1) -(a, 1, 1, a + 1, 0, 0) -(a, 1, 1, a + 1, 0, a) -(a, 1, 1, a + 1, 0, a + 1) -(a, 1, 1, a + 1, 0, 1) -(a, 1, 1, a + 1, a, 0) -(a, 1, 1, a + 1, a, a) -(a, 1, 1, a + 1, a, a + 1) -(a, 1, 1, a + 1, a, 1) -(a, 1, 1, a + 1, a + 1, 0) -(a, 1, 1, a + 1, a + 1, a) -(a, 1, 1, a + 1, a + 1, a + 1) -(a, 1, 1, a + 1, a + 1, 1) -(a, 1, 1, a + 1, 1, 0) -(a, 1, 1, a + 1, 1, a) -(a, 1, 1, a + 1, 1, a + 1) -(a, 1, 1, a + 1, 1, 1) -(a, 1, 1, 1, 0, 0) -(a, 1, 1, 1, 0, a) -(a, 1, 1, 1, 0, a + 1) -(a, 1, 1, 1, 0, 1) -(a, 1, 1, 1, a, 0) -(a, 1, 1, 1, a, a) -(a, 1, 1, 1, a, a + 1) -(a, 1, 1, 1, a, 1) -(a, 1, 1, 1, a + 1, 0) -(a, 1, 1, 1, a + 1, a) -(a, 1, 1, 1, a + 1, a + 1) -(a, 1, 1, 1, a + 1, 1) -(a, 1, 1, 1, 1, 0) -(a, 1, 1, 1, 1, a) -(a, 1, 1, 1, 1, a + 1) -(a, 1, 1, 1, 1, 1) -(a + 1, 0, 0, 0, 0, 0) -(a + 1, 0, 0, 0, 0, a) -(a + 1, 0, 0, 0, 0, a + 1) -(a + 1, 0, 0, 0, 0, 1) -(a + 1, 0, 0, 0, a, 0) -(a + 1, 0, 0, 0, a, a) -(a + 1, 0, 0, 0, a, a + 1) -(a + 1, 0, 0, 0, a, 1) -(a + 1, 0, 0, 0, a + 1, 0) -(a + 1, 0, 0, 0, a + 1, a) -(a + 1, 0, 0, 0, a + 1, a + 1) -(a + 1, 0, 0, 0, a + 1, 1) -(a + 1, 0, 0, 0, 1, 0) -(a + 1, 0, 0, 0, 1, a) -(a + 1, 0, 0, 0, 1, a + 1) -(a + 1, 0, 0, 0, 1, 1) -(a + 1, 0, 0, a, 0, 0) -(a + 1, 0, 0, a, 0, a) -(a + 1, 0, 0, a, 0, a + 1) -(a + 1, 0, 0, a, 0, 1) -(a + 1, 0, 0, a, a, 0) -(a + 1, 0, 0, a, a, a) -(a + 1, 0, 0, a, a, a + 1) -(a + 1, 0, 0, a, a, 1) -(a + 1, 0, 0, a, a + 1, 0) -(a + 1, 0, 0, a, a + 1, a) -(a + 1, 0, 0, a, a + 1, a + 1) -(a + 1, 0, 0, a, a + 1, 1) -(a + 1, 0, 0, a, 1, 0) -(a + 1, 0, 0, a, 1, a) -(a + 1, 0, 0, a, 1, a + 1) -(a + 1, 0, 0, a, 1, 1) -(a + 1, 0, 0, a + 1, 0, 0) -(a + 1, 0, 0, a + 1, 0, a) -(a + 1, 0, 0, a + 1, 0, a + 1) -(a + 1, 0, 0, a + 1, 0, 1) -(a + 1, 0, 0, a + 1, a, 0) -(a + 1, 0, 0, a + 1, a, a) -(a + 1, 0, 0, a + 1, a, a + 1) -(a + 1, 0, 0, a + 1, a, 1) -(a + 1, 0, 0, a + 1, a + 1, 0) -(a + 1, 0, 0, a + 1, a + 1, a) -(a + 1, 0, 0, a + 1, a + 1, a + 1) -(a + 1, 0, 0, a + 1, a + 1, 1) -(a + 1, 0, 0, a + 1, 1, 0) -(a + 1, 0, 0, a + 1, 1, a) -(a + 1, 0, 0, a + 1, 1, a + 1) -(a + 1, 0, 0, a + 1, 1, 1) -(a + 1, 0, 0, 1, 0, 0) -(a + 1, 0, 0, 1, 0, a) -(a + 1, 0, 0, 1, 0, a + 1) -(a + 1, 0, 0, 1, 0, 1) -(a + 1, 0, 0, 1, a, 0) -(a + 1, 0, 0, 1, a, a) -(a + 1, 0, 0, 1, a, a + 1) -(a + 1, 0, 0, 1, a, 1) -(a + 1, 0, 0, 1, a + 1, 0) -(a + 1, 0, 0, 1, a + 1, a) -(a + 1, 0, 0, 1, a + 1, a + 1) -(a + 1, 0, 0, 1, a + 1, 1) -(a + 1, 0, 0, 1, 1, 0) -(a + 1, 0, 0, 1, 1, a) -(a + 1, 0, 0, 1, 1, a + 1) -(a + 1, 0, 0, 1, 1, 1) -(a + 1, 0, a, 0, 0, 0) -(a + 1, 0, a, 0, 0, a) -(a + 1, 0, a, 0, 0, a + 1) -(a + 1, 0, a, 0, 0, 1) -(a + 1, 0, a, 0, a, 0) -(a + 1, 0, a, 0, a, a) -(a + 1, 0, a, 0, a, a + 1) -(a + 1, 0, a, 0, a, 1) -(a + 1, 0, a, 0, a + 1, 0) -(a + 1, 0, a, 0, a + 1, a) -(a + 1, 0, a, 0, a + 1, a + 1) -(a + 1, 0, a, 0, a + 1, 1) -(a + 1, 0, a, 0, 1, 0) -(a + 1, 0, a, 0, 1, a) -(a + 1, 0, a, 0, 1, a + 1) -(a + 1, 0, a, 0, 1, 1) -(a + 1, 0, a, a, 0, 0) -(a + 1, 0, a, a, 0, a) -(a + 1, 0, a, a, 0, a + 1) -(a + 1, 0, a, a, 0, 1) -(a + 1, 0, a, a, a, 0) -(a + 1, 0, a, a, a, a) -(a + 1, 0, a, a, a, a + 1) -(a + 1, 0, a, a, a, 1) -(a + 1, 0, a, a, a + 1, 0) -(a + 1, 0, a, a, a + 1, a) -(a + 1, 0, a, a, a + 1, a + 1) -(a + 1, 0, a, a, a + 1, 1) -(a + 1, 0, a, a, 1, 0) -(a + 1, 0, a, a, 1, a) -(a + 1, 0, a, a, 1, a + 1) -(a + 1, 0, a, a, 1, 1) -(a + 1, 0, a, a + 1, 0, 0) -(a + 1, 0, a, a + 1, 0, a) -(a + 1, 0, a, a + 1, 0, a + 1) -(a + 1, 0, a, a + 1, 0, 1) -(a + 1, 0, a, a + 1, a, 0) -(a + 1, 0, a, a + 1, a, a) -(a + 1, 0, a, a + 1, a, a + 1) -(a + 1, 0, a, a + 1, a, 1) -(a + 1, 0, a, a + 1, a + 1, 0) -(a + 1, 0, a, a + 1, a + 1, a) -(a + 1, 0, a, a + 1, a + 1, a + 1) -(a + 1, 0, a, a + 1, a + 1, 1) -(a + 1, 0, a, a + 1, 1, 0) -(a + 1, 0, a, a + 1, 1, a) -(a + 1, 0, a, a + 1, 1, a + 1) -(a + 1, 0, a, a + 1, 1, 1) -(a + 1, 0, a, 1, 0, 0) -(a + 1, 0, a, 1, 0, a) -(a + 1, 0, a, 1, 0, a + 1) -(a + 1, 0, a, 1, 0, 1) -(a + 1, 0, a, 1, a, 0) -(a + 1, 0, a, 1, a, a) -(a + 1, 0, a, 1, a, a + 1) -(a + 1, 0, a, 1, a, 1) -(a + 1, 0, a, 1, a + 1, 0) -(a + 1, 0, a, 1, a + 1, a) -(a + 1, 0, a, 1, 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a + 1, 0, a) -(a + 1, 0, 1, a + 1, 0, a + 1) -(a + 1, 0, 1, a + 1, 0, 1) -(a + 1, 0, 1, a + 1, a, 0) -(a + 1, 0, 1, a + 1, a, a) -(a + 1, 0, 1, a + 1, a, a + 1) -(a + 1, 0, 1, a + 1, a, 1) -(a + 1, 0, 1, a + 1, a + 1, 0) -(a + 1, 0, 1, a + 1, a + 1, a) -(a + 1, 0, 1, a + 1, a + 1, a + 1) -(a + 1, 0, 1, a + 1, a + 1, 1) -(a + 1, 0, 1, a + 1, 1, 0) -(a + 1, 0, 1, a + 1, 1, a) -(a + 1, 0, 1, a + 1, 1, a + 1) -(a + 1, 0, 1, a + 1, 1, 1) -(a + 1, 0, 1, 1, 0, 0) -(a + 1, 0, 1, 1, 0, a) -(a + 1, 0, 1, 1, 0, a + 1) -(a + 1, 0, 1, 1, 0, 1) -(a + 1, 0, 1, 1, a, 0) -(a + 1, 0, 1, 1, a, a) -(a + 1, 0, 1, 1, a, a + 1) -(a + 1, 0, 1, 1, a, 1) -(a + 1, 0, 1, 1, a + 1, 0) -(a + 1, 0, 1, 1, a + 1, a) -(a + 1, 0, 1, 1, a + 1, a + 1) -(a + 1, 0, 1, 1, a + 1, 1) -(a + 1, 0, 1, 1, 1, 0) -(a + 1, 0, 1, 1, 1, a) -(a + 1, 0, 1, 1, 1, a + 1) -(a + 1, 0, 1, 1, 1, 1) -(a + 1, a, 0, 0, 0, 0) -(a + 1, a, 0, 0, 0, a) -(a + 1, a, 0, 0, 0, a + 1) -(a + 1, a, 0, 0, 0, 1) -(a + 1, a, 0, 0, a, 0) -(a + 1, a, 0, 0, a, a) -(a + 1, a, 0, 0, a, a + 1) -(a + 1, a, 0, 0, a, 1) -(a + 1, a, 0, 0, a + 1, 0) -(a + 1, a, 0, 0, a + 1, a) -(a + 1, a, 0, 0, a + 1, a + 1) -(a + 1, a, 0, 0, a + 1, 1) -(a + 1, a, 0, 0, 1, 0) -(a + 1, a, 0, 0, 1, a) -(a + 1, a, 0, 0, 1, a + 1) -(a + 1, a, 0, 0, 1, 1) -(a + 1, a, 0, a, 0, 0) -(a + 1, a, 0, a, 0, a) -(a + 1, a, 0, a, 0, a + 1) -(a + 1, a, 0, a, 0, 1) -(a + 1, a, 0, a, a, 0) -(a + 1, a, 0, a, a, a) -(a + 1, a, 0, a, a, a + 1) -(a + 1, a, 0, a, a, 1) -(a + 1, a, 0, a, a + 1, 0) -(a + 1, a, 0, a, a + 1, a) -(a + 1, a, 0, a, a + 1, a + 1) -(a + 1, a, 0, a, a + 1, 1) -(a + 1, a, 0, a, 1, 0) -(a + 1, a, 0, a, 1, a) -(a + 1, a, 0, a, 1, a + 1) -(a + 1, a, 0, a, 1, 1) -(a + 1, a, 0, a + 1, 0, 0) -(a + 1, a, 0, a + 1, 0, a) -(a + 1, a, 0, a + 1, 0, a + 1) -(a + 1, a, 0, a + 1, 0, 1) -(a + 1, a, 0, a + 1, a, 0) -(a + 1, a, 0, a + 1, a, a) -(a + 1, a, 0, a + 1, a, a + 1) -(a + 1, a, 0, a + 1, a, 1) -(a + 1, a, 0, a + 1, a + 1, 0) -(a + 1, a, 0, a + 1, a + 1, a) -(a + 1, a, 0, a + 1, a + 1, a + 1) -(a + 1, a, 0, a + 1, a + 1, 1) -(a + 1, a, 0, a + 1, 1, 0) -(a + 1, a, 0, a + 1, 1, a) -(a + 1, a, 0, a + 1, 1, a + 1) -(a + 1, a, 0, a + 1, 1, 1) -(a + 1, a, 0, 1, 0, 0) -(a + 1, a, 0, 1, 0, a) -(a + 1, a, 0, 1, 0, a + 1) -(a + 1, a, 0, 1, 0, 1) -(a + 1, a, 0, 1, a, 0) -(a + 1, a, 0, 1, a, a) -(a + 1, a, 0, 1, a, a + 1) -(a + 1, a, 0, 1, a, 1) -(a + 1, a, 0, 1, a + 1, 0) -(a + 1, a, 0, 1, a + 1, a) -(a + 1, a, 0, 1, a + 1, a + 1) -(a + 1, a, 0, 1, a + 1, 1) -(a + 1, a, 0, 1, 1, 0) -(a + 1, a, 0, 1, 1, a) -(a + 1, a, 0, 1, 1, a + 1) -(a + 1, a, 0, 1, 1, 1) -(a + 1, a, a, 0, 0, 0) -(a + 1, a, a, 0, 0, a) -(a + 1, a, a, 0, 0, a + 1) -(a + 1, a, a, 0, 0, 1) -(a + 1, a, a, 0, a, 0) -(a + 1, a, a, 0, a, a) -(a + 1, a, a, 0, a, a + 1) -(a + 1, a, a, 0, a, 1) -(a + 1, a, a, 0, a + 1, 0) -(a + 1, a, a, 0, a + 1, a) -(a + 1, a, a, 0, a + 1, a + 1) -(a + 1, a, a, 0, a + 1, 1) -(a + 1, a, a, 0, 1, 0) -(a + 1, a, a, 0, 1, a) -(a + 1, a, a, 0, 1, a + 1) -(a + 1, a, a, 0, 1, 1) -(a + 1, a, a, a, 0, 0) -(a + 1, a, a, a, 0, a) -(a + 1, a, a, a, 0, a + 1) -(a + 1, a, a, a, 0, 1) -(a + 1, a, a, a, a, 0) -(a + 1, a, a, a, a, a) -(a + 1, a, a, a, a, a + 1) -(a + 1, a, a, a, a, 1) -(a + 1, a, a, a, a + 1, 0) -(a + 1, a, a, a, a + 1, a) -(a + 1, a, a, a, a + 1, a + 1) -(a + 1, a, a, a, a + 1, 1) -(a + 1, a, a, a, 1, 0) -(a + 1, a, a, a, 1, a) -(a + 1, a, a, a, 1, a + 1) -(a + 1, a, a, a, 1, 1) -(a + 1, a, a, a + 1, 0, 0) -(a + 1, a, a, a + 1, 0, a) -(a + 1, a, a, a + 1, 0, a + 1) -(a + 1, a, a, a + 1, 0, 1) -(a + 1, a, a, a + 1, a, 0) -(a + 1, a, a, a + 1, a, a) -(a + 1, a, a, a + 1, a, a + 1) -(a + 1, a, a, a + 1, a, 1) -(a + 1, a, a, a + 1, a + 1, 0) -(a + 1, a, a, a + 1, a + 1, a) -(a + 1, a, a, a + 1, a + 1, a + 1) -(a + 1, a, a, a + 1, a + 1, 1) -(a + 1, a, a, a + 1, 1, 0) -(a + 1, a, a, a + 1, 1, a) -(a + 1, a, a, a + 1, 1, a + 1) -(a + 1, a, a, a + 1, 1, 1) -(a + 1, a, a, 1, 0, 0) -(a + 1, a, a, 1, 0, a) -(a + 1, a, a, 1, 0, a + 1) -(a + 1, a, a, 1, 0, 1) -(a + 1, a, a, 1, a, 0) -(a + 1, a, a, 1, a, a) -(a + 1, a, a, 1, a, a + 1) -(a + 1, a, a, 1, a, 1) -(a + 1, a, a, 1, a + 1, 0) -(a + 1, a, a, 1, a + 1, a) -(a + 1, a, a, 1, a + 1, a + 1) -(a + 1, a, a, 1, a + 1, 1) -(a + 1, a, a, 1, 1, 0) -(a + 1, a, a, 1, 1, a) -(a + 1, a, a, 1, 1, a + 1) -(a + 1, a, a, 1, 1, 1) -(a + 1, a, a + 1, 0, 0, 0) -(a + 1, a, a + 1, 0, 0, a) -(a + 1, a, a + 1, 0, 0, a + 1) -(a + 1, a, a + 1, 0, 0, 1) -(a + 1, a, a + 1, 0, a, 0) -(a + 1, a, a + 1, 0, a, a) -(a + 1, a, a + 1, 0, a, a + 1) -(a + 1, a, a + 1, 0, a, 1) -(a + 1, a, a + 1, 0, a + 1, 0) -(a + 1, a, a + 1, 0, a + 1, a) -(a + 1, a, a + 1, 0, a + 1, a + 1) -(a + 1, a, a + 1, 0, a + 1, 1) -(a + 1, a, a + 1, 0, 1, 0) -(a + 1, a, a + 1, 0, 1, a) -(a + 1, a, a + 1, 0, 1, a + 1) -(a + 1, a, a + 1, 0, 1, 1) -(a + 1, a, a + 1, a, 0, 0) -(a + 1, a, a + 1, a, 0, a) -(a + 1, a, a + 1, a, 0, a + 1) -(a + 1, a, a + 1, a, 0, 1) -(a + 1, a, a + 1, a, a, 0) -(a + 1, a, a + 1, a, a, a) -(a + 1, a, a + 1, a, a, a + 1) -(a + 1, a, a + 1, a, a, 1) -(a + 1, a, a + 1, a, a + 1, 0) -(a + 1, a, a + 1, a, a + 1, a) -(a + 1, a, a + 1, a, a + 1, a + 1) -(a + 1, a, a + 1, a, a + 1, 1) -(a + 1, a, a + 1, a, 1, 0) -(a + 1, a, a + 1, a, 1, a) -(a + 1, a, a + 1, a, 1, a + 1) -(a + 1, a, a + 1, a, 1, 1) -(a + 1, a, a + 1, a + 1, 0, 0) -(a + 1, a, a + 1, a + 1, 0, a) -(a + 1, a, a + 1, a + 1, 0, a + 1) -(a + 1, a, a + 1, a + 1, 0, 1) -(a + 1, a, a + 1, a + 1, a, 0) -(a + 1, a, a + 1, a + 1, a, a) -(a + 1, a, a + 1, a + 1, a, a + 1) -(a + 1, a, a + 1, a + 1, a, 1) -(a + 1, a, a + 1, a + 1, a + 1, 0) -(a + 1, a, a + 1, a + 1, a + 1, a) -(a + 1, a, a + 1, a + 1, a + 1, a + 1) -(a + 1, a, a + 1, a + 1, a + 1, 1) -(a + 1, a, a + 1, a + 1, 1, 0) -(a + 1, a, a + 1, a + 1, 1, a) -(a + 1, a, a + 1, a + 1, 1, a + 1) -(a + 1, a, a + 1, a + 1, 1, 1) -(a + 1, a, a + 1, 1, 0, 0) -(a + 1, a, a + 1, 1, 0, a) -(a + 1, a, a + 1, 1, 0, a + 1) -(a + 1, a, a + 1, 1, 0, 1) -(a + 1, a, a + 1, 1, a, 0) -(a + 1, a, a + 1, 1, a, a) -(a + 1, a, a + 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1, 0, a, 1, a + 1) -(a + 1, 1, 0, a, 1, 1) -(a + 1, 1, 0, a + 1, 0, 0) -(a + 1, 1, 0, a + 1, 0, a) -(a + 1, 1, 0, a + 1, 0, a + 1) -(a + 1, 1, 0, a + 1, 0, 1) -(a + 1, 1, 0, a + 1, a, 0) -(a + 1, 1, 0, a + 1, a, a) -(a + 1, 1, 0, a + 1, a, a + 1) -(a + 1, 1, 0, a + 1, a, 1) -(a + 1, 1, 0, a + 1, a + 1, 0) -(a + 1, 1, 0, a + 1, a + 1, a) -(a + 1, 1, 0, a + 1, a + 1, a + 1) -(a + 1, 1, 0, a + 1, a + 1, 1) -(a + 1, 1, 0, a + 1, 1, 0) -(a + 1, 1, 0, a + 1, 1, a) -(a + 1, 1, 0, a + 1, 1, a + 1) -(a + 1, 1, 0, a + 1, 1, 1) -(a + 1, 1, 0, 1, 0, 0) -(a + 1, 1, 0, 1, 0, a) -(a + 1, 1, 0, 1, 0, a + 1) -(a + 1, 1, 0, 1, 0, 1) -(a + 1, 1, 0, 1, a, 0) -(a + 1, 1, 0, 1, a, a) -(a + 1, 1, 0, 1, a, a + 1) -(a + 1, 1, 0, 1, a, 1) -(a + 1, 1, 0, 1, a + 1, 0) -(a + 1, 1, 0, 1, a + 1, a) -(a + 1, 1, 0, 1, a + 1, a + 1) -(a + 1, 1, 0, 1, a + 1, 1) -(a + 1, 1, 0, 1, 1, 0) -(a + 1, 1, 0, 1, 1, a) -(a + 1, 1, 0, 1, 1, a + 1) -(a + 1, 1, 0, 1, 1, 1) -(a + 1, 1, a, 0, 0, 0) -(a + 1, 1, a, 0, 0, a) -(a + 1, 1, a, 0, 0, a + 1) -(a + 1, 1, a, 0, 0, 1) -(a + 1, 1, a, 0, a, 0) -(a + 1, 1, a, 0, a, a) -(a + 1, 1, a, 0, a, a + 1) -(a + 1, 1, a, 0, a, 1) -(a + 1, 1, a, 0, a + 1, 0) -(a + 1, 1, a, 0, a + 1, a) -(a + 1, 1, a, 0, a + 1, a + 1) -(a + 1, 1, a, 0, a + 1, 1) -(a + 1, 1, a, 0, 1, 0) -(a + 1, 1, a, 0, 1, a) -(a + 1, 1, a, 0, 1, a + 1) -(a + 1, 1, a, 0, 1, 1) -(a + 1, 1, a, a, 0, 0) -(a + 1, 1, a, a, 0, a) -(a + 1, 1, a, a, 0, a + 1) -(a + 1, 1, a, a, 0, 1) -(a + 1, 1, a, a, a, 0) -(a + 1, 1, a, a, a, a) -(a + 1, 1, a, a, a, a + 1) -(a + 1, 1, a, a, a, 1) -(a + 1, 1, a, a, a + 1, 0) -(a + 1, 1, a, a, a + 1, a) -(a + 1, 1, a, a, a + 1, a + 1) -(a + 1, 1, a, a, a + 1, 1) -(a + 1, 1, a, a, 1, 0) -(a + 1, 1, a, a, 1, a) -(a + 1, 1, a, a, 1, a + 1) -(a + 1, 1, a, a, 1, 1) -(a + 1, 1, a, a + 1, 0, 0) -(a + 1, 1, a, a + 1, 0, a) -(a + 1, 1, a, a + 1, 0, a + 1) -(a + 1, 1, a, a + 1, 0, 1) -(a + 1, 1, a, a + 1, a, 0) -(a + 1, 1, a, a + 1, a, a) -(a + 1, 1, a, a + 1, a, a + 1) -(a + 1, 1, a, a + 1, a, 1) -(a + 1, 1, a, a + 1, a + 1, 0) -(a + 1, 1, a, a + 1, a + 1, a) -(a + 1, 1, a, a + 1, a + 1, a + 1) -(a + 1, 1, a, a + 1, a + 1, 1) -(a + 1, 1, a, a + 1, 1, 0) -(a + 1, 1, a, a + 1, 1, a) -(a + 1, 1, a, a + 1, 1, a + 1) -(a + 1, 1, a, a + 1, 1, 1) -(a + 1, 1, a, 1, 0, 0) -(a + 1, 1, a, 1, 0, a) -(a + 1, 1, a, 1, 0, a + 1) -(a + 1, 1, a, 1, 0, 1) -(a + 1, 1, a, 1, a, 0) -(a + 1, 1, a, 1, a, a) -(a + 1, 1, a, 1, a, a + 1) -(a + 1, 1, a, 1, a, 1) -(a + 1, 1, a, 1, a + 1, 0) -(a + 1, 1, a, 1, a + 1, a) -(a + 1, 1, a, 1, a + 1, a + 1) -(a + 1, 1, a, 1, a + 1, 1) -(a + 1, 1, a, 1, 1, 0) -(a + 1, 1, a, 1, 1, a) -(a + 1, 1, a, 1, 1, a + 1) -(a + 1, 1, a, 1, 1, 1) -(a + 1, 1, a + 1, 0, 0, 0) -(a + 1, 1, a + 1, 0, 0, a) -(a + 1, 1, a + 1, 0, 0, a + 1) -(a + 1, 1, a + 1, 0, 0, 1) -(a + 1, 1, a + 1, 0, a, 0) -(a + 1, 1, a + 1, 0, a, a) -(a + 1, 1, a + 1, 0, a, a + 1) -(a + 1, 1, a + 1, 0, a, 1) -(a + 1, 1, a + 1, 0, a + 1, 0) -(a + 1, 1, a + 1, 0, a + 1, a) -(a + 1, 1, a + 1, 0, a + 1, a + 1) -(a + 1, 1, a + 1, 0, a + 1, 1) -(a + 1, 1, a + 1, 0, 1, 0) -(a + 1, 1, a + 1, 0, 1, a) -(a + 1, 1, a + 1, 0, 1, a + 1) -(a + 1, 1, a + 1, 0, 1, 1) -(a + 1, 1, a + 1, a, 0, 0) -(a + 1, 1, a + 1, a, 0, a) -(a + 1, 1, a + 1, a, 0, a + 1) -(a + 1, 1, a + 1, a, 0, 1) -(a + 1, 1, a + 1, a, a, 0) -(a + 1, 1, a + 1, a, a, a) -(a + 1, 1, a + 1, a, a, a + 1) -(a + 1, 1, a + 1, a, a, 1) -(a + 1, 1, a + 1, a, a + 1, 0) -(a + 1, 1, a + 1, a, a + 1, a) -(a + 1, 1, a + 1, a, a + 1, a + 1) -(a + 1, 1, a + 1, a, a + 1, 1) -(a + 1, 1, a + 1, a, 1, 0) -(a + 1, 1, a + 1, a, 1, a) -(a + 1, 1, a + 1, a, 1, a + 1) -(a + 1, 1, a + 1, a, 1, 1) -(a + 1, 1, a + 1, a + 1, 0, 0) -(a + 1, 1, a + 1, a + 1, 0, a) -(a + 1, 1, a + 1, a + 1, 0, a + 1) -(a + 1, 1, a + 1, a + 1, 0, 1) -(a + 1, 1, a + 1, a + 1, a, 0) -(a + 1, 1, a + 1, a + 1, a, a) -(a + 1, 1, a + 1, a + 1, a, a + 1) -(a + 1, 1, a + 1, a + 1, a, 1) -(a + 1, 1, a + 1, a + 1, a + 1, 0) -(a + 1, 1, a + 1, a + 1, a + 1, a) -(a + 1, 1, a + 1, a + 1, a + 1, a + 1) -(a + 1, 1, a + 1, a + 1, a + 1, 1) -(a + 1, 1, a + 1, a + 1, 1, 0) -(a + 1, 1, a + 1, a + 1, 1, a) -(a + 1, 1, a + 1, a + 1, 1, a + 1) -(a + 1, 1, a + 1, a + 1, 1, 1) -(a + 1, 1, a + 1, 1, 0, 0) -(a + 1, 1, a + 1, 1, 0, a) -(a + 1, 1, a + 1, 1, 0, a + 1) -(a + 1, 1, a + 1, 1, 0, 1) -(a + 1, 1, a + 1, 1, a, 0) -(a + 1, 1, a + 1, 1, a, a) -(a + 1, 1, a + 1, 1, a, a + 1) -(a + 1, 1, a + 1, 1, a, 1) -(a + 1, 1, a + 1, 1, a + 1, 0) -(a + 1, 1, a + 1, 1, a + 1, a) -(a + 1, 1, a + 1, 1, a + 1, a + 1) -(a + 1, 1, a + 1, 1, a + 1, 1) -(a + 1, 1, a + 1, 1, 1, 0) -(a + 1, 1, a + 1, 1, 1, a) -(a + 1, 1, a + 1, 1, 1, a + 1) -(a + 1, 1, a + 1, 1, 1, 1) -(a + 1, 1, 1, 0, 0, 0) -(a + 1, 1, 1, 0, 0, a) -(a + 1, 1, 1, 0, 0, a + 1) -(a + 1, 1, 1, 0, 0, 1) -(a + 1, 1, 1, 0, a, 0) -(a + 1, 1, 1, 0, a, a) -(a + 1, 1, 1, 0, a, a + 1) -(a + 1, 1, 1, 0, a, 1) -(a + 1, 1, 1, 0, a + 1, 0) -(a + 1, 1, 1, 0, a + 1, a) -(a + 1, 1, 1, 0, a + 1, a + 1) -(a + 1, 1, 1, 0, a + 1, 1) -(a + 1, 1, 1, 0, 1, 0) -(a + 1, 1, 1, 0, 1, a) -(a + 1, 1, 1, 0, 1, a + 1) -(a + 1, 1, 1, 0, 1, 1) -(a + 1, 1, 1, a, 0, 0) -(a + 1, 1, 1, a, 0, a) -(a + 1, 1, 1, a, 0, a + 1) -(a + 1, 1, 1, a, 0, 1) -(a + 1, 1, 1, a, a, 0) -(a + 1, 1, 1, a, a, a) -(a + 1, 1, 1, a, a, a + 1) -(a + 1, 1, 1, a, a, 1) -(a + 1, 1, 1, a, a + 1, 0) -(a + 1, 1, 1, a, a + 1, a) -(a + 1, 1, 1, a, a + 1, a + 1) -(a + 1, 1, 1, a, a + 1, 1) -(a + 1, 1, 1, a, 1, 0) -(a + 1, 1, 1, a, 1, a) -(a + 1, 1, 1, a, 1, a + 1) -(a + 1, 1, 1, a, 1, 1) -(a + 1, 1, 1, a + 1, 0, 0) -(a + 1, 1, 1, a + 1, 0, a) -(a + 1, 1, 1, a + 1, 0, a + 1) -(a + 1, 1, 1, a + 1, 0, 1) -(a + 1, 1, 1, a + 1, a, 0) -(a + 1, 1, 1, a + 1, a, a) -(a + 1, 1, 1, a + 1, a, a + 1) -(a + 1, 1, 1, a + 1, a, 1) -(a + 1, 1, 1, a + 1, a + 1, 0) -(a + 1, 1, 1, a + 1, a + 1, a) -(a + 1, 1, 1, a + 1, a + 1, a + 1) -(a + 1, 1, 1, a + 1, a + 1, 1) -(a + 1, 1, 1, a + 1, 1, 0) -(a + 1, 1, 1, a + 1, 1, a) -(a + 1, 1, 1, a + 1, 1, a + 1) -(a + 1, 1, 1, a + 1, 1, 1) -(a + 1, 1, 1, 1, 0, 0) -(a + 1, 1, 1, 1, 0, a) -(a + 1, 1, 1, 1, 0, a + 1) -(a + 1, 1, 1, 1, 0, 1) -(a + 1, 1, 1, 1, a, 0) -(a + 1, 1, 1, 1, a, a) -(a + 1, 1, 1, 1, a, a + 1) -(a + 1, 1, 1, 1, a, 1) -(a + 1, 1, 1, 1, a + 1, 0) -(a + 1, 1, 1, 1, a + 1, a) -(a + 1, 1, 1, 1, a + 1, a + 1) -(a + 1, 1, 1, 1, a + 1, 1) -(a + 1, 1, 1, 1, 1, 0) -(a + 1, 1, 1, 1, 1, a) -(a + 1, 1, 1, 1, 1, a + 1) -(a + 1, 1, 1, 1, 1, 1) -(1, 0, 0, 0, 0, 0) -(1, 0, 0, 0, 0, a) -(1, 0, 0, 0, 0, a + 1) -(1, 0, 0, 0, 0, 1) -(1, 0, 0, 0, a, 0) -(1, 0, 0, 0, a, a) -(1, 0, 0, 0, a, a + 1) -(1, 0, 0, 0, a, 1) -(1, 0, 0, 0, a + 1, 0) -(1, 0, 0, 0, a + 1, a) -(1, 0, 0, 0, a + 1, a + 1) -(1, 0, 0, 0, a + 1, 1) -(1, 0, 0, 0, 1, 0) -(1, 0, 0, 0, 1, a) -(1, 0, 0, 0, 1, a + 1) -(1, 0, 0, 0, 1, 1) -(1, 0, 0, a, 0, 0) -(1, 0, 0, a, 0, a) -(1, 0, 0, a, 0, a + 1) -(1, 0, 0, a, 0, 1) -(1, 0, 0, a, a, 0) -(1, 0, 0, a, a, a) -(1, 0, 0, a, a, a + 1) -(1, 0, 0, a, a, 1) -(1, 0, 0, a, a + 1, 0) -(1, 0, 0, a, a + 1, a) -(1, 0, 0, a, a + 1, a + 1) -(1, 0, 0, a, a + 1, 1) -(1, 0, 0, a, 1, 0) -(1, 0, 0, a, 1, a) -(1, 0, 0, a, 1, a + 1) -(1, 0, 0, a, 1, 1) -(1, 0, 0, a + 1, 0, 0) -(1, 0, 0, a + 1, 0, a) -(1, 0, 0, a + 1, 0, a + 1) -(1, 0, 0, a + 1, 0, 1) -(1, 0, 0, a + 1, a, 0) -(1, 0, 0, a + 1, a, a) -(1, 0, 0, a + 1, a, a + 1) -(1, 0, 0, a + 1, a, 1) -(1, 0, 0, a + 1, a + 1, 0) -(1, 0, 0, a + 1, a + 1, a) -(1, 0, 0, a + 1, a + 1, a + 1) -(1, 0, 0, a + 1, a + 1, 1) -(1, 0, 0, a + 1, 1, 0) -(1, 0, 0, a + 1, 1, a) -(1, 0, 0, a + 1, 1, a + 1) -(1, 0, 0, a + 1, 1, 1) -(1, 0, 0, 1, 0, 0) -(1, 0, 0, 1, 0, a) -(1, 0, 0, 1, 0, a + 1) -(1, 0, 0, 1, 0, 1) -(1, 0, 0, 1, a, 0) -(1, 0, 0, 1, a, a) -(1, 0, 0, 1, a, a + 1) -(1, 0, 0, 1, a, 1) -(1, 0, 0, 1, a + 1, 0) -(1, 0, 0, 1, a + 1, a) -(1, 0, 0, 1, a + 1, a + 1) -(1, 0, 0, 1, a + 1, 1) -(1, 0, 0, 1, 1, 0) -(1, 0, 0, 1, 1, a) -(1, 0, 0, 1, 1, a + 1) -(1, 0, 0, 1, 1, 1) -(1, 0, a, 0, 0, 0) -(1, 0, a, 0, 0, a) -(1, 0, a, 0, 0, a + 1) -(1, 0, a, 0, 0, 1) -(1, 0, a, 0, a, 0) -(1, 0, a, 0, a, a) -(1, 0, a, 0, a, a + 1) -(1, 0, a, 0, a, 1) -(1, 0, a, 0, a + 1, 0) -(1, 0, a, 0, a + 1, a) -(1, 0, a, 0, a + 1, a + 1) -(1, 0, a, 0, a + 1, 1) -(1, 0, a, 0, 1, 0) -(1, 0, a, 0, 1, a) -(1, 0, a, 0, 1, a + 1) -(1, 0, a, 0, 1, 1) -(1, 0, a, a, 0, 0) -(1, 0, a, a, 0, a) -(1, 0, a, a, 0, a + 1) -(1, 0, a, a, 0, 1) -(1, 0, a, a, a, 0) -(1, 0, a, a, a, a) -(1, 0, a, a, a, a + 1) -(1, 0, a, a, a, 1) -(1, 0, a, a, a + 1, 0) -(1, 0, a, a, a + 1, a) -(1, 0, a, a, a + 1, a + 1) -(1, 0, a, a, a + 1, 1) -(1, 0, a, a, 1, 0) -(1, 0, a, a, 1, a) -(1, 0, a, a, 1, a + 1) -(1, 0, a, a, 1, 1) -(1, 0, a, a + 1, 0, 0) -(1, 0, a, a + 1, 0, a) -(1, 0, a, a + 1, 0, a + 1) -(1, 0, a, a + 1, 0, 1) -(1, 0, a, a + 1, a, 0) -(1, 0, a, a + 1, a, a) -(1, 0, a, a + 1, a, a + 1) -(1, 0, a, a + 1, a, 1) -(1, 0, a, a + 1, a + 1, 0) -(1, 0, a, a + 1, a + 1, a) -(1, 0, a, a + 1, a + 1, a + 1) -(1, 0, a, a + 1, a + 1, 1) -(1, 0, a, a + 1, 1, 0) -(1, 0, a, a + 1, 1, a) -(1, 0, a, a + 1, 1, a + 1) -(1, 0, a, a + 1, 1, 1) -(1, 0, a, 1, 0, 0) -(1, 0, a, 1, 0, a) -(1, 0, a, 1, 0, a + 1) -(1, 0, a, 1, 0, 1) -(1, 0, a, 1, a, 0) -(1, 0, a, 1, a, a) -(1, 0, a, 1, a, a + 1) -(1, 0, a, 1, a, 1) -(1, 0, a, 1, a + 1, 0) -(1, 0, a, 1, a + 1, a) -(1, 0, a, 1, a + 1, a + 1) -(1, 0, a, 1, a + 1, 1) -(1, 0, a, 1, 1, 0) -(1, 0, a, 1, 1, a) -(1, 0, a, 1, 1, a + 1) -(1, 0, a, 1, 1, 1) -(1, 0, a + 1, 0, 0, 0) -(1, 0, a + 1, 0, 0, a) -(1, 0, a + 1, 0, 0, a + 1) -(1, 0, a + 1, 0, 0, 1) -(1, 0, a + 1, 0, a, 0) -(1, 0, a + 1, 0, a, a) -(1, 0, a + 1, 0, a, a + 1) -(1, 0, a + 1, 0, a, 1) -(1, 0, a + 1, 0, a + 1, 0) -(1, 0, a + 1, 0, a + 1, a) -(1, 0, a + 1, 0, a + 1, a + 1) -(1, 0, a + 1, 0, a + 1, 1) -(1, 0, a + 1, 0, 1, 0) -(1, 0, a + 1, 0, 1, a) -(1, 0, a + 1, 0, 1, a + 1) -(1, 0, a + 1, 0, 1, 1) -(1, 0, a + 1, a, 0, 0) -(1, 0, a + 1, a, 0, a) -(1, 0, a + 1, a, 0, a + 1) -(1, 0, a + 1, a, 0, 1) -(1, 0, a + 1, a, a, 0) -(1, 0, a + 1, a, a, a) -(1, 0, a + 1, a, a, a + 1) -(1, 0, a + 1, a, a, 1) -(1, 0, a + 1, a, a + 1, 0) -(1, 0, a + 1, a, a + 1, a) -(1, 0, a + 1, a, a + 1, a + 1) -(1, 0, a + 1, a, a + 1, 1) -(1, 0, a + 1, a, 1, 0) -(1, 0, a + 1, a, 1, a) -(1, 0, a + 1, a, 1, a + 1) -(1, 0, a + 1, a, 1, 1) -(1, 0, a + 1, a + 1, 0, 0) -(1, 0, a + 1, a + 1, 0, a) -(1, 0, a + 1, a + 1, 0, a + 1) -(1, 0, a + 1, a + 1, 0, 1) -(1, 0, a + 1, a + 1, a, 0) -(1, 0, a + 1, a + 1, a, a) -(1, 0, a + 1, a + 1, a, a + 1) -(1, 0, a + 1, a + 1, a, 1) -(1, 0, a + 1, a + 1, a + 1, 0) -(1, 0, a + 1, a + 1, a + 1, a) -(1, 0, a + 1, a + 1, a + 1, a + 1) -(1, 0, a + 1, a + 1, a + 1, 1) -(1, 0, a + 1, a + 1, 1, 0) -(1, 0, a + 1, a + 1, 1, a) -(1, 0, a + 1, a + 1, 1, a + 1) -(1, 0, a + 1, a + 1, 1, 1) -(1, 0, a + 1, 1, 0, 0) -(1, 0, a + 1, 1, 0, a) -(1, 0, a + 1, 1, 0, a + 1) -(1, 0, a + 1, 1, 0, 1) -(1, 0, a + 1, 1, a, 0) -(1, 0, a + 1, 1, a, a) -(1, 0, a + 1, 1, a, a + 1) -(1, 0, a + 1, 1, a, 1) -(1, 0, a + 1, 1, a + 1, 0) -(1, 0, a + 1, 1, a + 1, a) -(1, 0, a + 1, 1, a + 1, a + 1) -(1, 0, a + 1, 1, a + 1, 1) -(1, 0, a + 1, 1, 1, 0) -(1, 0, a + 1, 1, 1, a) -(1, 0, a + 1, 1, 1, a + 1) -(1, 0, a + 1, 1, 1, 1) -(1, 0, 1, 0, 0, 0) -(1, 0, 1, 0, 0, a) -(1, 0, 1, 0, 0, a + 1) -(1, 0, 1, 0, 0, 1) -(1, 0, 1, 0, a, 0) -(1, 0, 1, 0, a, a) -(1, 0, 1, 0, a, a + 1) -(1, 0, 1, 0, a, 1) -(1, 0, 1, 0, a + 1, 0) -(1, 0, 1, 0, a + 1, a) -(1, 0, 1, 0, a + 1, a + 1) -(1, 0, 1, 0, a + 1, 1) -(1, 0, 1, 0, 1, 0) -(1, 0, 1, 0, 1, a) -(1, 0, 1, 0, 1, a + 1) -(1, 0, 1, 0, 1, 1) -(1, 0, 1, a, 0, 0) -(1, 0, 1, a, 0, a) -(1, 0, 1, a, 0, a + 1) -(1, 0, 1, a, 0, 1) -(1, 0, 1, a, a, 0) -(1, 0, 1, a, a, a) -(1, 0, 1, a, a, a + 1) -(1, 0, 1, a, a, 1) -(1, 0, 1, a, a + 1, 0) -(1, 0, 1, a, a + 1, a) -(1, 0, 1, a, a + 1, a + 1) -(1, 0, 1, a, a + 1, 1) -(1, 0, 1, a, 1, 0) -(1, 0, 1, a, 1, a) -(1, 0, 1, a, 1, a + 1) -(1, 0, 1, a, 1, 1) -(1, 0, 1, a + 1, 0, 0) -(1, 0, 1, a + 1, 0, a) -(1, 0, 1, a + 1, 0, a + 1) -(1, 0, 1, a + 1, 0, 1) -(1, 0, 1, a + 1, a, 0) -(1, 0, 1, a + 1, a, a) -(1, 0, 1, a + 1, a, a + 1) -(1, 0, 1, a + 1, a, 1) -(1, 0, 1, a + 1, a + 1, 0) -(1, 0, 1, a + 1, a + 1, a) -(1, 0, 1, a + 1, a + 1, a + 1) -(1, 0, 1, a + 1, a + 1, 1) -(1, 0, 1, a + 1, 1, 0) -(1, 0, 1, a + 1, 1, a) -(1, 0, 1, a + 1, 1, a + 1) -(1, 0, 1, a + 1, 1, 1) -(1, 0, 1, 1, 0, 0) -(1, 0, 1, 1, 0, a) -(1, 0, 1, 1, 0, a + 1) -(1, 0, 1, 1, 0, 1) -(1, 0, 1, 1, a, 0) -(1, 0, 1, 1, a, a) -(1, 0, 1, 1, a, a + 1) -(1, 0, 1, 1, a, 1) -(1, 0, 1, 1, a + 1, 0) -(1, 0, 1, 1, a + 1, a) -(1, 0, 1, 1, a + 1, a + 1) -(1, 0, 1, 1, a + 1, 1) -(1, 0, 1, 1, 1, 0) -(1, 0, 1, 1, 1, a) -(1, 0, 1, 1, 1, a + 1) -(1, 0, 1, 1, 1, 1) -(1, a, 0, 0, 0, 0) -(1, a, 0, 0, 0, a) -(1, a, 0, 0, 0, a + 1) -(1, a, 0, 0, 0, 1) -(1, a, 0, 0, a, 0) -(1, a, 0, 0, a, a) -(1, a, 0, 0, a, a + 1) -(1, a, 0, 0, a, 1) -(1, a, 0, 0, a + 1, 0) -(1, a, 0, 0, a + 1, a) -(1, a, 0, 0, a + 1, a + 1) -(1, a, 0, 0, a + 1, 1) -(1, a, 0, 0, 1, 0) -(1, a, 0, 0, 1, a) -(1, a, 0, 0, 1, a + 1) -(1, a, 0, 0, 1, 1) -(1, a, 0, a, 0, 0) -(1, a, 0, a, 0, a) -(1, a, 0, a, 0, a + 1) -(1, a, 0, a, 0, 1) -(1, a, 0, a, a, 0) -(1, a, 0, a, a, a) 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1, 0) -(1, a, a + 1, 1, a + 1, a) -(1, a, a + 1, 1, a + 1, a + 1) -(1, a, a + 1, 1, a + 1, 1) -(1, a, a + 1, 1, 1, 0) -(1, a, a + 1, 1, 1, a) -(1, a, a + 1, 1, 1, a + 1) -(1, a, a + 1, 1, 1, 1) -(1, a, 1, 0, 0, 0) -(1, a, 1, 0, 0, a) -(1, a, 1, 0, 0, a + 1) -(1, a, 1, 0, 0, 1) -(1, a, 1, 0, a, 0) -(1, a, 1, 0, a, a) -(1, a, 1, 0, a, a + 1) -(1, a, 1, 0, a, 1) -(1, a, 1, 0, a + 1, 0) -(1, a, 1, 0, a + 1, a) -(1, a, 1, 0, a + 1, a + 1) -(1, a, 1, 0, a + 1, 1) -(1, a, 1, 0, 1, 0) -(1, a, 1, 0, 1, a) -(1, a, 1, 0, 1, a + 1) -(1, a, 1, 0, 1, 1) -(1, a, 1, a, 0, 0) -(1, a, 1, a, 0, a) -(1, a, 1, a, 0, a + 1) -(1, a, 1, a, 0, 1) -(1, a, 1, a, a, 0) -(1, a, 1, a, a, a) -(1, a, 1, a, a, a + 1) -(1, a, 1, a, a, 1) -(1, a, 1, a, a + 1, 0) -(1, a, 1, a, a + 1, a) -(1, a, 1, a, a + 1, a + 1) -(1, a, 1, a, a + 1, 1) -(1, a, 1, a, 1, 0) -(1, a, 1, a, 1, a) -(1, a, 1, a, 1, a + 1) -(1, a, 1, a, 1, 1) -(1, a, 1, a + 1, 0, 0) -(1, a, 1, a + 1, 0, a) -(1, a, 1, a + 1, 0, a + 1) -(1, a, 1, a + 1, 0, 1) 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0, 0) -(1, a + 1, 0, 1, 0, a) -(1, a + 1, 0, 1, 0, a + 1) -(1, a + 1, 0, 1, 0, 1) -(1, a + 1, 0, 1, a, 0) -(1, a + 1, 0, 1, a, a) -(1, a + 1, 0, 1, a, a + 1) -(1, a + 1, 0, 1, a, 1) -(1, a + 1, 0, 1, a + 1, 0) -(1, a + 1, 0, 1, a + 1, a) -(1, a + 1, 0, 1, a + 1, a + 1) -(1, a + 1, 0, 1, a + 1, 1) -(1, a + 1, 0, 1, 1, 0) -(1, a + 1, 0, 1, 1, a) -(1, a + 1, 0, 1, 1, a + 1) -(1, a + 1, 0, 1, 1, 1) -(1, a + 1, a, 0, 0, 0) -(1, a + 1, a, 0, 0, a) -(1, a + 1, a, 0, 0, a + 1) -(1, a + 1, a, 0, 0, 1) -(1, a + 1, a, 0, a, 0) -(1, a + 1, a, 0, a, a) -(1, a + 1, a, 0, a, a + 1) -(1, a + 1, a, 0, a, 1) -(1, a + 1, a, 0, a + 1, 0) -(1, a + 1, a, 0, a + 1, a) -(1, a + 1, a, 0, a + 1, a + 1) -(1, a + 1, a, 0, a + 1, 1) -(1, a + 1, a, 0, 1, 0) -(1, a + 1, a, 0, 1, a) -(1, a + 1, a, 0, 1, a + 1) -(1, a + 1, a, 0, 1, 1) -(1, a + 1, a, a, 0, 0) -(1, a + 1, a, a, 0, a) -(1, a + 1, a, a, 0, a + 1) -(1, a + 1, a, a, 0, 1) -(1, a + 1, a, a, a, 0) -(1, a + 1, a, a, a, a) -(1, a + 1, a, a, a, a + 1) -(1, a + 1, a, a, a, 1) -(1, a + 1, a, a, a + 1, 0) -(1, a + 1, a, a, a + 1, a) -(1, a + 1, a, a, a + 1, a + 1) -(1, a + 1, a, a, a + 1, 1) -(1, a + 1, a, a, 1, 0) -(1, a + 1, a, a, 1, a) -(1, a + 1, a, a, 1, a + 1) -(1, a + 1, a, a, 1, 1) -(1, a + 1, a, a + 1, 0, 0) -(1, a + 1, a, a + 1, 0, a) -(1, a + 1, a, a + 1, 0, a + 1) -(1, a + 1, a, a + 1, 0, 1) -(1, a + 1, a, a + 1, a, 0) -(1, a + 1, a, a + 1, a, a) -(1, a + 1, a, a + 1, a, a + 1) -(1, a + 1, a, a + 1, a, 1) -(1, a + 1, a, a + 1, a + 1, 0) -(1, a + 1, a, a + 1, a + 1, a) -(1, a + 1, a, a + 1, a + 1, a + 1) -(1, a + 1, a, a + 1, a + 1, 1) -(1, a + 1, a, a + 1, 1, 0) -(1, a + 1, a, a + 1, 1, a) -(1, a + 1, a, a + 1, 1, a + 1) -(1, a + 1, a, a + 1, 1, 1) -(1, a + 1, a, 1, 0, 0) -(1, a + 1, a, 1, 0, a) -(1, a + 1, a, 1, 0, a + 1) -(1, a + 1, a, 1, 0, 1) -(1, a + 1, a, 1, a, 0) -(1, a + 1, a, 1, a, a) -(1, a + 1, a, 1, a, a + 1) -(1, a + 1, a, 1, a, 1) -(1, a + 1, a, 1, a + 1, 0) -(1, a + 1, a, 1, a + 1, a) -(1, a + 1, a, 1, a + 1, a + 1) -(1, a + 1, a, 1, a + 1, 1) -(1, a + 1, a, 1, 1, 0) -(1, a + 1, a, 1, 1, a) -(1, a + 1, a, 1, 1, a + 1) -(1, a + 1, a, 1, 1, 1) -(1, a + 1, a + 1, 0, 0, 0) -(1, a + 1, a + 1, 0, 0, a) -(1, a + 1, a + 1, 0, 0, a + 1) -(1, a + 1, a + 1, 0, 0, 1) -(1, a + 1, a + 1, 0, a, 0) -(1, a + 1, a + 1, 0, a, a) -(1, a + 1, a + 1, 0, a, a + 1) -(1, a + 1, a + 1, 0, a, 1) -(1, a + 1, a + 1, 0, a + 1, 0) -(1, a + 1, a + 1, 0, a + 1, a) -(1, a + 1, a + 1, 0, a + 1, a + 1) -(1, a + 1, a + 1, 0, a + 1, 1) -(1, a + 1, a + 1, 0, 1, 0) -(1, a + 1, a + 1, 0, 1, a) -(1, a + 1, a + 1, 0, 1, a + 1) -(1, a + 1, a + 1, 0, 1, 1) -(1, a + 1, a + 1, a, 0, 0) -(1, a + 1, a + 1, a, 0, a) -(1, a + 1, a + 1, a, 0, a + 1) -(1, a + 1, a + 1, a, 0, 1) -(1, a + 1, a + 1, a, a, 0) -(1, a + 1, a + 1, a, a, a) -(1, a + 1, a + 1, a, a, a + 1) -(1, a + 1, a + 1, a, a, 1) -(1, a + 1, a + 1, a, a + 1, 0) -(1, a + 1, a + 1, a, a + 1, a) -(1, a + 1, a + 1, a, a + 1, a + 1) -(1, a + 1, a + 1, a, a + 1, 1) -(1, a + 1, a + 1, a, 1, 0) -(1, a + 1, a + 1, a, 1, a) -(1, a + 1, a + 1, a, 1, a + 1) -(1, a + 1, a + 1, a, 1, 1) -(1, a + 1, a + 1, a + 1, 0, 0) -(1, a + 1, a + 1, a + 1, 0, a) -(1, a + 1, a + 1, a + 1, 0, a + 1) -(1, a + 1, a + 1, a + 1, 0, 1) -(1, a + 1, a + 1, a + 1, a, 0) -(1, a + 1, a + 1, a + 1, a, a) -(1, a + 1, a + 1, a + 1, a, a + 1) -(1, a + 1, a + 1, a + 1, a, 1) -(1, a + 1, a + 1, a + 1, a + 1, 0) -(1, a + 1, a + 1, a + 1, a + 1, a) -(1, a + 1, a + 1, a + 1, a + 1, a + 1) -(1, a + 1, a + 1, a + 1, a + 1, 1) -(1, a + 1, a + 1, a + 1, 1, 0) -(1, a + 1, a + 1, a + 1, 1, a) -(1, a + 1, a + 1, a + 1, 1, a + 1) -(1, a + 1, a + 1, a + 1, 1, 1) -(1, a + 1, a + 1, 1, 0, 0) -(1, a + 1, a + 1, 1, 0, a) -(1, a + 1, a + 1, 1, 0, a + 1) -(1, a + 1, a + 1, 1, 0, 1) -(1, a + 1, a + 1, 1, a, 0) -(1, a + 1, a + 1, 1, a, a) -(1, a + 1, a + 1, 1, a, a + 1) -(1, a + 1, a + 1, 1, a, 1) -(1, a + 1, a + 1, 1, a + 1, 0) -(1, a + 1, a + 1, 1, a + 1, a) -(1, a + 1, a + 1, 1, a + 1, a + 1) -(1, a + 1, a + 1, 1, a + 1, 1) -(1, a + 1, a + 1, 1, 1, 0) -(1, a + 1, a + 1, 1, 1, a) -(1, a + 1, a + 1, 1, 1, a + 1) -(1, a + 1, a + 1, 1, 1, 1) -(1, a + 1, 1, 0, 0, 0) -(1, a + 1, 1, 0, 0, a) -(1, a + 1, 1, 0, 0, a + 1) -(1, a + 1, 1, 0, 0, 1) -(1, a + 1, 1, 0, a, 0) -(1, a + 1, 1, 0, a, a) -(1, a + 1, 1, 0, a, a + 1) -(1, a + 1, 1, 0, a, 1) -(1, a + 1, 1, 0, a + 1, 0) -(1, a + 1, 1, 0, a + 1, a) -(1, a + 1, 1, 0, a + 1, a + 1) -(1, a + 1, 1, 0, a + 1, 1) -(1, a + 1, 1, 0, 1, 0) -(1, a + 1, 1, 0, 1, a) -(1, a + 1, 1, 0, 1, a + 1) -(1, a + 1, 1, 0, 1, 1) -(1, a + 1, 1, a, 0, 0) -(1, a + 1, 1, a, 0, a) -(1, a + 1, 1, a, 0, a + 1) -(1, a + 1, 1, a, 0, 1) -(1, a + 1, 1, a, a, 0) -(1, a + 1, 1, a, a, a) -(1, a + 1, 1, a, a, a + 1) -(1, a + 1, 1, a, a, 1) -(1, a + 1, 1, a, a + 1, 0) -(1, a + 1, 1, a, a + 1, a) -(1, a + 1, 1, a, a + 1, a + 1) -(1, a + 1, 1, a, a + 1, 1) -(1, a + 1, 1, a, 1, 0) -(1, a + 1, 1, a, 1, a) -(1, a + 1, 1, a, 1, a + 1) -(1, a + 1, 1, a, 1, 1) -(1, a + 1, 1, a + 1, 0, 0) -(1, a + 1, 1, a + 1, 0, a) -(1, a + 1, 1, a + 1, 0, a + 1) -(1, a + 1, 1, a + 1, 0, 1) -(1, a + 1, 1, a + 1, a, 0) -(1, a + 1, 1, a + 1, a, a) -(1, a + 1, 1, a + 1, a, a + 1) -(1, a + 1, 1, a + 1, a, 1) -(1, a + 1, 1, a + 1, a + 1, 0) -(1, a + 1, 1, a + 1, a + 1, a) -(1, a + 1, 1, a + 1, a + 1, a + 1) -(1, a + 1, 1, a + 1, a + 1, 1) -(1, a + 1, 1, a + 1, 1, 0) -(1, a + 1, 1, a + 1, 1, a) -(1, a + 1, 1, a + 1, 1, a + 1) -(1, a + 1, 1, a + 1, 1, 1) -(1, a + 1, 1, 1, 0, 0) -(1, a + 1, 1, 1, 0, a) -(1, a + 1, 1, 1, 0, a + 1) -(1, a + 1, 1, 1, 0, 1) -(1, a + 1, 1, 1, a, 0) -(1, a + 1, 1, 1, a, a) -(1, a + 1, 1, 1, a, a + 1) -(1, a + 1, 1, 1, a, 1) -(1, a + 1, 1, 1, a + 1, 0) -(1, a + 1, 1, 1, a + 1, a) -(1, a + 1, 1, 1, a + 1, a + 1) -(1, a + 1, 1, 1, a + 1, 1) -(1, a + 1, 1, 1, 1, 0) -(1, a + 1, 1, 1, 1, a) -(1, a + 1, 1, 1, 1, a + 1) -(1, a + 1, 1, 1, 1, 1) -(1, 1, 0, 0, 0, 0) -(1, 1, 0, 0, 0, a) -(1, 1, 0, 0, 0, a + 1) -(1, 1, 0, 0, 0, 1) -(1, 1, 0, 0, a, 0) -(1, 1, 0, 0, a, a) -(1, 1, 0, 0, a, a + 1) -(1, 1, 0, 0, a, 1) -(1, 1, 0, 0, a + 1, 0) -(1, 1, 0, 0, a + 1, a) -(1, 1, 0, 0, a + 1, a + 1) -(1, 1, 0, 0, a + 1, 1) -(1, 1, 0, 0, 1, 0) -(1, 1, 0, 0, 1, a) -(1, 1, 0, 0, 1, a + 1) -(1, 1, 0, 0, 1, 1) -(1, 1, 0, a, 0, 0) -(1, 1, 0, a, 0, a) -(1, 1, 0, a, 0, a + 1) -(1, 1, 0, a, 0, 1) -(1, 1, 0, a, a, 0) -(1, 1, 0, a, a, a) -(1, 1, 0, a, a, a + 1) -(1, 1, 0, a, a, 1) -(1, 1, 0, a, a + 1, 0) -(1, 1, 0, a, a + 1, a) -(1, 1, 0, a, a + 1, a + 1) -(1, 1, 0, a, a + 1, 1) -(1, 1, 0, a, 1, 0) -(1, 1, 0, a, 1, a) -(1, 1, 0, a, 1, a + 1) -(1, 1, 0, a, 1, 1) -(1, 1, 0, a + 1, 0, 0) -(1, 1, 0, a + 1, 0, a) -(1, 1, 0, a + 1, 0, a + 1) -(1, 1, 0, a + 1, 0, 1) -(1, 1, 0, a + 1, a, 0) -(1, 1, 0, a + 1, a, a) -(1, 1, 0, a + 1, a, a + 1) -(1, 1, 0, a + 1, a, 1) -(1, 1, 0, a + 1, a + 1, 0) -(1, 1, 0, a + 1, a + 1, a) -(1, 1, 0, a + 1, a + 1, a + 1) -(1, 1, 0, a + 1, a + 1, 1) -(1, 1, 0, a + 1, 1, 0) -(1, 1, 0, a + 1, 1, a) -(1, 1, 0, a + 1, 1, a + 1) -(1, 1, 0, a + 1, 1, 1) -(1, 1, 0, 1, 0, 0) -(1, 1, 0, 1, 0, a) -(1, 1, 0, 1, 0, a + 1) -(1, 1, 0, 1, 0, 1) -(1, 1, 0, 1, a, 0) -(1, 1, 0, 1, a, a) -(1, 1, 0, 1, a, a + 1) -(1, 1, 0, 1, a, 1) -(1, 1, 0, 1, a + 1, 0) -(1, 1, 0, 1, a + 1, a) -(1, 1, 0, 1, a + 1, a + 1) -(1, 1, 0, 1, a + 1, 1) -(1, 1, 0, 1, 1, 0) -(1, 1, 0, 1, 1, a) -(1, 1, 0, 1, 1, a + 1) -(1, 1, 0, 1, 1, 1) -(1, 1, a, 0, 0, 0) -(1, 1, a, 0, 0, a) -(1, 1, a, 0, 0, a + 1) -(1, 1, a, 0, 0, 1) -(1, 1, a, 0, a, 0) -(1, 1, a, 0, a, a) -(1, 1, a, 0, a, a + 1) -(1, 1, a, 0, a, 1) -(1, 1, a, 0, a + 1, 0) -(1, 1, a, 0, a + 1, a) -(1, 1, a, 0, a + 1, a + 1) -(1, 1, a, 0, a + 1, 1) -(1, 1, a, 0, 1, 0) -(1, 1, a, 0, 1, a) -(1, 1, a, 0, 1, a + 1) -(1, 1, a, 0, 1, 1) -(1, 1, a, a, 0, 0) -(1, 1, a, a, 0, a) -(1, 1, a, a, 0, a + 1) -(1, 1, a, a, 0, 1) -(1, 1, a, a, a, 0) -(1, 1, a, a, a, a) -(1, 1, a, a, a, a + 1) -(1, 1, a, a, a, 1) -(1, 1, a, a, a + 1, 0) -(1, 1, a, a, a + 1, a) -(1, 1, a, a, a + 1, a + 1) -(1, 1, a, a, a + 1, 1) -(1, 1, a, a, 1, 0) -(1, 1, a, a, 1, a) -(1, 1, a, a, 1, a + 1) -(1, 1, a, a, 1, 1) -(1, 1, a, a + 1, 0, 0) -(1, 1, a, a + 1, 0, a) -(1, 1, a, a + 1, 0, a + 1) -(1, 1, a, a + 1, 0, 1) -(1, 1, a, a + 1, a, 0) -(1, 1, a, a + 1, a, a) -(1, 1, a, a + 1, a, a + 1) -(1, 1, a, a + 1, a, 1) -(1, 1, a, a + 1, a + 1, 0) -(1, 1, a, a + 1, a + 1, a) -(1, 1, a, a + 1, a + 1, a + 1) -(1, 1, a, a + 1, a + 1, 1) -(1, 1, a, a + 1, 1, 0) -(1, 1, a, a + 1, 1, a) -(1, 1, a, a + 1, 1, a + 1) -(1, 1, a, a + 1, 1, 1) -(1, 1, a, 1, 0, 0) -(1, 1, a, 1, 0, a) -(1, 1, a, 1, 0, a + 1) -(1, 1, a, 1, 0, 1) -(1, 1, a, 1, a, 0) -(1, 1, a, 1, a, a) -(1, 1, a, 1, a, a + 1) -(1, 1, a, 1, a, 1) -(1, 1, a, 1, a + 1, 0) -(1, 1, a, 1, a + 1, a) -(1, 1, a, 1, a + 1, a + 1) -(1, 1, a, 1, a + 1, 1) -(1, 1, a, 1, 1, 0) -(1, 1, a, 1, 1, a) -(1, 1, a, 1, 1, a + 1) -(1, 1, a, 1, 1, 1) -(1, 1, a + 1, 0, 0, 0) -(1, 1, a + 1, 0, 0, a) -(1, 1, a + 1, 0, 0, a + 1) -(1, 1, a + 1, 0, 0, 1) -(1, 1, a + 1, 0, a, 0) -(1, 1, a + 1, 0, a, a) -(1, 1, a + 1, 0, a, a + 1) -(1, 1, a + 1, 0, a, 1) -(1, 1, a + 1, 0, a + 1, 0) -(1, 1, a + 1, 0, a + 1, a) -(1, 1, a + 1, 0, a + 1, a + 1) -(1, 1, a + 1, 0, a + 1, 1) -(1, 1, a + 1, 0, 1, 0) -(1, 1, a + 1, 0, 1, a) -(1, 1, a + 1, 0, 1, a + 1) -(1, 1, a + 1, 0, 1, 1) -(1, 1, a + 1, a, 0, 0) -(1, 1, a + 1, a, 0, a) -(1, 1, a + 1, a, 0, a + 1) -(1, 1, a + 1, a, 0, 1) -(1, 1, a + 1, a, a, 0) -(1, 1, a + 1, a, a, a) -(1, 1, a + 1, a, a, a + 1) -(1, 1, a + 1, a, a, 1) -(1, 1, a + 1, a, a + 1, 0) -(1, 1, a + 1, a, a + 1, a) -(1, 1, a + 1, a, a + 1, a + 1) -(1, 1, a + 1, a, a + 1, 1) -(1, 1, a + 1, a, 1, 0) -(1, 1, a + 1, a, 1, a) -(1, 1, a + 1, a, 1, a + 1) -(1, 1, a + 1, a, 1, 1) -(1, 1, a + 1, a + 1, 0, 0) -(1, 1, a + 1, a + 1, 0, a) -(1, 1, a + 1, a + 1, 0, a + 1) -(1, 1, a + 1, a + 1, 0, 1) -(1, 1, a + 1, a + 1, a, 0) -(1, 1, a + 1, a + 1, a, a) -(1, 1, a + 1, a + 1, a, a + 1) -(1, 1, a + 1, a + 1, a, 1) -(1, 1, a + 1, a + 1, a + 1, 0) -(1, 1, a + 1, a + 1, a + 1, a) -(1, 1, a + 1, a + 1, a + 1, a + 1) -(1, 1, a + 1, a + 1, a + 1, 1) -(1, 1, a + 1, a + 1, 1, 0) -(1, 1, a + 1, a + 1, 1, a) -(1, 1, a + 1, a + 1, 1, a + 1) -(1, 1, a + 1, a + 1, 1, 1) -(1, 1, a + 1, 1, 0, 0) -(1, 1, a + 1, 1, 0, a) -(1, 1, a + 1, 1, 0, a + 1) -(1, 1, a + 1, 1, 0, 1) -(1, 1, a + 1, 1, a, 0) -(1, 1, a + 1, 1, a, a) -(1, 1, a + 1, 1, a, a + 1) -(1, 1, a + 1, 1, a, 1) -(1, 1, a + 1, 1, a + 1, 0) -(1, 1, a + 1, 1, a + 1, a) -(1, 1, a + 1, 1, a + 1, a + 1) -(1, 1, a + 1, 1, a + 1, 1) -(1, 1, a + 1, 1, 1, 0) -(1, 1, a + 1, 1, 1, a) -(1, 1, a + 1, 1, 1, a + 1) -(1, 1, a + 1, 1, 1, 1) -(1, 1, 1, 0, 0, 0) -(1, 1, 1, 0, 0, a) -(1, 1, 1, 0, 0, a + 1) -(1, 1, 1, 0, 0, 1) -(1, 1, 1, 0, a, 0) -(1, 1, 1, 0, a, a) -(1, 1, 1, 0, a, a + 1) -(1, 1, 1, 0, a, 1) -(1, 1, 1, 0, a + 1, 0) -(1, 1, 1, 0, a + 1, a) -(1, 1, 1, 0, a + 1, a + 1) -(1, 1, 1, 0, a + 1, 1) -(1, 1, 1, 0, 1, 0) -(1, 1, 1, 0, 1, a) -(1, 1, 1, 0, 1, a + 1) -(1, 1, 1, 0, 1, 1) -(1, 1, 1, a, 0, 0) -(1, 1, 1, a, 0, a) -(1, 1, 1, a, 0, a + 1) -(1, 1, 1, a, 0, 1) -(1, 1, 1, a, a, 0) -(1, 1, 1, a, a, a) -(1, 1, 1, a, a, a + 1) -(1, 1, 1, a, a, 1) -(1, 1, 1, a, a + 1, 0) -(1, 1, 1, a, a + 1, a) -(1, 1, 1, a, a + 1, a + 1) -(1, 1, 1, a, a + 1, 1) -(1, 1, 1, a, 1, 0) -(1, 1, 1, a, 1, a) -(1, 1, 1, a, 1, a + 1) -(1, 1, 1, a, 1, 1) -(1, 1, 1, a + 1, 0, 0) -(1, 1, 1, a + 1, 0, a) -(1, 1, 1, a + 1, 0, a + 1) -(1, 1, 1, a + 1, 0, 1) -(1, 1, 1, a + 1, a, 0) -(1, 1, 1, a + 1, a, a) -(1, 1, 1, a + 1, a, a + 1) -(1, 1, 1, a + 1, a, 1) -(1, 1, 1, a + 1, a + 1, 0) -(1, 1, 1, a + 1, a + 1, a) -(1, 1, 1, a + 1, a + 1, a + 1) -(1, 1, 1, a + 1, a + 1, 1) -(1, 1, 1, a + 1, 1, 0) -(1, 1, 1, a + 1, 1, a) -(1, 1, 1, a + 1, 1, a + 1) -(1, 1, 1, a + 1, 1, 1) -(1, 1, 1, 1, 0, 0) -(1, 1, 1, 1, 0, a) -(1, 1, 1, 1, 0, a + 1) -(1, 1, 1, 1, 0, 1) -(1, 1, 1, 1, a, 0) -(1, 1, 1, 1, a, a) -(1, 1, 1, 1, a, a + 1) -(1, 1, 1, 1, a, 1) -(1, 1, 1, 1, a + 1, 0) -(1, 1, 1, 1, a + 1, a) -(1, 1, 1, 1, a + 1, a + 1) -(1, 1, 1, 1, a + 1, 1) -(1, 1, 1, 1, 1, 0) -(1, 1, 1, 1, 1, a) -(1, 1, 1, 1, 1, a + 1) -(1, 1, 1, 1, 1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA*vector(v1)[?7h[?12l[?25h[?25l[?7l*vector(v1)[?7h[?12l[?25h[?25l[?7lsage: A*vector(v1) -[?7h[?12l[?25h[?2004l[?7h(0, 1, a + 1, 0, 1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA*vector(v1)[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  print(v1) -....:  if A*vector(v1) == v1 and B*vector(v1) == v1: -....:  for v2 in product(*pr): -....:  if A*vector(v2) == v2 and B*vector(v2) == v2: -....:  print(v1, v2) -....:  for v3 in product(*pr): -....:  if A*vector(v3) == v3 + v2 + a^2*v1 and B*vector(v3) == v3 + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 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[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lan[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() - [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreturn ceil((3*M-2)/4)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - -forv1 in product(*pr): -....:  result += 1[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: result = 0 -....: for v1 in product(*pr): -....:  result += 1 -....:  -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - - [?7h[?12l[?25h[?25l[?7lresult = 0[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: result -[?7h[?12l[?25h[?2004l[?7h4096 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - [?7h[?12l[?25h[?25l[?7lresult[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: result.factor() -[?7h[?12l[?25h[?2004l[?7h2^12 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*v1 and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*v1 and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [26], in () - 6 if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): - 7 for v3 in product(*pr): -----> 8 if A*vector(v3) == vector(v3) + vector(v2) + a**Integer(2)*v1 and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): - 9 print(v1, v2, v3) - -TypeError: can't multiply sequence by non-int of type 'sage.rings.finite_rings.element_givaro.FiniteField_givaroElement' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, 0, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, 0, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, a, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, a, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, a, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, a, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, a + 1, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, a + 1, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, a + 1, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, a + 1, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, 1, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, 1, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, 1, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (0, 0, 1, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, 0, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, 0, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, 0, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, a, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, a, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, a, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, a, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, a + 1, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, a + 1, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, a + 1, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, a + 1, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, 1, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, 1, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, 1, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a, 0, 1, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, 0, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, 0, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, 0, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, a, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, a, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, a, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, a, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, a + 1, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, a + 1, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, a + 1, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, a + 1, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, 1, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, 1, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, 1, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (a + 1, 0, 1, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, 0, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, 0, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, 0, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, a, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, a, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, a, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, a, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, a + 1, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, a + 1, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, a + 1, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, a + 1, 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, 1, 0, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, 1, a, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, 1, a + 1, 0, 0) -(0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0) (1, 0, 1, 1, 0, 0) -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [27], in () - 6 if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): - 7 for v3 in product(*pr): -----> 8 if A*vector(v3) == vector(v3) + vector(v2) + a**Integer(2)*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): - 9 print(v1, v2, v3) - -File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:543, in sage.modules.free_module_element.vector() - 541 - 542 try: ---> 543 from numpy import ndarray - 544 except ImportError: - 545 pass - -File :1053, in _handle_fromlist(module, fromlist, import_, recursive) - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: v1 -[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lL[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrCode[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7listrage(0, 3)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: M = matrix([v1, v1, v1]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix([v1, v1, v1])[?7h[?12l[?25h[?25l[?7lsage: M -[?7h[?12l[?25h[?2004l[?7h[0 0 0 0 0 0] -[0 0 0 0 0 0] -[0 0 0 0 0 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  M = matrix(v1, v2, v3) -....:  if M.rank() == 3: -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3)from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  M = matrix(v1, v2, v3) -....:  if M.rank() == 3: -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  M = matrix(v1, v2, v3) -....:  if M.rank() == 3: -....:  print(v1, v2, v3)from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  M = matrix(v1, v2, v3) -....:  if M.rank() == 3: -....:  print(v1, v2, v3) -[?7h[?12l[?25h[?2004l Input In [31] - print(v1, v2, v3)from itertools import product - ^ -SyntaxError: invalid syntax - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  M = matrix(v1, v2, v3) -....:  if M.rank() == 3: -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  M = matrix(v1, v2, v3) -....:  if M.rank() == 3: -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [32], in () - 7 for v3 in product(*pr): - 8 if A*vector(v3) == vector(v3) + vector(v2) + a**Integer(2)*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -----> 9 M = matrix(v1, v2, v3) - 10 if M.rank() == Integer(3): - 11 print(v1, v2, v3) - -File /ext/sage/9.7/src/sage/matrix/constructor.pyx:643, in sage.matrix.constructor.matrix() - 641 """ - 642 immutable = kwds.pop('immutable', False) ---> 643 M = MatrixArgs(*args, **kwds).matrix() - 644 if immutable: - 645 M.set_immutable() - -File /ext/sage/9.7/src/sage/matrix/args.pyx:355, in sage.matrix.args.MatrixArgs.__init__() - 353 if argi == argc: return - 354 ---> 355 raise TypeError("too many arguments in matrix constructor") - 356 - 357 def __repr__(self): - -TypeError: too many arguments in matrix constructor -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  M = matrix([v1, v2, v3]) -....:  if M.rank() == 3: -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v2) + a^2*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): -....:  M = matrix([v1, v2, v3]) -....:  if M.rank() == 3: -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (0, 0, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a, 0, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (a + 1, 0, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (0, 0, 0, a + 1, 0, 0) (1, 0, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (0, a + 1, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a, a + 1, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (a + 1, a + 1, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a, 0, 0, a + 1, 0, 0) (1, a + 1, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (0, 1, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a, 1, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (a + 1, 1, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (a + 1, 0, 0, a + 1, 0, 0) (1, 1, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (0, a, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a, a, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (a + 1, a, 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, 0, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, 0, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, 0, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, 0, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, a, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, a, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, a, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, a, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, a + 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, a + 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, a + 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, a + 1, 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, 1, 0, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, 1, a, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, 1, a + 1, a + 1, 0) -(0, 0, a, 0, 0, 0) (1, 0, 0, a + 1, 0, 0) (1, a, 1, 1, a + 1, 0) -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [33], in () - 6 if A*vector(v2) == vector(v2) and B*vector(v2) == vector(v2): - 7 for v3 in product(*pr): -----> 8 if A*vector(v3) == vector(v3) + vector(v2) + a**Integer(2)*vector(v1) and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): - 9 M = matrix([v1, v2, v3]) - 10 if M.rank() == Integer(3): - -File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:543, in sage.modules.free_module_element.vector() - 541 - 542 try: ---> 543 from numpy import ndarray - 544 except ImportError: - 545 pass - -File :1053, in _handle_fromlist(module, fromlist, import_, recursive) - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) + a^2*vector(v1) and B*vector(v2) == vector(v2)+ vector(v1): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v1) and B*vector(v3) == vector(v3) +vector(v1): -....:  M = matrix([v1, v2, v3]) -....:  if M.rank() == 3: -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l....:  print(v1, v2, v3) -....: [?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) + a^2*vector(v1) and B*vector(v2) == vector(v2)+ vector(v1): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v1) and B*vector(v3) == vector(v3) +vector(v1): -....:  M = matrix([v1, v2, v3]) -....:  if M.rank() == 3: -....:  print(v1, v2, v3) -....:  -[?7h[?12l[?25h[?2004l(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (0, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (a + 1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 0, 0, 0) (1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (0, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (a + 1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a, 0, 0) (1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (0, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (a + 1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, a + 1, 0, 0) (1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (0, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (a + 1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, 0, 1, 0, 0) (1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (0, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (a + 1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 0, 0, 0) (1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (0, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (a + 1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a, 0, 0) (1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (0, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (a + 1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, a + 1, 0, 0) (1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (0, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (a + 1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a, 1, 0, 0) (1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (0, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (a + 1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, 0, 0, 0) (1, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (0, 1, 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, 0, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, 0, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, 0, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, 0, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, a, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, a, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, a, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, a, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, a + 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, a + 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, a + 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, a + 1, 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, 1, 0, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, 1, a, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, 1, a + 1, 0, a + 1) -(a, 0, 0, 0, 0, 0) (0, a, a + 1, a, 0, 0) (a, 1, 1, 1, 0, a + 1) -^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [34], in () - 6 if A*vector(v2) == vector(v2) + a**Integer(2)*vector(v1) and B*vector(v2) == vector(v2)+ vector(v1): - 7 for v3 in product(*pr): -----> 8 if A*vector(v3) == vector(v3) + vector(v1) and B*vector(v3) == vector(v3) +vector(v1): - 9 M = matrix([v1, v2, v3]) - 10 if M.rank() == Integer(3): - -File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector() - 578 sparse = False - 579 ---> 580 v, R = prepare(v, R, degree) - 581 - 582 M = FreeModule(R, len(v), bool(sparse)) - -File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare() - 676 except TypeError: - 677 pass ---> 678 v = Sequence(v, universe=R, use_sage_types=True) - 679 ring = v.universe() - 680 if not is_Ring(ring): - -File /ext/sage/9.7/src/sage/structure/sequence.py:263, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) - 261 pass - 262 else: ---> 263 if is_MPolynomialRing(universe) or isinstance(universe, BooleanMonomialMonoid) or (is_QuotientRing(universe) and is_MPolynomialRing(universe.cover_ring())): - 264 return PolynomialSequence(x, universe, immutable=immutable, cr=cr, cr_str=cr_str) - 266 return Sequence_generic(x, universe, check, immutable, cr, cr_str, use_sage_types) - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA*vector(v1)[?7h[?12l[?25h[?25l[?7lS = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), - ( ((a + 1)*z0 + z1) * dx, 0 ), - ( (x) * dx, 0 ), - ( (0) * dx, z1/x ), - ( (a*x*z0 + x*z1) * dx, z0*z1/x ), - ( (a*z0 + z1) * dx, z0*z1/x^2 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: from itertools import product -....: pr = [F for _ in range(6)] -....: for v1 in product(*pr): -....:  if A*vector(v1) == vector(v1) and B*vector(v1) == vector(v1): -....:  for v2 in product(*pr): -....:  if A*vector(v2) == vector(v2) + a^2*vector(v1) and B*vector(v2) == vector(v2)+ vector(v1): -....:  for v3 in product(*pr): -....:  if A*vector(v3) == vector(v3) + vector(v1) and B*vector(v3) == vector(v3) +vector(v1): -....:  M = matrix([v1, v2, v3]) -....:  if M.rank() == 3: -....:  print(v1, v2, v3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l - - - - -and B2== vector(v2): - -2+ a^21and B*vector(v3) == vector(v3) + a*vector(v2) + a*vector(v1): - - -()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l - - - - - - - -v1, v2, v3) - -()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() -()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l() -()[?7h[?12l[?25h[?25l[?7l() -[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l[v1, v2, v3]) - -()[?7h[?12l[?25h[?25l[?7l -[][?7h[?12l[?25h[?25l[?7l[] -[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l() -()[?7h[?12l[?25h[?25l[?7l() -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l+ a^21and B*vector(v2) == vector(v2)+ vector(v1): - -1and B3== vector(v3) +vector(v1):[?7h[?12l[?25h[?25l[?7l -[][?7h[?12l[?25h[?25l[?7l[] -[?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l() -()[?7h[?12l[?25h[?25l[?7l() -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis() -  -  -  -  -  -  -  -  -  - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7l= as_cover(P1, [(P1.x)^3, a*(P1.x)^3], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(P1.x)^3], prec = 20)[?7h[?12l[?25h[?25l[?7l(P1.x)^3], prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l5], prec = 20)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^3, (P1.x)^5], prec = 200) -[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__() - 279 try: ---> 280 if a.parent() is not K: - 281 a = K.coerce(a) - -AttributeError: 'tuple' object has no attribute 'parent' - -During handling of the above exception, another exception occurred: - -KeyboardInterrupt Traceback (most recent call last) -Input In [36], in () -----> 1 AS = as_cover(P1, [(P1.x)**Integer(3), (P1.x)**Integer(5)], prec = Integer(200)) - -File :45, in __init__(self, C, list_of_fcts, branch_points, prec) - -File :196, in artin_schreier_transform(power_series, prec) - -File :12, in new_reverse(power_series, prec) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1829 if x: - 1830 raise ValueError("must not specify %s keyword and positional argument" % name) --> 1831 a = self(kwds[name]) - 1832 del kwds[name] - 1833 try: - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() - 1850 x = x[0] - 1851 --> 1852 return self.__u(*x)*(x[0]**self.__n) - 1853 - 1854 def __pari__(self): - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__() - 363 x[0] = a - 364 x = tuple(x) ---> 365 return self.__f(x) - 366 - 367 def _unsafe_mutate(self, i, value): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__() - 281 a = K.coerce(a) - 282 except (TypeError, AttributeError, NotImplementedError): ---> 283 return Polynomial.__call__(self, a) - 284 - 285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial())) - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() - 896 return result - 897 pol._compiled = CompiledPolynomialFunction(pol.list()) ---> 898 return pol._compiled.eval(a) - 899 - 900 def compose_trunc(self, Polynomial other, long n): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval() - 123 cdef object temp - 124 try: ---> 125 pd_eval(self._dag, x, self._coeffs) #see further down - 126 temp = self._dag.value #for an explanation - 127 pd_clean(self._dag) #of these 3 lines - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - - [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (37 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (36 times)] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 505 - 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: ---> 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) - 509 self.value = self.left.value * self.right.value + coeffs[self.index] - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() - 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: - 352 if pd.value is None: ---> 353 pd.eval(vars, coeffs) - 354 pd.hits += 1 - 355 - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() - 507 pd_eval(self.left, vars, coeffs) - 508 pd_eval(self.right, vars, coeffs) ---> 509 self.value = self.left.value * self.right.value + coeffs[self.index] - 510 pd_clean(self.left) - 511 pd_clean(self.right) - -File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__() - 1512 cdef int cl = classify_elements(left, right) - 1513 if HAVE_SAME_PARENT(cl): --> 1514 return (left)._mul_(right) - 1515 if BOTH_ARE_ELEMENT(cl): - 1516 return coercion_model.bin_op(left, right, mul) - -File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_() - 911 cdef LaurentSeries right = right_r - 912 return type(self)(self._parent, ---> 913 self.__u * right.__u, - 914 self.__n + right.__n) - 915 - -File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__() - 1512 cdef int cl = classify_elements(left, right) - 1513 if HAVE_SAME_PARENT(cl): --> 1514 return (left)._mul_(right) - 1515 if BOTH_ARE_ELEMENT(cl): - 1516 return coercion_model.bin_op(left, right, mul) - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_() - 538 """ - 539 prec = self._mul_prec(right_r) ---> 540 return PowerSeries_poly(self._parent, - 541 self.__f * (right_r).__f, - 542 prec=prec, - -File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() - 42 ValueError: series has negative valuation - 43 """ ----> 44 R = parent._poly_ring() - 45 if isinstance(f, Element): - 46 if (f)._parent is R: - -File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) - 958 pass - 959 return False ---> 961 def _poly_ring(self): - 962 """ - 963  Return the underlying polynomial ring used to represent elements of - 964  this power series ring. - (...) - 970  Univariate Polynomial Ring in t over Integer Ring - 971  """ - 972 return self.__poly_ring - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1 = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(F)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l. = PolynomialRing(F)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(2)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, (P1.x)^5], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1 = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7lsage: P1 = superelliptic(x, 1) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1 = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7lRx. = PoynomalRing(GF(2))[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(2)) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7lP1 = supereliptc(x, 1)[?7h[?12l[?25h[?25l[?7lRx. = PoynomalRing(GF(2))[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, (P1.x)^5], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^3, (P1.x)^5], prec = 200) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, (P1.x)^5], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis2(threshold = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(threshold = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = as_cover(P1, [(P1.x)^3, (P1.x)^5], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l7], prec = 20)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(P1, [(P1.x)^3, (P1.x)^7], prec = 200) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(P1, [(P1.x)^3, (P1.x)^7], prec = 200)[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?7h[(1) * dx, - (x^2*z0 + z1) * dx, - (z0) * dx, - (x) * dx, - (x*z0) * dx, - (x^2) * dx, - (x^3) * dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), - ( (x^2*z0 + z1) * dx, 0 ), - ( (z0) * dx, 0 ), - ( (x) * dx, 0 ), - ( (x*z0) * dx, 0 ), - ( (x^2) * dx, 0 ), - ( (x^3) * dx, 0 ), - ( (x^5) * dx, z1/x ), - ( (0) * dx, z0/x ), - ( (x^5*z0 + x*z1) * dx, z0*z1/x ), - ( (x^4) * dx, z1/x^2 ), - ( (x^4*z0 + z1) * dx, z0*z1/x^2 ), - ( (x^3*z0) * dx, z0*z1/x^3 ), - ( (x^2*z0) * dx, z0*z1/x^4 )] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() -[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage -┌────────────────────────────────────────────────────────────────────┐ -│ SageMath version 9.7, Release Date: 2022-09-19 │ -│ Using Python 3.10.5. Type "help()" for help. │ -└────────────────────────────────────────────────────────────────────┘ -]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l5 3 4 2 -9 3 6 4 -9 7 7 5 -13 3 8 6 -13 7 9 7 -13 11 10 8 -17 3 10 8 -17 7 11 9 -17 11 12 10 -17 15 13 11 -21 3 12 10 -21 7 13 11 -21 11 14 12 -21 15 15 13 -21 19 16 14 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -NameError Traceback (most recent call last) -Input In [2], in () -----> 1 C - -NameError: name 'C' is not defined -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1, 0) ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [3], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :327, in coordinates(self, basis) - -TypeError: 'superelliptic' object is not callable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1, 0) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [4], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :338, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1, 0) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) -aux.omega0.omega.cartier() ((-x + 1)/y) dx ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [6], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :339, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) -aux.omega0.omega.cartier() ((-x + 1)/y) dx ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [7], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :340, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) -aux.omega0.omega.cartier() ((-x + 1)/y) dx ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [8], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :340, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function.numerator().exponents()[?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = b[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0] -[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = F.gens()[0][?7h[?12l[?25h[?25l[?7lutom(b[0]).reduce(), (4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0]).reduce(), (4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l() == 4*b[0]+ 6*b[1][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: autom(b[0]) - b[0] -[?7h[?12l[?25h[?2004l[?7h(V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-C.x^6 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^2*C.y + C.x*C.y)) *C.dx[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^6 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^2*C.y + C.x*C.y)) *C.dx -[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-C.x^6 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^2*C.y + C.x*C.y)) *C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-C.x^6 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^2*C.y + C.x*C.y)) *C.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-C.x^6 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^2*C.y + C.x*C.y)) *C.dx).expansion_at_infty() -[?7h[?12l[?25h[?2004l[?7h2*t^-8 + t^-6 + t^-4 + t^-2 + 2 + O(t^2) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].coordinates(basis = b)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lordinates(basis = b)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates() -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (0, [0], 0) -aux V(smth) (0, [0], 0) -aux.omega0.omega.cartier() 0 dx ---------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [13], in () -----> 1 b[Integer(0)].coordinates() - -File :341, in coordinates(self, basis) - -TypeError: 'superelliptic_cech' object is not iterable -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) -aux.omega0.omega.cartier() ((-x + 1)/y) dx ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [14], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :340, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l].coordinates()[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates() -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (0, [0], 0) -aux V(smth) (0, [0], 0) -aux.omega0.omega.cartier() 0 dx ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/misc/functional.py:999, in lift(x) - 998 try: ---> 999 return x.lift() - 1000 except AttributeError: - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'lift' - -During handling of the above exception, another exception occurred: - -ArithmeticError Traceback (most recent call last) -Input In [15], in () -----> 1 b[Integer(0)].coordinates() - -File :341, in coordinates(self, basis) - -File :341, in (.0) - -File /ext/sage/9.7/src/sage/misc/functional.py:1001, in lift(x) - 999 return x.lift() - 1000 except AttributeError: --> 1001 raise ArithmeticError("no lift defined.") - -ArithmeticError: no lift defined. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) -aux.omega0.omega.cartier() ((-x + 1)/y) dx ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [16], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :340, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates() -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (0, [0], 0) -aux V(smth) (0, [0], 0) -aux.omega0.omega.cartier() 0 dx -[, ] ---------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -File /ext/sage/9.7/src/sage/misc/functional.py:999, in lift(x) - 998 try: ---> 999 return x.lift() - 1000 except AttributeError: - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'lift' - -During handling of the above exception, another exception occurred: - -ArithmeticError Traceback (most recent call last) -Input In [17], in () -----> 1 b[Integer(0)].coordinates() - -File :342, in coordinates(self, basis) - -File :342, in (.0) - -File /ext/sage/9.7/src/sage/misc/functional.py:1001, in lift(x) - 999 return x.lift() - 1000 except AttributeError: --> 1001 raise ArithmeticError("no lift defined.") - -ArithmeticError: no lift defined. -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a.f)[?7h[?12l[?25h[?25l[?7lsage: c = C.x.teichmuller() * C.y.teichmuller().diffn() + 3 * (C.x^3).teichmuller() * C.y.teichmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung() . -....: diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld - [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: c = C.de_rham_basis() -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.frobenius()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfc.cordinates()[?7h[?12l[?25h[?25l[?7loc.cordinates()[?7h[?12l[?25h[?25l[?7lrc.cordinates()[?7h[?12l[?25h[?25l[?7lfor c.cordinates()[?7h[?12l[?25h[?25l[?7lac.cordinates()[?7h[?12l[?25h[?25l[?7l c.cordinates()[?7h[?12l[?25h[?25l[?7lic.cordinates()[?7h[?12l[?25h[?25l[?7lnc.cordinates()[?7h[?12l[?25h[?25l[?7lin c.cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in c.coordinates(): -....: [?7h[?12l[?25h[?25l[?7lprint(v1)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ltype(a))[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(a)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(type(a)) -....: [?7h[?12l[?25h[?25l[?7lsage: for a in c.coordinates(): -....:  print(type(a)) -....:  -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [19], in () -----> 1 for a in c.coordinates(): - 2 print(type(a)) - -AttributeError: 'list' object has no attribute 'coordinates' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in c.coordinates(): -....:  print(type(a))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[.cordinates():[?7h[?12l[?25h[?25l[?7l0.cordinates():[?7h[?12l[?25h[?25l[?7l[0].cordinates():[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l -()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(type(a)) -....: [?7h[?12l[?25h[?25l[?7lsage: for a in c[0].coordinates(): -....:  print(type(a)) -....:  -[?7h[?12l[?25h[?2004l - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laIntegers(5)(2)[?7h[?12l[?25h[?25l[?7l Integers(5)(2)[?7h[?12l[?25h[?25l[?7l=Integers(5)(2)[?7h[?12l[?25h[?25l[?7l Integers(5)(2)[?7h[?12l[?25h[?25l[?7lsage: a = Integers(5)(2) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = Integers(5)(2)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: a^3 -[?7h[?12l[?25h[?2004l[?7h3 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ZZ(a) -[?7h[?12l[?25h[?2004l[?7h2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) -aux.omega0.omega.cartier() ((-x + 1)/y) dx ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [24], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :340, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lZZ(a)[?7h[?12l[?25h[?25l[?7la^3[?7h[?12l[?25h[?25l[?7l = Integers(5)(2)[?7h[?12l[?25h[?25l[?7lsage: for a in c[0].coordinates(): -....:  print(type(a))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l.coordinates(): -()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lc =C.de_rham_basis() - [?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates() -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (0, [0], 0) -aux V(smth) (0, [0], 0) -aux.omega0.omega.cartier() 0 dx -[?7h[1, 0] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = matrix([v1, v1, v1])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltrix([v1, v1, v1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l[[])[?7h[?12l[?25h[?25l[?7l[[]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7l,]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l[[])[?7h[?12l[?25h[?25l[?7l6])[?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l4])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = matrix([[4, 4], [6, 4]) -....: [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  -....: [?7h[?12l[?25h[?25l[?7l....:  -....: [?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l....: ; -....: [?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: M = matrix([[4, 4], [6, 4]) -....:  -....:  -....: ; -....: ) -[?7h[?12l[?25h[?2004l Input In [26] - M = matrix([[Integer(4), Integer(4)], [Integer(6), Integer(4)]) - ^ -SyntaxError: closing parenthesis ')' does not match opening parenthesis '[' - -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = matrix([[4, 4], [6, 4]) -....:  -....:  -....: ; -....: )[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l() - [?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: M = matrix([[4, 4], [6, 4]]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7lM = matrix([[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3 -[?7h[?12l[?25h[?2004l[?7h[352 288] -[432 352] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: 352%9 -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l352%9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l%9[?7h[?12l[?25h[?25l[?7l%9[?7h[?12l[?25h[?25l[?7l%9[?7h[?12l[?25h[?25l[?7l2%9[?7h[?12l[?25h[?25l[?7l8%9[?7h[?12l[?25h[?25l[?7l8%9[?7h[?12l[?25h[?25l[?7l8%9[?7h[?12l[?25h[?25l[?7l%9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 288%9 -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0] -[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].coordinates()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[0].r() -[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^3[?7h[?12l[?25h[?25l[?7lutom(b[0]) - b[0][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l(b[0]) - b[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l4b[0][?7h[?12l[?25h[?25l[?7l*b[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]-[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: autom(b[0]) - 4*b[0]-5*b[1] -[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -File :59, in __mul__(self, other) - -File :226, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1002 try: --> 1003 return self(str(element)) - 1004 except TypeError: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 990 element = element.replace("^","**") ---> 991 element = eval(element, d, {}) - 992 except (SyntaxError, NameError): - -File :1, in  - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: - -During handling of the above exception, another exception occurred: - -AttributeError Traceback (most recent call last) -Input In [33], in () -----> 1 autom(b[Integer(0)]) - Integer(4)*b[Integer(0)]-Integer(5)*b[Integer(1)] - -File :301, in __sub__(self, other) - -File :266, in __init__(self, omega0, f) - -File :88, in diffn(self) - -File :100, in diffn(self) - -File :66, in __mul__(self, other) - -File :63, in __mul__(self, other) - -AttributeError: 'superelliptic_function' object has no attribute 'form' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]) - 4*b[0]-5*b[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*b[1][?7h[?12l[?25h[?25l[?7l6*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]) - 4*b[0]-6*b[1] -[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- -KeyboardInterrupt Traceback (most recent call last) -Input In [34], in () -----> 1 autom(b[Integer(0)]) - Integer(4)*b[Integer(0)]-Integer(6)*b[Integer(1)] - -File :393, in autom(self) - -File :266, in __init__(self, omega0, f) - -File :219, in __sub__(self, other) - -File :229, in __add__(self, other) - -File :65, in __mul__(self, other) - -File :82, in __pow__(self, exp) - -File :14, in __init__(self, C, g) - -File :216, in reduction(C, g) - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) - 636 ring_one = self.ring().one() - 637 try: ---> 638 return self._element_class(self, x, ring_one, coerce=coerce) - 639 except (TypeError, ValueError): - 640 pass - -File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() - 112 FieldElement.__init__(self, parent) - 113 if coerce: ---> 114 self.__numerator = parent.ring()(numerator) - 115 self.__denominator = parent.ring()(denominator) - 116 else: - -File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() - 895 if mor is not None: - 896 if no_extra_args: ---> 897 return mor._call_(x) - 898 else: - 899 return mor._call_with_args(x, args, kwds) - -File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() - 154 cdef Parent C = self._codomain - 155 try: ---> 156 return C._element_constructor(x) - 157 except Exception: - 158 if print_warnings: - -File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() - 1001 - 1002 try: --> 1003 return self(str(element)) - 1004 except TypeError: - 1005 pass - -File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() - 192 except AttributeError: - 193 return super().__repr__() ---> 194 result = reprfunc() - 195 if isinstance(result, str): - 196 return result - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_() - 2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3 - 2689 """ --> 2690 return self._repr() - 2691 - 2692 def _latex_(self, name=None): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr() - 2654 if n != m-1: - 2655 s += " + " --> 2656 x = y = repr(x) - 2657 if y.find("-") == 0: - 2658 y = y[1:] - -File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() - 192 except AttributeError: - 193 return super().__repr__() ---> 194 result = reprfunc() - 195 if isinstance(result, str): - 196 return result - -File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:340, in sage.rings.fraction_field_FpT.FpTElement._repr_() - 338 return repr(self.numer()) - 339 else: ---> 340 numer_s = repr(self.numer()) - 341 denom_s = repr(self.denom()) - 342 if '-' in numer_s or '+' in numer_s: - -File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() - 192 except AttributeError: - 193 return super().__repr__() ---> 194 result = reprfunc() - 195 if isinstance(result, str): - 196 return result - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_() - 2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3 - 2689 """ --> 2690 return self._repr() - 2691 - 2692 def _latex_(self, name=None): - -File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2667, in sage.rings.polynomial.polynomial_element.Polynomial._repr() - 2665 else: - 2666 var = "" --> 2667 s += "%s%s"%(x,var) - 2668 s = s.replace(" + -", " - ") - 2669 s = re.sub(r' 1(\.0+)?\*',' ', s) - -File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() - -KeyboardInterrupt: -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]) - 4*b[0]-6*b[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l()4*b[0][?7h[?12l[?25h[?25l[?7l([]4*b[0][?7h[?12l[?25h[?25l[?7l[4*b[0][?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l4*b[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 4*b[0] -[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^5 + x^3)/y) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^5 + x^3)/y) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: 6*b[1] -[?7h[?12l[?25h[?2004l[?7h(V(((-x^4)/(x^2*y - y)) dx), V(((x^2 + 2)/x^2)*y), V(((-x^4)/(x^2*y - y)) dx) + dV([((2*x^2 + 1)/x^2)*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l = C2.de_rhm_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A = 4*b[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C2.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B = 6*b[1] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: C = autom(b[0]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = autom(b[0])[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: C - A - B -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [40], in () -----> 1 C - A - B - -File :301, in __sub__(self, other) - -File :219, in __sub__(self, other) - -File :229, in __add__(self, other) - -File :65, in __mul__(self, other) - -AttributeError: 'superelliptic_drw_cech' object has no attribute 'x' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC - A - B[?7h[?12l[?25h[?25l[?7lsage: C -[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 + x^6 - x^4 + x^3 - 1)/(x^2*y - x*y)) dx) + dV([((2*x^3 + 2*x + 1)/(x^2 + 2*x))*y]), V((1/(x + 1))*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 + x^6 - x^4 + x^3 - 1)/(x^2*y - x*y)) dx) + dV([((2*x^4 + 2*x^3 + x^2 + x + 1)/(x^3 + 2*x))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) -aux.omega0.omega.cartier() ((-x + 1)/y) dx ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [42], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :340, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l - A - B[?7h[?12l[?25h[?25l[?7l=autom(b[0])[?7h[?12l[?25h[?25l[?7lB6*b[1][?7h[?12l[?25h[?25l[?7lA40[?7h[?12l[?25h[?25l[?7lsage: A = 4*b[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = 4*b[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l - A - B[?7h[?12l[?25h[?25l[?7l=autom(b[0])[?7h[?12l[?25h[?25l[?7lB6*b[1][?7h[?12l[?25h[?25l[?7lsage: B = 6*b[1] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = 6*b[1][?7h[?12l[?25h[?25l[?7lA40[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l - A - B[?7h[?12l[?25h[?25l[?7l=autom(b[0])[?7h[?12l[?25h[?25l[?7lsage: C = autom(b[0]) -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = autom(b[0])[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: C-A-B -[?7h[?12l[?25h[?2004l[?7h(V(((-x^6 + x^3 - x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V(((2*x^3 + 2*x^2 + 1)/(x^3 + x^2))*y), V(((-x^6 + x^3 - x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2/x^2*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC-A-B[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA-B[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C-A-B[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: (C-A-B).omega0.omega.frobenius -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [47], in () -----> 1 (C-A-B).omega0.omega.frobenius - -AttributeError: 'superelliptic_form' object has no attribute 'frobenius' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C-A-B).omega0.omega.frobenius[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C-A-B).omega0.omega.frobenius() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [48], in () -----> 1 (C-A-B).omega0.omega.frobenius() - -AttributeError: 'superelliptic_form' object has no attribute 'frobenius' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C-A-B).omega0.omega.frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C-A-B).omega0.omega.F() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [49], in () -----> 1 (C-A-B).omega0.omega.F() - -AttributeError: 'superelliptic_form' object has no attribute 'F' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C-A-B).omega0.omega.F()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lf()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7lo()[?7h[?12l[?25h[?25l[?7lb()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7lu()[?7h[?12l[?25h[?25l[?7ls()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C-A-B).omega0.frobenius() -[?7h[?12l[?25h[?2004l[?7h((x^2 + x + 1)/(x^2*y + x*y)) dx -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].r()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0] -[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y])) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l(1, 0) -aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) -aux.omega0.omega.cartier() ((-x + 1)/y) dx ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [52], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :340, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller().diffn() -[?7h[?12l[?25h[?2004l[?7h[1] d[x] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004laux.h2, decomposition_g0_g8(aux.h2, prec=prec) ((x^4 + x^2 + 1)/x^3)*y (x*y, 1/x^3*y, 1/x*y) ((x^4 + 2)/x^3)*y -aux.h2, decomposition_g0_g8(aux.h2, prec=prec) (x^6/(x^2 + 2))*y ((x^6/(x^2 + 2))*y, 0, 0) (x^6/(x^2 + 2))*y -(1, 0) -aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) -aux.omega0.omega.cartier() ((-x + 1)/y) dx ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [54], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :340, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y[?7h[?12l[?25h[?25l[?7lsage: ((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y -[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)/x^3)*y -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y[?7h[?12l[?25h[?25l[?7le((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcomposition_omega0_omega8(fff)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff)[1].expansion_at_infty() - decomposition_g0_g8  - decomposition_omega0_omega8 - - - [?7h[?12l[?25h[?25l[?7lg0_g8 - decomposition_g0_g8  - - [?7h[?12l[?25h[?25l[?7l((3*a).f) - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y) -[?7h[?12l[?25h[?2004l[?7h(x*y, 1/x^3*y, 1/x*y) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  - - - [?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]+[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(((C.x^4 + C.x^ 2 -....:  + C.one)/C.x^3)*C.y)[?7h[?12l[?25h[?25l[?7l( -)[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y)[0] + decomposition_g0_g8(((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y)[1]+decomposition_g0_g8(((C.x^4 + C.x^ 2 -....:  + C.one)/C.x^3)*C.y)[2] - ((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y)[0] + decomposition_g0_g8(((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y)[1]+decomposition_g0_g8(((C.x^4 + C.x^ 2 -....:  + C.one)/C.x^3)*C.y)[2] - ((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7ld - [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lposition_g0_g8(((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y)[0] + decomposition_g0_g8(((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y)[1]+decomposition_g0_g8(((C.x^4 + C.x^ 2 -....:  + C.one)/C.x^3)*C.y)[2] - ((C.x^4 + C.x^2 + C.one)/C.x^3)*C.y[?7h[?12l[?25h[?25l[?7losition -....:  + C.one)/C.x decomposition 2 + C.one)/C.x^3)*C.y - decomposition_g0_g8  - decomposition_omega0_omega8 - - [?7h[?12l[?25h[?25l[?7l - decomposition  - - - [?7h[?12l[?25h[?25l[?7l_g0_g8 -  decomposition  - decomposition_g0_g8 [?7h[?12l[?25h[?25l[?7lomea0_omega8 - - decomposition_g0_g8  - decomposition_omega0_omega8[?7h[?12l[?25h[?25l[?7l(fff)[1].expansion_at_infty() - - - -[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lxi.omega0)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(C.x*(C.y)^(-1).C.dx) -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -AttributeError Traceback (most recent call last) -Input In [58], in () -----> 1 decomposition_omega0_omega8(C.x*(C.y)**(-Integer(1)).C.dx) - -File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() - 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' - 493 """ ---> 494 return self.getattr_from_category(name) - 495 - 496 cdef getattr_from_category(self, name): - -File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() - 505 else: - 506 cls = P._abstract_element_class ---> 507 return getattr_from_other_class(self, cls, name) - 508 - 509 def __dir__(self): - -File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() - 359 dummy_error_message.cls = type(self) - 360 dummy_error_message.name = name ---> 361 raise AttributeError(dummy_error_message) - 362 attribute = attr - 363 # Check for a descriptor (__get__ in Python) - -AttributeError: 'sage.rings.integer.Integer' object has no attribute 'C' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(C.x*(C.y)^(-1).C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()C.dx)[?7h[?12l[?25h[?25l[?7l()*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(C.x*(C.y)^(-1)*C.dx) -[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 0 dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(C.x*(C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(C.x*(C.y)^(-1)*C.dx + (C.x)^(-2)*C.dx) -[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 0 dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(C.x*(C.y)^(-1)*C.dx + (C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l(C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8((C.x)^(-2)*C.dx) -[?7h[?12l[?25h[?2004l[?7h(0 dx, 0 dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-2)*C.dx).residue() -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).residue()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)*C.dx).residue()[?7h[?12l[?25h[?25l[?7l1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-1)*C.dx).residue() -[?7h[?12l[?25h[?2004l[?7h1 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004laux.h2, decomposition_g0_g8(aux.h2, prec=prec) ((x^4 + x^2 + 1)/x^3)*y (x*y, 2/x^3*y, 1/x*y) ((x^4 + 1)/x^3)*y -component, q, r 0 0 0 -component, q, r (2*x^6 + 2*x^4 + 1)/x 2*x^5 + 2*x^3 1 -aux.h2, decomposition_g0_g8(aux.h2, prec=prec) (x^6/(x^2 + 2))*y ((x^6/(x^2 + 2))*y, 0, 0) (x^6/(x^2 + 2))*y -component, q, r 0 0 0 -component, q, r (2*x^10 + 2*x^8 + 2*x^6 + 2)/(x^2 + 2) 2*x^8 + x^6 2 -(1, 0) -aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y])) -aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx)) -aux.omega0.omega.cartier() ((-x + 1)/y) dx ---------------------------------------------------------------------------- -KeyError Traceback (most recent call last) -Input In [64], in () -----> 1 load('init.sage') - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :28, in  - -File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() - 173 - 174 if sage.repl.load.is_loadable_filename(filename): ---> 175 sage.repl.load.load(filename, globals()) - 176 return - 177 - -File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) - 270 add_attached_file(fpath) - 271 with open(fpath) as f: ---> 272 exec(preparse_file(f.read()) + "\n", globals) - 273 elif ext == '.spyx' or ext == '.pyx': - 274 if attach: - -File :17, in  - -File :340, in coordinates(self, basis) - -File :66, in coordinates(self) - -KeyError: (1, 1) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8((C.x)^(-2)*C.dx) -[?7h[?12l[?25h[?2004lcomponent, q, r 0 0 0 -component, q, r 0 0 0 -[?7h(0 dx, 0 dx) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lonvert_superfct_into_AS(a.f)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().residue()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-2)*C.dx).jth_component() -[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- -TypeError Traceback (most recent call last) -Input In [66], in () -----> 1 ((C.x)**(-Integer(2))*C.dx).jth_component() - -TypeError: superelliptic_form.jth_component() missing 1 required positional argument: 'j' -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-2)*C.dx).jth_component(0) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-2)*C.dx).jth_component(1) -[?7h[?12l[?25h[?2004l[?7h0 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-2)*C.dx).jth_component(2) -[?7h[?12l[?25h[?2004l[?7h(x^2 + 2)/x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() -[?7h[?12l[?25h[?2004l[?7h[(1/y) dx] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.expanson(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() -[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7lsage: a = C.de_rham_basis()[0] -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l.f[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.coordinates() -[?7h[?12l[?25h[?2004l[?7h(1, 0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.coordinates()[?7h[?12l[?25h[?25l[?7l = C.e_rham_basis()[0][?7h[?12l[?25h[?25l[?7lC.de_rham_bsis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.x).jth_component(2)[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-2)*C.dx).jth_component(2) -[?7h[?12l[?25h[?2004l[?7h(x^2 + 2)/x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component(2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-2)*C.dx).jth_component(0) -[?7h[?12l[?25h[?2004l[?7h(x^2 + 2)/x -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') -[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-2)*C.dx).jth_component(0) -[?7h[?12l[?25h[?2004l[?7h1/x^2 -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7lC)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l.)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7ly)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l^(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l-)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l1)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l*(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(0) +;152m)[?7h[?12l[?25h[?25l[?7l^(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l-)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l1)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l*(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(0) [?7h[?12l[?25h[?2004l[?7h0 [?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(1) [?7h[?12l[?25h[?2004l[?7h1/x^2 @@ -56968,4 +23778,6521 @@ File :63, in __mul__(self, other) [?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() [?7h[?12l[?25h[?2004l ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ gcd .. -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git \ No newline at end of file +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status +On branch master +Your branch is up to date with 'origin/master'. + +Changes not staged for commit: + (use "git add ..." to update what will be committed) + (use "git restore ..." to discard changes in working directory) + modified: sage/.run.term-0.term + modified: sage/drafty/draft.sage + modified: sage/superelliptic_drw/de_rham_witt_lift.sage + modified: sage/superelliptic_drw/regular_form.sage + modified: sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage + modified: sage/superelliptic_drw/superelliptic_drw_cech.sage + +Untracked files: + (use "git add ..." to include in what will be committed) + .crystalline_p2.ipynb.sage-jupyter2 + .deRhamComputation.ipynb.sage-jupyter2 + .elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2 + .git.x11-0.term + .superelliptic.ipynb.sage-jupyter2 + .superelliptic_alpha.ipynb.sage-jupyter2 + .superelliptic_arbitrary_field.ipynb.sage-jupyter2 + git.x11 + sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2 + sage/drafty/2gpcovers.sage + sage/drafty/as_cartier.sage + sage/drafty/better_trace.sage + sage/drafty/cartier_image_representation.sage + sage/drafty/convert_superelliptic_into_AS.sage + sage/drafty/draft4.sage + sage/drafty/draft5.sage + sage/drafty/draft6.sage + sage/drafty/draft7.sage + sage/drafty/draft8.sage + sage/drafty/draft_klein_covers.sage + sage/drafty/lift_to_de_rham.sage + sage/drafty/pole_numbers.sage + sage/superelliptic/frobenius_kernel.sage + superelliptic_arbitrary_field.ipynb + +no changes added to commit (use "git add" and/or "git commit -a") +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit - mm ""p"r"z"e"d" "z"m"i"n"a"""a"n"a" "w" "e"x"p"a"n"s"i"o"n" "a"t" "i"n"f"t"y" "w" "s"u"p"e"r"e"l"l"i"p"t"i"c" +[master eda1cca] przed zmiana w expansion at infty w superelliptic + 6 files changed, 1599 insertions(+), 62 deletions(-) + rewrite sage/drafty/draft.sage (94%) +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push +Username for 'https://git.wmi.amu.edu.pl': jgarnek +Password for 'https://jgarnek@git.wmi.amu.edu.pl': +Enumerating objects: 21, done. +Counting objects: 4% (1/21) Counting objects: 9% (2/21) Counting objects: 14% (3/21) Counting objects: 19% (4/21) Counting objects: 23% (5/21) Counting objects: 28% (6/21) Counting objects: 33% (7/21) Counting objects: 38% (8/21) Counting objects: 42% (9/21) Counting objects: 47% (10/21) Counting objects: 52% (11/21) Counting objects: 57% (12/21) Counting objects: 61% (13/21) Counting objects: 66% (14/21) Counting objects: 71% (15/21) Counting objects: 76% (16/21) Counting objects: 80% (17/21) Counting objects: 85% (18/21) Counting objects: 90% (19/21) Counting objects: 95% (20/21) Counting objects: 100% (21/21) Counting objects: 100% (21/21), done. +Delta compression using up to 4 threads +Compressing objects: 9% (1/11) Compressing objects: 18% (2/11) Compressing objects: 27% (3/11) Compressing objects: 36% (4/11) Compressing objects: 45% (5/11) Compressing objects: 54% (6/11) Compressing objects: 63% (7/11) Compressing objects: 72% (8/11) Compressing objects: 81% (9/11) Compressing objects: 90% (10/11) Compressing objects: 100% (11/11) Compressing objects: 100% (11/11), done. +Writing objects: 9% (1/11) Writing objects: 18% (2/11) Writing objects: 27% (3/11) Writing objects: 36% (4/11) Writing objects: 45% (5/11) Writing objects: 54% (6/11) Writing objects: 63% (7/11) Writing objects: 72% (8/11) Writing objects: 81% (9/11) Writing objects: 90% (10/11) Writing objects: 100% (11/11) Writing objects: 100% (11/11), 12.06 KiB | 81.00 KiB/s, done. +Total 11 (delta 9), reused 0 (delta 0) +remote: . Processing 1 references +remote: Processed 1 references in total +To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git + a9d055a..eda1cca master -> master +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage/; sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: load('tests + tests  + tests.sage + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + tests  + + [?7h[?12l[?25h[?25l[?7l. + + +[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') +[?7h[?12l[?25h[?2004lExpansion at infty test: +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [1], in () +----> 1 load('tests.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :3, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +NameError: name 'superelliptic' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') +[?7h[?12l[?25h[?2004lExpansion at infty test: +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [3], in () +----> 1 load('tests.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :3, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :8, in  + +File :120, in expansion_at_infty(self, place, prec) + +NameError: name 'fct' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') +[?7h[?12l[?25h[?2004lExpansion at infty test: +--------------------------------------------------------------------------- +UnboundLocalError Traceback (most recent call last) +Input In [5], in () +----> 1 load('tests.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :3, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :8, in  + +File :115, in expansion_at_infty(self, place, prec) + +UnboundLocalError: local variable 'f' referenced before assignment +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage') +[?7h[?12l[?25h[?2004lExpansion at infty test: +True +True True +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [8], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :11, in  + +File :44, in crystalline_cohomology_basis(self, prec, info) + +File :29, in de_rham_witt_lift(cech_class, prec) + +File :7, in decomposition_g0_g8(fct, prec) + +File :107, in coordinates(self, basis, basis_holo, prec) + +File :79, in serre_duality_pairing(self, fct, prec) + +File :143, in expansion_at_infty(self, place, prec) + +TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [9], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :11, in  + +File :44, in crystalline_cohomology_basis(self, prec, info) + +File :29, in de_rham_witt_lift(cech_class, prec) + +File :7, in decomposition_g0_g8(fct, prec) + +File :107, in coordinates(self, basis, basis_holo, prec) + +File :79, in serre_duality_pairing(self, fct, prec) + +File :143, in expansion_at_infty(self, place, prec) + +TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly^2[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn().expansion_at_infty() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [10], in () +----> 1 C.y.diffn().expansion_at_infty() + +File :143, in expansion_at_infty(self, place, prec) + +TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTraceback (most recent call last): + + File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code + exec(code_obj, self.user_global_ns, self.user_ns) + + Input In [11] in  + load('init.sage') + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :3 in  + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :144 + dx_series = C.x_series[place = place] + ^ +SyntaxError: invalid syntax. Maybe you meant '==' or ':=' instead of '='? + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [12], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :11, in  + +File :44, in crystalline_cohomology_basis(self, prec, info) + +File :29, in de_rham_witt_lift(cech_class, prec) + +File :7, in decomposition_g0_g8(fct, prec) + +File :107, in coordinates(self, basis, basis_holo, prec) + +File :79, in serre_duality_pairing(self, fct, prec) + +File :145, in expansion_at_infty(self, place, prec) + +TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn().expansion_at_infty() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [13], in () +----> 1 C.y.diffn().expansion_at_infty() + +File :145, in expansion_at_infty(self, place, prec) + +TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [14], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :11, in  + +File :44, in crystalline_cohomology_basis(self, prec, info) + +File :32, in de_rham_witt_lift(cech_class, prec) + +File :37, in decomposition_omega0_omega8(omega, prec) + +ValueError: (((4*x^50 + x^46 + 2*x^44 + 2*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + x^32 + 2*x^28 + 3*x^22 + 4*x^18 + x^16 + x^14 + x^12 + 3*x^10 + 3*x^6 + 4*x^4 + 1)/(x^30 + 3*x^28 + 3*x^26 + x^24))*y) dx has non zero residue! +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 2*C.y*C.y.diffn() +[?7h[?12l[?25h[?2004l[?7h(-2*x^2 + 1) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y*C.y.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 2*C.y*C.y.diffn().expansion_at_infty() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File :58, in __mul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + +AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'form' + +During handling of the above exception, another exception occurred: + +AttributeError Traceback (most recent call last) +Input In [17], in () +----> 1 Integer(2)*C.y*C.y.diffn().expansion_at_infty() + +File :63, in __mul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y*C.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.y*C.y.difn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (2*C.y*C.y.diffn()).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h3*t^-6 + 2*t^-2 + 4*t^2 + t^6 + 4*t^10 + 3*t^14 + 2*t^18 + 3*t^22 + 2*t^26 + 3*t^30 + 4*t^34 + t^38 + 4*t^42 + t^46 + 4*t^50 + O(t^94) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.y*C.y.diffn()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l^).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l ).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l-).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l ).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l-).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (-C.x).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h4*t^-2 + t^2 + t^6 + 2*t^10 + 4*t^18 + 2*t^22 + 2*t^26 + 4*t^30 + 2*t^38 + t^42 + t^46 + 2*t^50 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ldx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-C.dx).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h4*t^-2 + t^2 + t^6 + 2*t^10 + 4*t^18 + 2*t^22 + 2*t^26 + 4*t^30 + 2*t^38 + t^42 + t^46 + 2*t^50 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lxexpasion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.diffn().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.x.difn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: -C.x.diffn().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h4*t^-2 + t^2 + t^6 + 2*t^10 + 4*t^18 + 2*t^22 + 2*t^26 + 4*t^30 + 2*t^38 + t^42 + t^46 + 2*t^50 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpasion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7ht^-3 + 4*t + 4*t^5 + 3*t^9 + t^17 + 3*t^21 + 3*t^25 + t^29 + 3*t^37 + 4*t^41 + 4*t^45 + 3*t^49 + O(t^97) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lxdiff().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lyprec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyC.y.expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7lyC.y.expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l C.y.expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l=C.y.expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l C.y.expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: yy = C.y.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: xx = C.x.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2- (xx^3 - xx + 1)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l- (xx^3 - xx + 1)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: yy^2 - (xx^3 - xx) +[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 3*t^2 + 3*t^6 + t^10 + 2*t^18 + t^22 + t^26 + 2*t^30 + t^38 + 3*t^42 + 3*t^46 + t^50 + O(t^94) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^3 - xx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x)[?7h[?12l[?25h[?25l[?7l+ x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: yy^2 - (xx^3 + xx) +[?7h[?12l[?25h[?2004l[?7hO(t^94) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lyprec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiff().expansion_at_infty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h4*t^-3 + t^5 + 2*t^9 + 4*t^17 + 2*t^21 + 2*t^25 + 4*t^29 + 2*t^37 + t^41 + t^45 + 2*t^49 + O(t^97) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^3 + xx)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn() +[?7h[?12l[?25h[?2004l[?7h((-x^2 - 2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lxexpasion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiff().expansion_at_infty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.diffn() +[?7h[?12l[?25h[?2004l[?7h1 dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.diffn()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.x.diffn().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +Computing 0. basis element +Computing 1. basis element +Computing 2. basis element +Computing 3. basis element +Computing 4. basis element +Computing 5. basis element +Computing 6. basis element +Computing 7. basis element +Computing 8. basis element +Computing 9. basis element +Computing 10. basis element +Computing 11. basis element +Computing 12. basis element +Computing 13. basis element +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1 = C1.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: B1 +[?7h[?12l[?25h[?2004l[?7h[([(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^114 + 3*x^110 + x^108 + 2*x^106 + 3*x^104 + x^100 + x^90 + 3*x^88 + 2*x^84 + 3*x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 2*x^70 + x^66 + 3*x^64 + 4*x^62 + x^60 + x^58 + 3*x^56 + 2*x^48 + 3*x^44 + 3*x^42 + 2*x^36 + x^34 + 2*x^32 + 4*x^30 + 2*x^28 + 4*x^26 + 2*x^24 + 3*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y), [(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^34 + 4*x^32 + 4*x^30 + 3*x^28 + 3*x^26 + 3*x^24 + 2*x^22 + 4*x^20 + 4*x^16 + x^14 + x^12 + 3*x^10 + x^8 + 4*x^6 + 3*x^4 + x^2 + 2)/(x^42 + 2*x^38 + 3*x^34 + 3*x^32 + 4*x^30 + 2*x^28 + 2*x^22 + x^18 + 3*x^12 + 4*x^10 + x^8 + 3*x^6 + x^4))*y])), + ([(1/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 - 2*x^31 + 2*x^25 - 2*x^23 + x^21 - 2*x^19 + x^17 - x^15 - x^13 + 2*x^11 - 2*x^9 - 2*x^7 + x^5 + x^3 + x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^119 + 3*x^115 + x^113 + 2*x^111 + 3*x^109 + x^105 + x^95 + 3*x^93 + 2*x^89 + 3*x^87 + 2*x^85 + 2*x^83 + 3*x^81 + 2*x^75 + x^71 + 3*x^69 + 4*x^67 + x^65 + x^63 + 3*x^61 + 2*x^53 + 3*x^49 + 3*x^47 + 2*x^41 + x^39 + 2*x^37 + 4*x^35 + 2*x^33 + 4*x^31 + 2*x^29 + 3*x^25 + 2*x^23 + 4*x^21 + 3*x^19 + 4*x^15 + 4*x^13 + 4*x^11 + 4*x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^88 + 4*x^84 + x^82 + 3*x^80 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + x^58 + 3*x^56 + 2*x^54 + 3*x^52 + x^50 + 4*x^46 + 3*x^44 + x^42 + 2*x^40 + x^38 + 3*x^36 + 2*x^34 + 4*x^28 + x^26 + 2*x^24 + 4*x^22 + x^20 + x^18 + 4*x^16 + 2*x^14 + 4*x^12 + 3*x^8 + 3*x^4 + 4*x^2 + 3)/x^7)*y), [(1/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 - 2*x^31 + 2*x^25 - 2*x^23 + x^21 - 2*x^19 + x^17 - x^15 - x^13 + 2*x^11 - 2*x^9 - 2*x^7 + x^5 + x^3 + x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + 3*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + x^14 + 4*x^12 + 2*x^10 + 4*x^8 + 2*x^4 + 2*x^2 + 2)/(x^45 + 2*x^41 + 3*x^37 + 3*x^35 + 4*x^33 + 2*x^31 + 2*x^25 + x^21 + 3*x^15 + 4*x^13 + x^11 + 3*x^9 + x^7))*y])), + ([(x/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 - x^34 + x^32 - 2*x^30 + 2*x^28 - x^26 - 2*x^24 - 2*x^20 - 2*x^18 - 2*x^16 + x^14 + x^12 + x^10 - 2*x^8 + x^6 + 2*x^4 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^124 + 3*x^120 + x^118 + 2*x^116 + 3*x^114 + x^110 + x^100 + 3*x^98 + 2*x^94 + 3*x^92 + 2*x^90 + 2*x^88 + 3*x^86 + 2*x^80 + x^76 + 3*x^74 + 4*x^72 + x^70 + x^68 + 3*x^66 + 2*x^58 + 3*x^54 + 3*x^52 + 2*x^46 + x^44 + 2*x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 2*x^34 + 3*x^30 + 2*x^28 + 4*x^26 + 3*x^24 + 4*x^20 + 4*x^18 + 4*x^16 + 4*x^14)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^92 + 4*x^88 + x^86 + 3*x^84 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 4*x^50 + 3*x^48 + x^46 + 2*x^44 + x^42 + 3*x^40 + 2*x^38 + 4*x^32 + x^30 + 2*x^28 + 4*x^26 + x^24 + x^22 + 4*x^20 + 2*x^18 + 4*x^16 + 3*x^12 + 3*x^8 + 4*x^6 + 3*x^4 + 3)/x^6)*y), [(x/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 - x^34 + x^32 - 2*x^30 + 2*x^28 - x^26 - 2*x^24 - 2*x^20 - 2*x^18 - 2*x^16 + x^14 + x^12 + x^10 - 2*x^8 + x^6 + 2*x^4 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^36 + 3*x^34 + 3*x^32 + x^30 + 4*x^28 + 3*x^26 + 2*x^24 + 4*x^22 + 2*x^20 + 4*x^16 + 4*x^14 + 4*x^12 + 3*x^8 + 4*x^4 + x^2 + 2)/(x^44 + 2*x^40 + 3*x^36 + 3*x^34 + 4*x^32 + 2*x^30 + 2*x^24 + x^20 + 3*x^14 + 4*x^12 + x^10 + 3*x^8 + x^6))*y])), + ([(x^2/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^33 + 2*x^31 + x^29 - x^27 + x^25 - x^21 - x^19 + 2*x^17 + 2*x^15 - x^13 - 2*x^11 + 2*x^9 + x^7 + 2*x^5 + x^3 + 2*x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^129 + 3*x^125 + x^123 + 2*x^121 + 3*x^119 + x^115 + x^105 + 3*x^103 + 2*x^99 + 3*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 2*x^85 + x^81 + 3*x^79 + 4*x^77 + x^75 + x^73 + 3*x^71 + 2*x^63 + 3*x^59 + 3*x^57 + 2*x^51 + x^49 + 2*x^47 + 4*x^45 + 2*x^43 + 4*x^41 + 2*x^39 + 3*x^35 + 2*x^33 + 4*x^31 + 3*x^29 + 4*x^25 + 4*x^23 + 4*x^21 + 4*x^19)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^7)*y), [(x^2/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^33 + 2*x^31 + x^29 - x^27 + x^25 - x^21 - x^19 + 2*x^17 + 2*x^15 - x^13 - 2*x^11 + 2*x^9 + x^7 + 2*x^5 + x^3 + 2*x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^45 + 2*x^41 + 3*x^37 + 3*x^35 + 4*x^33 + 2*x^31 + 2*x^25 + x^21 + 3*x^15 + 4*x^13 + x^11 + 3*x^9 + x^7))*y])), + ([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^134 + 3*x^130 + x^128 + 2*x^126 + 3*x^124 + x^120 + x^110 + 3*x^108 + 2*x^104 + 3*x^102 + 2*x^100 + 2*x^98 + 3*x^96 + 2*x^90 + x^86 + 3*x^84 + 4*x^82 + x^80 + x^78 + 3*x^76 + 2*x^68 + 3*x^64 + 3*x^62 + 2*x^56 + x^54 + 2*x^52 + 4*x^50 + 2*x^48 + 4*x^46 + 2*x^44 + 3*x^40 + 2*x^38 + 4*x^36 + 3*x^34 + 4*x^30 + 4*x^28 + 4*x^26 + 4*x^24)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^2)*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])), + ([(x^4/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 + x^31 - x^29 - 2*x^27 + 2*x^23 - x^21 + x^19 + 2*x^15 + x^13 - x^11 - x^9 + x^5 + x^3 - x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^139 + 3*x^135 + x^133 + 2*x^131 + 3*x^129 + x^125 + x^115 + 3*x^113 + 2*x^109 + 3*x^107 + 2*x^105 + 2*x^103 + 3*x^101 + 2*x^95 + x^91 + 3*x^89 + 4*x^87 + x^85 + x^83 + 3*x^81 + 2*x^73 + 3*x^69 + 3*x^67 + 2*x^61 + x^59 + 2*x^57 + 4*x^55 + 2*x^53 + 4*x^51 + 2*x^49 + 3*x^45 + 2*x^43 + 4*x^41 + 3*x^39 + 4*x^35 + 4*x^33 + 4*x^31 + 4*x^29)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^106 + 4*x^102 + x^100 + 3*x^98 + 4*x^94 + 2*x^92 + 4*x^90 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^78 + x^76 + 3*x^74 + 2*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + x^60 + 2*x^58 + x^56 + 3*x^54 + 2*x^52 + 4*x^46 + x^44 + 2*x^42 + 4*x^40 + x^38 + x^36 + 4*x^34 + 2*x^32 + 4*x^30 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + 3*x^14 + 2*x^12 + 3*x^10 + 4*x^8 + 3*x^2 + 3)/x^5)*y), [(x^4/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 + x^31 - x^29 - 2*x^27 + 2*x^23 - x^21 + x^19 + 2*x^15 + x^13 - x^11 - x^9 + x^5 + x^3 - x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^34 + 3*x^32 + 2*x^30 + 2*x^28 + x^26 + x^24 + 4*x^22 + 3*x^20 + x^18 + 2*x^16 + 4*x^14 + x^10 + 3*x^4 + 3*x^2 + 2)/(x^43 + 2*x^39 + 3*x^35 + 3*x^33 + 4*x^31 + 2*x^29 + 2*x^23 + x^19 + 3*x^13 + 4*x^11 + x^9 + 3*x^7 + x^5))*y])), + ([(x^5/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-2*x^42 + x^38 - 2*x^36 - 2*x^32 + x^30 + 2*x^28 - 2*x^24 + x^22 - x^20 + 2*x^18 - 2*x^14 - 2*x^10 + 2*x^8 + x^6 - 2*x^4 + 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^144 + 3*x^140 + x^138 + 2*x^136 + 3*x^134 + x^130 + x^120 + 3*x^118 + 2*x^114 + 3*x^112 + 2*x^110 + 2*x^108 + 3*x^106 + 2*x^100 + x^96 + 3*x^94 + 4*x^92 + x^90 + x^88 + 3*x^86 + 2*x^78 + 3*x^74 + 3*x^72 + 2*x^66 + x^64 + 2*x^62 + 4*x^60 + 2*x^58 + 4*x^56 + 2*x^54 + 3*x^50 + 2*x^48 + 4*x^46 + 3*x^44 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^112 + 4*x^108 + x^106 + 3*x^104 + 4*x^100 + 2*x^98 + 4*x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 3*x^76 + x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + x^62 + 3*x^60 + 2*x^58 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + x^44 + x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 3*x^32 + 3*x^28 + 4*x^26 + 3*x^24 + 3*x^20 + 2*x^18 + 3*x^16 + 4*x^14 + 3*x^8 + 3*x^6 + 4*x^2 + 3)/x^6)*y), [(x^5/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-2*x^42 + x^38 - 2*x^36 - 2*x^32 + x^30 + 2*x^28 - 2*x^24 + x^22 - x^20 + 2*x^18 - 2*x^14 - 2*x^10 + 2*x^8 + x^6 - 2*x^4 + 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^22 + x^20 + 4*x^18 + 2*x^16 + 2*x^14 + x^10 + 3*x^8 + x^6 + 2*x^2 + 2)/(x^44 + 2*x^40 + 3*x^36 + 3*x^34 + 4*x^32 + 2*x^30 + 2*x^24 + x^20 + 3*x^14 + 4*x^12 + x^10 + 3*x^8 + x^6))*y])), + ([((3*x^12 + 3*x^8 + 3*x^2 + 4)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-2*x^77 - x^73 - 2*x^69 - x^67 - x^65 + 2*x^61 + x^59 - 2*x^57 - x^55 - x^49 + 2*x^45 + 2*x^43 + x^41 - x^37 - x^35 + 2*x^33 + x^31 + x^29 - x^25 + x^23 - x^21 + 2*x^17 - 2*x^15 - x^13 + 2*x^11 - x^7 + 2*x^5 - 2*x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^179 + 4*x^175 + 3*x^173 + x^171 + 4*x^169 + 3*x^165 + x^159 + 2*x^155 + 2*x^153 + x^151 + 4*x^147 + 4*x^145 + x^143 + 4*x^141 + 4*x^135 + 4*x^133 + 3*x^131 + x^129 + x^127 + 3*x^125 + 2*x^123 + 4*x^121 + 2*x^119 + x^115 + x^111 + x^107 + 2*x^103 + 4*x^99 + 2*x^95 + x^91 + 3*x^89 + x^87 + 3*x^85 + 4*x^83 + 3*x^81 + x^79 + 3*x^77 + x^73 + 2*x^71 + x^67 + 3*x^65 + x^63 + 4*x^61 + 3*x^59 + 4*x^57 + 2*x^55 + 3*x^51 + 2*x^49 + 3*x^47 + 2*x^45 + x^43 + 3*x^37 + 4*x^33 + 3*x^31 + 2*x^29 + 4*x^25 + 3*x^21 + 4*x^19 + x^15 + x^13 + x^11 + x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x*y] + V(((x^146 + 2*x^142 + 3*x^140 + 4*x^138 + 2*x^134 + x^132 + 2*x^130 + 2*x^126 + 3*x^124 + x^122 + x^120 + 3*x^118 + 3*x^116 + x^114 + 2*x^112 + x^110 + 3*x^108 + x^106 + 3*x^102 + x^100 + 2*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + 2*x^76 + 4*x^72 + x^70 + 4*x^68 + 2*x^66 + x^64 + 3*x^62 + 2*x^60 + 2*x^58 + 2*x^56 + 4*x^52 + x^50 + 2*x^48 + 2*x^46 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + x^26 + x^24 + 3*x^18 + 4*x^14 + x^12 + 4*x^10 + 2*x^8 + 3*x^6 + 4*x^4 + 3*x^2 + 1)/x^5)*y), [(4/(x^16 + 2*x^12 + 3*x^8 + x^6 + 4*x^4 + 4*x^2))*y] d[x] + V(((x^40 - x^38 + 2*x^34 - 2*x^32 - 2*x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - 2*x^16 + x^14 - x^12 - 2*x^10 - 2*x^8 + 2*x^6 - 2*x^4 - x^2 + 2)/(x^41*y + 2*x^37*y - 2*x^33*y - 2*x^31*y - x^29*y + 2*x^27*y + 2*x^21*y + x^17*y - 2*x^11*y - x^9*y + x^7*y - 2*x^5*y + x^3*y)) dx) + dV([((2*x^34 + x^30 + x^28 + 2*x^26 + 3*x^24 + x^20 + 3*x^18 + x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^2 + 4)/(x^43 + 2*x^39 + 3*x^35 + 3*x^33 + 4*x^31 + 2*x^29 + 2*x^23 + x^19 + 3*x^13 + 4*x^11 + x^9 + 3*x^7 + x^5))*y])), + ([((x^12 + 4*x^8 + 4*x^4 + x^2 + 1)/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^68 + 2*x^62 + x^60 - x^58 - 2*x^56 + x^54 - 2*x^52 + 2*x^50 - 2*x^42 - x^40 - 2*x^36 + 2*x^34 - x^32 + x^30 + 2*x^28 + x^26 + x^22 - 2*x^20 + 2*x^18 + 2*x^16 - 2*x^14 - 2*x^12 + x^10 + x^8 - x^6 + 2*x^4 + 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^174 + 3*x^170 + x^168 + 2*x^166 + 3*x^164 + x^160 + 3*x^154 + 3*x^150 + 2*x^148 + 3*x^146 + 4*x^144 + 3*x^142 + x^140 + 2*x^138 + 3*x^136 + 3*x^134 + 3*x^130 + x^128 + 4*x^126 + x^122 + x^120 + 2*x^116 + x^110 + x^106 + x^104 + x^102 + 4*x^100 + x^96 + 3*x^94 + x^86 + 3*x^84 + x^82 + x^80 + 3*x^78 + 3*x^76 + 2*x^72 + 3*x^70 + x^68 + 4*x^66 + 2*x^64 + x^62 + 3*x^60 + x^58 + 2*x^56 + 4*x^54 + x^52 + 2*x^50 + x^48 + 4*x^46 + 3*x^44 + x^40 + 2*x^36 + 2*x^32 + 3*x^30 + 4*x^26 + x^24 + 2*x^20 + x^18 + 3*x^16 + 2*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^2*y] + V(((2*x^142 + 4*x^138 + x^136 + 3*x^134 + 4*x^130 + 2*x^128 + 4*x^126 + x^120 + 4*x^118 + x^112 + 4*x^110 + 4*x^106 + x^104 + x^102 + 3*x^100 + x^98 + 4*x^96 + x^94 + 2*x^92 + x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + 2*x^76 + 4*x^74 + x^72 + 3*x^70 + 3*x^68 + x^66 + 2*x^64 + 2*x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 2*x^44 + 4*x^42 + x^40 + 3*x^38 + x^36 + 3*x^34 + 3*x^32 + 4*x^28 + 3*x^26 + 3*x^24 + 3*x^22 + x^18 + 3*x^16 + 4*x^14 + 4*x^6 + 3*x^4 + 4)/x^6)*y), [(2/(x^17 + 2*x^13 + 3*x^9 + x^7 + 4*x^5 + 4*x^3))*y] d[x] + V(((x^44 - x^42 - 2*x^40 - x^36 + 2*x^34 - x^32 - x^28 + x^26 - 2*x^24 + x^20 + 2*x^18 + x^12 - 2*x^10 - x^8 + 2*x^6 - 2*x^4 - 1)/(x^46*y + 2*x^42*y - 2*x^38*y - 2*x^36*y - x^34*y + 2*x^32*y + 2*x^26*y + x^22*y - 2*x^16*y - x^14*y + x^12*y - 2*x^10*y + x^8*y)) dx) + dV([((4*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 3*x^22 + x^20 + x^14 + 2*x^10 + 3*x^6 + 2*x^2 + 2)/(x^42 + 2*x^38 + 3*x^34 + 3*x^32 + 4*x^30 + 2*x^28 + 2*x^22 + x^18 + 3*x^12 + 4*x^10 + x^8 + 3*x^6 + x^4))*y])), + ([((4*x^10 + 3*x^2 + 4)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^67 + x^63 + 2*x^59 + 2*x^57 - 2*x^55 - 2*x^53 - 2*x^49 + x^47 - x^45 - 2*x^43 + x^41 - 2*x^39 + 2*x^37 + 2*x^35 + 2*x^33 - 2*x^27 - x^25 - x^23 - 2*x^21 + x^17 + 2*x^11 - x^9 + 2*x^5 + 2*x^3)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^169 + 2*x^165 + 4*x^163 + 3*x^161 + 2*x^159 + 4*x^155 + 4*x^145 + 2*x^143 + 3*x^139 + 2*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + x^129 + 2*x^125 + 3*x^123 + 4*x^119 + x^117 + 4*x^115 + 3*x^113 + 2*x^109 + 2*x^105 + 2*x^103 + 3*x^99 + x^97 + 3*x^93 + 2*x^91 + 2*x^89 + x^83 + x^81 + 2*x^79 + 2*x^77 + 3*x^75 + x^73 + 4*x^71 + 4*x^69 + x^67 + x^63 + 3*x^61 + 4*x^57 + 3*x^53 + x^51 + 3*x^47 + 2*x^45 + x^43 + 3*x^37 + 4*x^33 + 3*x^31 + 2*x^29 + 4*x^25 + 3*x^21 + 4*x^19 + x^15 + x^13 + x^11 + x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^3*y] + V(((3*x^138 + x^134 + 4*x^132 + 2*x^130 + x^126 + 3*x^124 + x^122 + 3*x^118 + 4*x^116 + 2*x^114 + 4*x^112 + 2*x^110 + 4*x^108 + 2*x^106 + 3*x^104 + 2*x^102 + 4*x^100 + x^98 + x^96 + 4*x^94 + 2*x^92 + 2*x^90 + 2*x^88 + 4*x^86 + x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 3*x^70 + 4*x^66 + x^64 + 4*x^62 + x^58 + 4*x^56 + 4*x^54 + x^52 + 2*x^50 + 3*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + x^34 + 4*x^32 + 3*x^30 + 3*x^26 + 2*x^22 + 3*x^20 + 3*x^18 + x^16 + x^14 + 4*x^12 + 2*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2 + 4)/x^7)*y), [(2/(x^16 + 2*x^12 + 3*x^8 + x^6 + 4*x^4 + 4*x^2))*y] d[x] + V(((2*x^44 + x^36 + x^34 - 2*x^32 - x^30 + x^24 + x^22 + 2*x^20 - 2*x^18 - 2*x^16 - x^14 - 2*x^12 - 2*x^10 + x^6 + x^4 - x^2 - 1)/(x^51*y + 2*x^47*y - 2*x^43*y - 2*x^41*y - x^39*y + 2*x^37*y + 2*x^31*y + x^27*y - 2*x^21*y - x^19*y + x^17*y - 2*x^15*y + x^13*y)) dx) + dV([((3*x^40 + 4*x^38 + 2*x^36 + x^34 + 2*x^32 + 2*x^30 + 3*x^26 + 2*x^24 + 3*x^22 + x^20 + x^18 + x^14 + x^12 + x^10 + 2*x^8 + 4*x^2 + 4)/(x^49 + 2*x^45 + 3*x^41 + 3*x^39 + 4*x^37 + 2*x^35 + 2*x^29 + x^25 + 3*x^19 + 4*x^17 + x^15 + 3*x^13 + x^11))*y])), + ([(2/(x^5 + 4*x))*y] d[x] + V(((x^32 - x^24 + 2*x^22 + x^18 + x^16 - x^14 + x^12 - 2*x^10 + x^6 - 2*x^4 + 2*x^2 - 1)/(x^8*y - 2*x^4*y + y)) dx) + dV([((4*x^134 + 2*x^128 + 4*x^126 + x^124 + 4*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + x^112 + x^110 + 4*x^108 + 3*x^104 + 2*x^102 + 4*x^98 + 2*x^96 + x^94 + x^92 + 4*x^88 + x^84 + 3*x^82 + 4*x^80 + 2*x^78 + 3*x^76 + 3*x^74 + x^70 + 4*x^68 + 3*x^66 + 2*x^64 + x^62 + 2*x^60 + 3*x^58 + 4*x^54 + 3*x^48 + 4*x^46 + 3*x^44 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 3*x^30 + 4*x^28 + 4*x^26 + x^22 + 3*x^18 + x^14 + 2*x^8 + 4*x^6 + 3*x^4)/(x^8 + 3*x^4 + 1))*y]), [2/x^4*y] + V(((4*x^132 + 3*x^128 + 2*x^126 + x^124 + 3*x^120 + 4*x^118 + 3*x^116 + x^112 + 2*x^110 + 3*x^106 + 4*x^104 + 2*x^102 + x^98 + 2*x^94 + x^92 + 4*x^90 + 2*x^88 + 3*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + 3*x^76 + 2*x^74 + 2*x^72 + x^70 + 2*x^68 + 4*x^66 + 4*x^62 + 4*x^60 + x^58 + x^56 + 3*x^54 + 2*x^52 + 3*x^48 + 3*x^44 + 3*x^42 + 4*x^40 + x^38 + 2*x^36 + 2*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + x^4 + 2)/x^6)*y), [(3/(x^19 + 2*x^15 + 3*x^11 + x^9 + 4*x^7 + 4*x^5))*y] d[x] + V(((2*x^54 - x^52 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 + 2*x^40 - 2*x^36 - 2*x^32 - x^30 - 2*x^28 - 2*x^26 + x^22 + 2*x^20 + 2*x^18 + x^16 - x^14 + x^12 + x^10 + 2*x^8 - x^4 - 2*x^2 - 1)/(x^56*y + 2*x^52*y - 2*x^48*y - 2*x^46*y - x^44*y + 2*x^42*y + 2*x^36*y + x^32*y - 2*x^26*y - x^24*y + x^22*y - 2*x^20*y + x^18*y)) dx) + dV([((3*x^46 + 4*x^44 + x^42 + 2*x^40 + 3*x^38 + 4*x^34 + x^32 + x^28 + x^26 + 3*x^24 + 2*x^22 + 2*x^20 + 3*x^18 + 2*x^16 + 3*x^14 + 2*x^12 + 4*x^6 + 4*x^4 + 4*x^2 + 4)/(x^54 + 2*x^50 + 3*x^46 + 3*x^44 + 4*x^42 + 2*x^40 + 2*x^34 + x^30 + 3*x^24 + 4*x^22 + x^20 + 3*x^18 + x^16))*y])), + ([((2*x^4 + 1)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^57 - 2*x^53 - 2*x^49 + x^47 - x^45 + x^43 - 2*x^41 - x^37 + 2*x^35 - 2*x^33 - x^31 + x^29 + 2*x^23 + x^21 + x^19 + x^17 - x^15 - x^13 - 2*x^11 + x^9 + x^7 + x^5 - 2*x^3 + x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^139 + x^135 + 2*x^133 + 4*x^131 + x^129 + 2*x^125 + 2*x^119 + 2*x^113 + 2*x^111 + 2*x^109 + x^107 + 4*x^103 + x^101 + 3*x^93 + 2*x^91 + 3*x^89 + x^87 + 4*x^85 + 4*x^83 + 4*x^81 + 2*x^75 + 4*x^73 + x^71 + 4*x^69 + x^65 + x^63 + 2*x^61 + 2*x^59 + 4*x^57 + 3*x^55 + x^53 + 3*x^51 + 2*x^49 + 3*x^47 + x^45 + 4*x^43 + 2*x^39 + 2*x^37 + 2*x^35 + 2*x^31 + 3*x^25 + 2*x^23 + 4*x^21 + 3*x^19 + 4*x^15 + 4*x^13 + 4*x^11 + 4*x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^5*y] + V(((4*x^106 + 3*x^102 + 2*x^100 + x^98 + 3*x^94 + 4*x^92 + 3*x^90 + x^86 + 2*x^84 + 3*x^80 + 4*x^78 + 2*x^76 + x^72 + 2*x^68 + 2*x^66 + 4*x^64 + 4*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^52 + 3*x^50 + x^48 + 3*x^46 + x^44 + 2*x^42 + 4*x^40 + 4*x^38 + 3*x^36 + x^34 + x^32 + 3*x^30 + x^24 + 3*x^22 + 2*x^20 + 2*x^18 + x^16 + x^12 + 3*x^8 + x^6 + 4)/x^5)*y), [((3*x^2 + 1)/(x^20 + 2*x^16 + 3*x^12 + x^10 + 4*x^8 + 4*x^6))*y] d[x] + V(((-x^60 + 2*x^56 - x^54 - x^52 - 2*x^50 + x^48 - 2*x^46 - x^44 + x^42 + x^40 - x^34 - 2*x^32 + x^30 - 2*x^24 - x^22 + x^20 - x^18 + 2*x^16 - 2*x^14 - x^12 + x^10 - 2*x^6 + x^4 + x^2 + 1)/(x^61*y + 2*x^57*y - 2*x^53*y - 2*x^51*y - x^49*y + 2*x^47*y + 2*x^41*y + x^37*y - 2*x^31*y - x^29*y + x^27*y - 2*x^25*y + x^23*y)) dx) + dV([((3*x^50 + 4*x^46 + x^44 + x^42 + x^40 + 2*x^38 + 4*x^36 + 2*x^34 + 4*x^32 + 4*x^30 + 4*x^28 + x^26 + 3*x^18 + 3*x^16 + x^14 + 3*x^12 + 2*x^10 + 4*x^6 + 4*x^4 + 4*x^2 + 4)/(x^59 + 2*x^55 + 3*x^51 + 3*x^49 + 4*x^47 + 2*x^45 + 2*x^39 + x^35 + 3*x^29 + 4*x^27 + x^25 + 3*x^23 + x^21))*y])), + ([((3*x^7 + 3*x^3)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^52 - 2*x^48 + x^44 - 2*x^40 + x^38 - x^36 + x^30 - x^28 + 2*x^26 + x^24 + x^22 + x^20 - 2*x^18 + 2*x^16 + 2*x^14 + 2*x^12 - 2*x^10 - 2*x^8 + x^6 + x^4 + 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^154 + 4*x^150 + 3*x^148 + x^146 + 4*x^144 + 3*x^140 + x^134 + 2*x^130 + 2*x^128 + x^126 + 4*x^122 + 4*x^120 + x^118 + 4*x^116 + 4*x^110 + 4*x^108 + 3*x^106 + x^102 + 4*x^100 + 4*x^98 + 3*x^96 + x^90 + x^88 + 3*x^86 + 3*x^84 + x^82 + 3*x^80 + 3*x^78 + 3*x^74 + x^72 + 2*x^70 + 2*x^68 + 2*x^66 + 4*x^62 + 4*x^60 + x^58 + 3*x^56 + 2*x^54 + x^52 + 4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^40 + x^38 + 2*x^36 + 4*x^34 + 2*x^30 + 2*x^28 + 2*x^26 + 2*x^24)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^6*y] + V(((x^120 + 2*x^116 + 3*x^114 + 4*x^112 + 2*x^108 + x^106 + 2*x^104 + 2*x^100 + 3*x^98 + x^96 + x^94 + 3*x^92 + 3*x^90 + x^88 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^76 + x^74 + x^70 + 3*x^68 + 2*x^66 + 4*x^64 + 3*x^62 + 2*x^60 + 4*x^52 + x^50 + x^48 + 2*x^46 + 2*x^44 + x^40 + 3*x^38 + 4*x^34 + 2*x^32 + 3*x^30 + x^28 + 2*x^26 + x^24 + 2*x^22 + 4*x^20 + 3*x^16 + x^14 + 4*x^12 + 2*x^10 + 3*x^8 + 3*x^6 + 2*x^4 + 2)/x^4)*y), [((2*x^2 + 4)/(x^19 + 4*x^17 + 3*x^15 + 2*x^13 + x^11 + 4*x^7))*y] d[x] + V(((-x^60 - 2*x^58 - 2*x^56 + x^54 - x^52 - x^50 + x^48 - x^46 + x^40 - 2*x^38 - 2*x^36 - x^30 - 2*x^28 + 2*x^24 + 2*x^22 + x^18 + x^14 - 2*x^12 + 2*x^10 - x^8 + 2*x^6 - x^4 - 2*x^2 + 1)/(x^62*y - x^60*y - 2*x^58*y + 2*x^56*y + x^54*y + 2*x^52*y + 2*x^50*y + 2*x^42*y - 2*x^40*y - 2*x^38*y + 2*x^36*y - 2*x^34*y - x^30*y + 2*x^28*y + x^26*y)) dx) + dV([((x^52 + x^46 + 2*x^44 + 2*x^42 + 3*x^40 + x^38 + 3*x^36 + x^34 + 3*x^30 + 3*x^28 + 3*x^26 + x^24 + 2*x^22 + 2*x^20 + 4*x^18 + 4*x^16 + 3*x^14 + 2*x^12 + 4*x^10 + 3*x^8 + 2*x^6 + 3*x^4 + x^2 + 4)/(x^60 + 3*x^58 + 2*x^54 + 4*x^52 + 3*x^50 + 4*x^48 + x^46 + 4*x^44 + x^42 + x^40 + 2*x^38 + x^36 + x^34 + 2*x^32 + 3*x^30 + x^28 + x^26))*y])), + ([(x^2/(x^10 + 3*x^6 + x^2 + 1))*y] d[x] + V(((-2*x^39 + 2*x^35 - 2*x^31 + 2*x^29 - x^27 + x^25 + 2*x^23 + x^19 - x^9 + 2*x^7 + 2*x^5 - x^3 - 2*x)/(x^30*y - x^26*y - 2*x^20*y - 2*x^16*y - 2*x^12*y + 2*x^10*y - 2*x^8*y - 2*x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^141 + 2*x^137 + x^135 + 4*x^133 + x^129 + 3*x^125 + 3*x^121 + x^117 + 2*x^115 + 2*x^113 + 3*x^111 + x^109 + 2*x^105 + 3*x^101 + 2*x^95 + 3*x^93 + 2*x^89 + 2*x^87 + 4*x^83 + 3*x^81 + x^79 + 4*x^77 + 4*x^73 + 4*x^71 + 3*x^69 + 2*x^67 + x^65 + 4*x^63 + 3*x^59 + 3*x^57 + 2*x^55 + 4*x^49 + x^47 + 4*x^43 + 3*x^41 + x^37 + 3*x^35 + 4*x^33 + 3*x^31 + 2*x^29 + 3*x^25 + 3*x^23 + x^21 + x^19)/(x^30 + 4*x^26 + 3*x^20 + 3*x^16 + 3*x^12 + 2*x^10 + 3*x^8 + 3*x^4 + 3*x^2 + 1))*y]), [2/x^7*y] + V(((2*x^118 + 4*x^114 + x^112 + 3*x^110 + 4*x^106 + 2*x^104 + 4*x^102 + x^96 + 4*x^94 + x^88 + 4*x^86 + 4*x^82 + x^80 + 3*x^78 + 3*x^76 + 4*x^70 + 2*x^62 + 4*x^60 + 4*x^58 + 2*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + x^46 + 4*x^42 + 4*x^38 + 4*x^36 + x^34 + 2*x^30 + 4*x^28 + 4*x^26 + 4*x^22 + 4*x^20 + 2*x^18 + 4*x^12 + 2*x^10 + 4*x^8 + 2*x^4 + 3*x^2 + 2)/x^7)*y), [((x^6 + 4*x^4 + 4*x^2 + 2)/(x^22 + 2*x^18 + 3*x^14 + x^12 + 4*x^10 + 4*x^8))*y] d[x] + V(((x^70 + 2*x^68 - x^66 - 2*x^64 - x^62 - 2*x^60 + x^56 + 2*x^54 - x^52 - 2*x^50 - x^48 - 2*x^46 + 2*x^44 - 2*x^42 + x^40 - x^38 - 2*x^36 - x^34 - 2*x^32 + x^30 + x^28 + x^26 - 2*x^24 + 2*x^20 + x^14 + 2*x^12 + x^10 - x^8 + x^6 - x^4 - x^2 + 2)/(x^71*y + 2*x^67*y - 2*x^63*y - 2*x^61*y - x^59*y + 2*x^57*y + 2*x^51*y + x^47*y - 2*x^41*y - x^39*y + x^37*y - 2*x^35*y + x^33*y)) dx) + dV([((x^60 + 2*x^56 + 4*x^54 + 4*x^52 + 2*x^50 + 3*x^46 + 2*x^44 + 4*x^40 + 3*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + 4*x^28 + 2*x^26 + x^24 + 2*x^22 + 4*x^20 + 2*x^16 + x^14 + 3*x^12 + 2*x^10 + 4*x^6 + 4*x^4 + 4*x^2 + 4)/(x^69 + 2*x^65 + 3*x^61 + 3*x^59 + 4*x^57 + 2*x^55 + 2*x^49 + x^45 + 3*x^39 + 4*x^37 + x^35 + 3*x^33 + x^31))*y]))] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(2):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: for b in B: +....: [?7h[?12l[?25h[?25l[?7lprint("a")[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(b.regular_form()) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in B: +....:  print(b.regular_form()) +....:  +[?7h[?12l[?25h[?2004l( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V((0) dy) + dV((x^16 + 2*x^14 + x^12 + 2*x^6 + 4*x^4 + 2*x^2)*y), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) ) +( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V((0) dy) + dV((3*x^21 + x^19 + 3*x^17)*y), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.nth_root(3)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: bor b in B1: +....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  +....: [?7h[?12l[?25h[?25l[?7lsage: bor b in B1: +....:  +....:  +[?7h[?12l[?25h[?2004l Input In [38] + bor b in B1: + ^ +SyntaxError: invalid syntax + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbor b in B1:[?7h[?12l[?25h[?25l[?7lsage: for b in B: +....:  print(b.regular_form())[?7h[?12l[?25h[?25l[?7lbor1: + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbor b in B1:[?7h[?12l[?25h[?25l[?7lfor: +....:  print(b.regular_form())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1:[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(b.regular_form()) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in B1: +....:  print(b.regular_form()) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [39], in () + 1 for b in B1: +----> 2 print(b.regular_form()) + +File :90, in regular_drw_cech(cocycle) + +File :83, in regular_drw_form(omega) + +File :12, in decomposition_g0_p2th_power(fct) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbor b in B1:[?7h[?12l[?25h[?25l[?7l =F(2)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B1[0].omega0.regular_form() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [40], in () +----> 1 B1[Integer(0)].omega0.regular_form() + +File :83, in regular_drw_form(omega) + +File :12, in decomposition_g0_p2th_power(fct) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laB1[0][?7h[?12l[?25h[?25l[?7luB1[0][?7h[?12l[?25h[?25l[?7ltB1[0][?7h[?12l[?25h[?25l[?7loB1[0][?7h[?12l[?25h[?25l[?7lmB1[0][?7h[?12l[?25h[?25l[?7l(B1[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(B1[0]).coordinates() +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +File :60, in __mul__(self, other) + +File :14, in __init__(self, C, g) + +File :253, in reduction(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1002 try: +-> 1003 return self(str(element)) + 1004 except TypeError: + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_() + 2689 """ +-> 2690 return self._repr() + 2691 + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr() + 2655 s += " + " +-> 2656 x = y = repr(x) + 2657 if y.find("-") == 0: + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:338, in sage.rings.fraction_field_FpT.FpTElement._repr_() + 337 if nmod_poly_degree(self._denom) == 0 and nmod_poly_get_coeff_ui(self._denom, 0) == 1: +--> 338 return repr(self.numer()) + 339 else: + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_() + 2689 """ +-> 2690 return self._repr() + 2691 + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr() + 2655 s += " + " +-> 2656 x = y = repr(x) + 2657 if y.find("-") == 0: + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: + +During handling of the above exception, another exception occurred: + +AttributeError Traceback (most recent call last) +Input In [41], in () +----> 1 autom(B1[Integer(0)]).coordinates() + +File :97, in coordinates(self, basis, prec) + +File :44, in crystalline_cohomology_basis(self, prec, info) + +File :25, in de_rham_witt_lift(cech_class, prec) + +File :15, in de_rham_witt_lift_form8(omega) + +File :90, in diffn(self, dy_w) + +File :99, in diffn(self, dy_w) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :149, in auxilliary_derivative(P) + +File :55, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :55, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + + [... skipping similar frames: __rmul__ at line 55 (4 times), sage.rings.integer.Integer.__mul__ at line 1964 (3 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (3 times)] + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :55, in __rmul__(self, other) + +File :84, in __add__(self, other) + +File :31, in __add__(self, other) + +File :63, in __mul__(self, other) + +AttributeError: 'superelliptic_function' object has no attribute 'form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B1[0]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(B1[0]).coordinates(basis = B1) +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [42], in () +----> 1 autom(B1[Integer(0)]).coordinates(basis = B1) + +File :26, in autom(self) + +File :23, in autom(self) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :82, in __pow__(self, exp) + +File :14, in __init__(self, C, g) + +File :253, in reduction(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 112 FieldElement.__init__(self, parent) + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + 116 else: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1001 + 1002 try: +-> 1003 return self(str(element)) + 1004 except TypeError: + 1005 pass + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 192 except AttributeError: + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + 196 return result + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:482, in sage.rings.fraction_field_element.FractionFieldElement._repr_() + 480 if self.is_zero(): + 481 return "0" +--> 482 s = "%s" % self.__numerator + 483 if self.__denominator != 1: + 484 denom_string = str( self.__denominator ) + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 192 except AttributeError: + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + 196 return result + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_() + 2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3 + 2689 """ +-> 2690 return self._repr() + 2691 + 2692 def _latex_(self, name=None): + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2667, in sage.rings.polynomial.polynomial_element.Polynomial._repr() + 2665 else: + 2666 var = "" +-> 2667 s += "%s%s"%(x,var) + 2668 s = s.replace(" + -", " - ") + 2669 s = re.sub(r' 1(\.0+)?\*',' ', s) + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l[0].regulr_form()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lomega0.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loB[0].omega0[?7h[?12l[?25h[?25l[?7lmB[0].omega0[?7h[?12l[?25h[?25l[?7l B[0].omega0[?7h[?12l[?25h[?25l[?7l=B[0].omega0[?7h[?12l[?25h[?25l[?7l B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lO = B[0].omega0[?7h[?12l[?25h[?25l[?7lM = B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: OM = B[0].omega0 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lO +  + [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = OM.r() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lOM = B[0].omega0[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(omega0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lO)[?7h[?12l[?25h[?25l[?7lM)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: OM - de_rham_witt_lift_form0(OM) +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [45], in () +----> 1 OM - de_rham_witt_lift_form0(OM) + +File :4, in de_rham_witt_lift_form0(omega) + +File :80, in regular_drw_form(omega) + +File :99, in diffn(self, dy_w) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__() + 2412 return x + 2413 +-> 2414 return coercion_model.bin_op(left, right, operator.mul) + 2415 + 2416 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :48, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File :31, in __add__(self, other) + +File :82, in __pow__(self, exp) + +File :14, in __init__(self, C, g) + +File :261, in reduction(C, g) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2321, in sage.rings.polynomial.polynomial_element.Polynomial.__truediv__() + 2319 # Same parents => bypass coercion + 2320 if have_same_parent(left, right): +-> 2321 return (left)._div_(right) + 2322 + 2323 # Try division of polynomial by a scalar + +File /ext/sage/9.7/src/sage/structure/element.pyx:2739, in sage.structure.element.RingElement._div_() + 2737 except AttributeError: + 2738 raise bin_op_exception('/', self, other) +-> 2739 return frac(self, other) + 2740 + 2741 def __divmod__(self, other): + +File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__() + 897 return mor._call_(x) + 898 else: +--> 899 return mor._call_with_args(x, args, kwds) + 900 + 901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {})) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:173, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args() + 171 else: + 172 if len(kwds) == 0: +--> 173 return C._element_constructor(x, *args) + 174 else: + 175 return C._element_constructor(x, *args, **kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:648, in FractionField_generic._element_constructor_(self, x, y, coerce) + 646 x, y = x.numerator() * y.denominator(), y.numerator() * x.denominator() + 647 try: +--> 648 return self._element_class(self, x, y, coerce=coerce) + 649 except (TypeError, ValueError): + 650 pass + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(OM)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: OM - de_rham_witt_lift_form0(om) +[?7h[?12l[?25h[?2004l[?7hV(((x^18 - x^16 + 2*x^14 + 2*x^12 + x^8 - 2*x^6 + 2*x^4 + 2*x^2 + 2)/y) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: OM.regular_form() +[?7h[?12l[?25h[?2004l[?7h[3*x*y] d[x] + [3*x^2 + 2] d[y] + V((0) dy) + dV((x^16 + 2*x^14 + x^12 + 2*x^6 + 4*x^4 + 2*x^2)*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM.regular_form()[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l=B[0].oega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l1[0].omega0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: OM = B1[0].omega0 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM = B1[0].omega0[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: OM.regular_form() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [49], in () +----> 1 OM.regular_form() + +File :83, in regular_drw_form(omega) + +File :12, in decomposition_g0_p2th_power(fct) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM.regular_form()[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: OM +[?7h[?12l[?25h[?2004l[?7h[(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^114 + 3*x^110 + x^108 + 2*x^106 + 3*x^104 + x^100 + x^90 + 3*x^88 + 2*x^84 + 3*x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 2*x^70 + x^66 + 3*x^64 + 4*x^62 + x^60 + x^58 + 3*x^56 + 2*x^48 + 3*x^44 + 3*x^42 + 2*x^36 + x^34 + 2*x^32 + 4*x^30 + 2*x^28 + 4*x^26 + 2*x^24 + 3*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = OM.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lOM.r()[?7h[?12l[?25h[?25l[?7lsage: om = OM.r() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = B1[0].omega0[?7h[?12l[?25h[?25l[?7l-de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lsage: OM - de_rham_witt_lift_form0(om) +[?7h[?12l[?25h[?2004l[?7hV(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....:  C = omega.curve +....:  omega_aux = omega.r() +....:  omega_aux = omega_aux.regular_form() +....:  aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....: ^Iprint('aux', aux) +....:  aux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....: ^Iprint('aux.omega, fct', aux.omega, fct) +....:  aux.h2 += fct^p +....: ^Iprint(aux.h2) +....:  aux.h2 = decomposition_g0_p2th_power(aux.h2)[0] +....:  result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....:  return result[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....:  C = omega.curve +....:  omega_aux = omega.r() +....:  omega_aux = omega_aux.regular_form() +....:  aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....: ^Iprint('aux', aux) +....:  aux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....: ^Iprint('aux.omega, fct', aux.omega, fct) +....:  aux.h2 += fct^p +....: ^Iprint(aux.h2) +....:  aux.h2 = decomposition_g0_p2th_power(aux.h2)[0] +....:  result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....:  return result +[?7h[?12l[?25h[?2004l Input In [53] + print('aux', aux) + ^ +TabError: inconsistent use of tabs and spaces in indentation + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....: ^IC = omega.curve +....: ^Iomega_aux = omega.r() +....: ^Iomega_aux = omega_aux.regular_form() +....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....: ^Iprint('aux', aux) +....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....: ^Iprint('aux.omega, fct', aux.omega, fct) +....: ^Iaux.h2 += fct^p +....: ^Iprint(aux.h2) +....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0] +....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l....: ^Ireturn result +....: [?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....: ^IC = omega.curve +....: ^Iomega_aux = omega.r() +....: ^Iomega_aux = omega_aux.regular_form() +....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....: ^Iprint('aux', aux) +....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....: ^Iprint('aux.omega, fct', aux.omega, fct) +....: ^Iaux.h2 += fct^p +....: ^Iprint(aux.h2) +....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0] +....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lraise ValueError("Test")[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: regular_drw_form(OM) +[?7h[?12l[?25h[?2004laux V(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx) +aux.omega, fct ((-2*x^790 + x^786 - x^782 + 2*x^780 + 2*x^778 - 2*x^776 + 2*x^774 - x^770 + x^766 + x^764 - 2*x^762 + 2*x^760 + x^756 + x^754 + x^752 + 2*x^744 - x^740 + x^736 - 2*x^732 - x^724 - x^720 - x^716 + x^714 - x^712 + 2*x^710 - x^708 - 2*x^706 - x^704 + x^702 + 2*x^700 - 2*x^698 + 2*x^696 - 2*x^694 + x^692 + 2*x^690 + 2*x^688 + 2*x^686 - 2*x^684 - x^682 - x^680 - x^678 - 2*x^676 - 2*x^672 + 2*x^666 + 2*x^664 - 2*x^662 - 2*x^660 - x^658 + 2*x^656 - 2*x^654 - x^646 - 2*x^644 + 2*x^640 + x^638 + 2*x^636 - 2*x^634 + x^632 - 2*x^630 - 2*x^628 + x^626 + x^624 - x^622 + x^620 + 2*x^616 - x^614 + x^612 - x^606 - 2*x^604 - 2*x^602 - 2*x^598 - 2*x^596 + x^594 - x^592 - x^590 + 2*x^588 - x^586 - 2*x^584 - 2*x^582 - x^576 - x^574 - x^572 - 2*x^570 - 2*x^568 + 2*x^566 - 2*x^564 + 2*x^558 - 2*x^556 + 2*x^552 + x^548 - x^546 + x^544 + x^542 - 2*x^540 - x^538 + 2*x^536 - 2*x^534 + x^530 - 2*x^528 + x^526 - x^524 - x^522 - 2*x^516 + x^512 + x^510 + x^508 + x^502 + 2*x^498 + x^496 - 2*x^494 - x^492 - x^490 - x^488 + x^486 + x^484 - 2*x^482 + 2*x^480 - 2*x^476 + x^474 + x^470 + x^468 + 2*x^466 - 2*x^464 - x^462 + x^460 - 2*x^458 - 2*x^456 - 2*x^454 - x^452 - x^450 - x^448 + 2*x^446 - x^444 - 2*x^442 + 2*x^438 + 2*x^436 + 2*x^434 - 2*x^430 + x^428 + x^426 + x^424 - 2*x^422 + x^418 - 2*x^416 + x^414 - x^410 - 2*x^408 + x^406 + x^404 - x^402 + 2*x^398 - x^396 + x^392 - x^390 + x^388 + x^386 + x^384 + 2*x^380 + x^378 + 2*x^376 + 2*x^372 + 2*x^370 + x^368 - x^366 - 2*x^362 + 2*x^358 + 2*x^356 - x^352 + x^350 - 2*x^348 + x^346 + x^344 - 2*x^342 - 2*x^340 + 2*x^336 - x^334 + x^332 + 2*x^330 - 2*x^328 - 2*x^326 - 2*x^324 + 2*x^318 - 2*x^314 + 2*x^310 - x^308 + x^306 + x^302 + 2*x^298 + 2*x^296 + x^294 + x^292 - 2*x^290 - x^288 - x^286 - x^284 + x^282 + 2*x^280 + x^278 - x^276 + 2*x^274 + x^272 + 2*x^270 - x^266 + 2*x^264 + x^262 - x^260 - 2*x^258 + 2*x^256 - 2*x^254 + 2*x^252 + x^250 + x^246 - 2*x^244 + x^242 - 2*x^240 - 2*x^236 - x^232 - x^224 + 2*x^222 + x^220 + x^218 + x^216 - x^214 + 2*x^212 + 2*x^210 + 2*x^208 + 2*x^206 + 2*x^204 + 2*x^200 + x^198 + 2*x^196 + x^194 + 2*x^192 - 2*x^188 + 2*x^186 - 2*x^180 + 2*x^178 + x^174 - 2*x^172 + x^170 - x^168 - x^166 + 2*x^164 + 2*x^160 - x^158 + x^156 - x^154 - 2*x^152 - 2*x^150 - x^148 - x^144 - 2*x^140 + 2*x^138 + 2*x^134 + 2*x^132 - 2*x^130 + x^128 - x^126 + x^122 + 2*x^116 + x^114 - x^112 - x^108 - x^106 - x^104 + x^102 - 2*x^100 + x^96 - x^94 - 2*x^92 + 2*x^90 - x^88 - x^86 + x^82 + 2*x^80 - x^78 + 2*x^74 - x^72 + x^70 - 2*x^68 + 2*x^66 + 2*x^64 - 2*x^62 - 2*x^60 + 2*x^58 - 2*x^56 + 2*x^54 - 2*x^50 + 2*x^48 - x^46 + x^42 - 2*x^40 + 2*x^38 + 2*x^36 + x^34 + 2*x^32 - x^30 - x^26 - x^24 - 2*x^22 - x^20 - 2*x^18 + x^12)/y) dx ((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [55], in () +----> 1 regular_drw_form(OM) + +Input In [54], in regular_drw_form(omega) + 9 aux.h2 += fct**p + 10 print(aux.h2) +---> 11 aux.h2 = decomposition_g0_p2th_power(aux.h2)[Integer(0)] + 12 result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) + 13 return result + +File :12, in decomposition_g0_p2th_power(fct) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....: ^IC = omega.curve +....: ^Iomega_aux = omega.r() +....: ^Iomega_aux = omega_aux.regular_form() +....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....: ^Iprint('aux', aux) +....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....: ^Iprint('aux.omega, fct', aux.omega, fct) +....: ^Iaux.h2 += fct^p +....: ^Iprint('\n aux.h2', aux.h2, '\n') +....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0] +....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l....: ^Ireturn result +....: [?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....: ^IC = omega.curve +....: ^Iomega_aux = omega.r() +....: ^Iomega_aux = omega_aux.regular_form() +....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....: ^Iprint('aux', aux) +....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....: ^Iprint('aux.omega, fct', aux.omega, fct) +....: ^Iaux.h2 += fct^p +....: ^Iprint('\n aux.h2', aux.h2, '\n') +....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0] +....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....: ^IC = omega.curve +....: ^Iomega_aux = omega.r() +....: ^Iomega_aux = omega_aux.regular_form() +....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....: ^Iprint('aux', aux) +....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....: ^Iprint('aux.omega, fct', aux.omega, fct) +....: ^Iaux.h2 += fct^p +....: ^Iprint('\n aux.h2', aux.h2, '\n') +....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0] +....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_drw_form(OM) +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7lsage: regular_drw_form(OM) +[?7h[?12l[?25h[?2004laux V(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx) +aux.omega, fct ((-2*x^790 + x^786 - x^782 + 2*x^780 + 2*x^778 - 2*x^776 + 2*x^774 - x^770 + x^766 + x^764 - 2*x^762 + 2*x^760 + x^756 + x^754 + x^752 + 2*x^744 - x^740 + x^736 - 2*x^732 - x^724 - x^720 - x^716 + x^714 - x^712 + 2*x^710 - x^708 - 2*x^706 - x^704 + x^702 + 2*x^700 - 2*x^698 + 2*x^696 - 2*x^694 + x^692 + 2*x^690 + 2*x^688 + 2*x^686 - 2*x^684 - x^682 - x^680 - x^678 - 2*x^676 - 2*x^672 + 2*x^666 + 2*x^664 - 2*x^662 - 2*x^660 - x^658 + 2*x^656 - 2*x^654 - x^646 - 2*x^644 + 2*x^640 + x^638 + 2*x^636 - 2*x^634 + x^632 - 2*x^630 - 2*x^628 + x^626 + x^624 - x^622 + x^620 + 2*x^616 - x^614 + x^612 - x^606 - 2*x^604 - 2*x^602 - 2*x^598 - 2*x^596 + x^594 - x^592 - x^590 + 2*x^588 - x^586 - 2*x^584 - 2*x^582 - x^576 - x^574 - x^572 - 2*x^570 - 2*x^568 + 2*x^566 - 2*x^564 + 2*x^558 - 2*x^556 + 2*x^552 + x^548 - x^546 + x^544 + x^542 - 2*x^540 - x^538 + 2*x^536 - 2*x^534 + x^530 - 2*x^528 + x^526 - x^524 - x^522 - 2*x^516 + x^512 + x^510 + x^508 + x^502 + 2*x^498 + x^496 - 2*x^494 - x^492 - x^490 - x^488 + x^486 + x^484 - 2*x^482 + 2*x^480 - 2*x^476 + x^474 + x^470 + x^468 + 2*x^466 - 2*x^464 - x^462 + x^460 - 2*x^458 - 2*x^456 - 2*x^454 - x^452 - x^450 - x^448 + 2*x^446 - x^444 - 2*x^442 + 2*x^438 + 2*x^436 + 2*x^434 - 2*x^430 + x^428 + x^426 + x^424 - 2*x^422 + x^418 - 2*x^416 + x^414 - x^410 - 2*x^408 + x^406 + x^404 - x^402 + 2*x^398 - x^396 + x^392 - x^390 + x^388 + x^386 + x^384 + 2*x^380 + x^378 + 2*x^376 + 2*x^372 + 2*x^370 + x^368 - x^366 - 2*x^362 + 2*x^358 + 2*x^356 - x^352 + x^350 - 2*x^348 + x^346 + x^344 - 2*x^342 - 2*x^340 + 2*x^336 - x^334 + x^332 + 2*x^330 - 2*x^328 - 2*x^326 - 2*x^324 + 2*x^318 - 2*x^314 + 2*x^310 - x^308 + x^306 + x^302 + 2*x^298 + 2*x^296 + x^294 + x^292 - 2*x^290 - x^288 - x^286 - x^284 + x^282 + 2*x^280 + x^278 - x^276 + 2*x^274 + x^272 + 2*x^270 - x^266 + 2*x^264 + x^262 - x^260 - 2*x^258 + 2*x^256 - 2*x^254 + 2*x^252 + x^250 + x^246 - 2*x^244 + x^242 - 2*x^240 - 2*x^236 - x^232 - x^224 + 2*x^222 + x^220 + x^218 + x^216 - x^214 + 2*x^212 + 2*x^210 + 2*x^208 + 2*x^206 + 2*x^204 + 2*x^200 + x^198 + 2*x^196 + x^194 + 2*x^192 - 2*x^188 + 2*x^186 - 2*x^180 + 2*x^178 + x^174 - 2*x^172 + x^170 - x^168 - x^166 + 2*x^164 + 2*x^160 - x^158 + x^156 - x^154 - 2*x^152 - 2*x^150 - x^148 - x^144 - 2*x^140 + 2*x^138 + 2*x^134 + 2*x^132 - 2*x^130 + x^128 - x^126 + x^122 + 2*x^116 + x^114 - x^112 - x^108 - x^106 - x^104 + x^102 - 2*x^100 + x^96 - x^94 - 2*x^92 + 2*x^90 - x^88 - x^86 + x^82 + 2*x^80 - x^78 + 2*x^74 - x^72 + x^70 - 2*x^68 + 2*x^66 + 2*x^64 - 2*x^62 - 2*x^60 + 2*x^58 - 2*x^56 + 2*x^54 - 2*x^50 + 2*x^48 - x^46 + x^42 - 2*x^40 + 2*x^38 + 2*x^36 + x^34 + 2*x^32 - x^30 - x^26 - x^24 - 2*x^22 - x^20 - 2*x^18 + x^12)/y) dx ((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y + + aux.h2 ((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y + +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [57], in () +----> 1 regular_drw_form(OM) + +Input In [56], in regular_drw_form(omega) + 9 aux.h2 += fct**p + 10 print('\n aux.h2', aux.h2, '\n') +---> 11 aux.h2 = decomposition_g0_p2th_power(aux.h2)[Integer(0)] + 12 result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) + 13 return result + +File :12, in decomposition_g0_p2th_power(fct) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C1.x^7 6 +....: 6 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2*C1.x ^ +....: 714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^664 + 2 +....: *C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1.x^61 2 +....:  + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 + 3*C 1 +....: .x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^506 + 3 * +....: C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2*C1.x ^ +....: 444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374 + C1 . +....: x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x^332 + +....:  3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^292 + C 1 +....: .x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1.x^226 +....: + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166 + 3* C +....: 1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1.x^12 4 +....:  + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 + 2*C1 . +....: x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 4*C1. x +....: ^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 + 3*C1 . +....: x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1.x^11 8 +....:  + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C1.x^8 8 +....:  + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^58 + 3 * +....: C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 + 2*C1 . +....: x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7lsage: ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C1.x^7 6 +....: 6 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2*C1.x ^ +....: 714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^664 + 2 +....: *C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1.x^61 2 +....:  + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 + 3*C 1 +....: .x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^506 + 3 * +....: C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2*C1.x ^ +....: 444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374 + C1 . +....: x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x^332 + +....:  3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^292 + C 1 +....: .x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1.x^226 +....: + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166 + 3* C +....: 1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1.x^12 4 +....:  + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 + 2*C1 . +....: x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 4*C1. x +....: ^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 + 3*C1 . +....: x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1.x^11 8 +....:  + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C1.x^8 8 +....:  + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^58 + 3 * +....: C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 + 2*C1 . +....: x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y +[?7h[?12l[?25h[?2004l[?7h((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C1.x^7 6 +....: 6 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2*C1.x ^ +....: 714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^664 + 2 +....: *C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1.x^61 2 +....:  + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 + 3*C 1 +....: .x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^506 + 3 * +....: C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2*C1.x ^ +....: 444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374 + C1 . +....: x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x^332 + +....:  3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^292 + C 1 +....: .x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1.x^226 +....: + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166 + 3* C +....: 1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1.x^12 4 +....:  + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 + 2*C1 . +....: x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 4*C1. x +....: ^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 + 3*C1 . +....: x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1.x^11 8 +....:  + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C1.x^8 8 +....:  + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^58 + 3 * +....: C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 + 2*C1 . +....: x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7lfor b in B1:[?7h[?12l[?25h[?25l[?7l1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C 1 +....: .x^766 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2 * +....: C1.x^714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^6 6 +....: 4 + 2*C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1 . +....: x^612 + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 + +....:  3*C1.x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^50 6 +....:  + 3*C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2 * +....: C1.x^444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374 +....: + C1.x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x ^ +....: 332 + 3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^29 2 +....:  + C1.x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1. x +....: ^226 + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166 +....: + 3*C1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1 . +....: x^124 + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 + +....: 2*C1.x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 4 +....: *C1.x^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 + +....: 3*C1.x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1 . +....: x^118 + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C 1 +....: .x^88 + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^5 8 +....:  + 3*C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 + +....: 2*C1.x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7lsage: f1 = ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C 1 +....: .x^766 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2 * +....: C1.x^714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^6 6 +....: 4 + 2*C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1 . +....: x^612 + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 + +....:  3*C1.x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^50 6 +....:  + 3*C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2 * +....: C1.x^444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374 +....: + C1.x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x ^ +....: 332 + 3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^29 2 +....:  + C1.x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1. x +....: ^226 + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166 +....: + 3*C1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1 . +....: x^124 + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 + +....: 2*C1.x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 4 +....: *C1.x^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 + +....: 3*C1.x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1 . +....: x^118 + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C 1 +....: .x^88 + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^5 8 +....:  + 3*C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 + +....: 2*C1.x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C 1 +....: .x^766 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2 * +....: C1.x^714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^6 6 +....: 4 + 2*C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1 . +....: x^612 + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 + +....:  3*C1.x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^50 6 +....:  + 3*C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2 * +....: C1.x^444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374   +....: + C1.x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x ^ +....: 332 + 3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^29 2 +....:  + C1.x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1. x +....: ^226 + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166   +....: + 3*C1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1 . +....: x^124 + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 +   +....: 2*C1.x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 4 +....: *C1.x^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 +   +....: 3*C1.x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1 . +....: x^118 + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C 1 +....: .x^88 + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^5 8 +....:  + 3*C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 +   +....: 2*C1.x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.coordinates() +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.diffn() +[?7h[?12l[?25h[?2004l[?7h0 dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lf1.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.diffn().int() +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7ldecomposition_g0_p2th_power(aux.h2)[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7lf)[0][?7h[?12l[?25h[?25l[?7l1)[0][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_p2th_power(f1)[0] +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [62], in () +----> 1 decomposition_g0_p2th_power(f1)[Integer(0)] + +File :12, in decomposition_g0_p2th_power(fct) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1.diffn().int()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f2 = f1.pth_root() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_p2th_power(f1)[0][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_p2th_power(f1)[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l2)[0][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_p2th_power(f2)[0] +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [64], in () +----> 1 decomposition_g0_p2th_power(f2)[Integer(0)] + +File :11, in decomposition_g0_p2th_power(fct) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2 = f1.pth_root()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f2.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f2.diffn().int() +[?7h[?12l[?25h[?2004l[?7h((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2.diffn().int()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ldecomposition_g0_p2th_power(f2)[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lth_power(f2)[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_pth_power(f2)[0] +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [67], in () +----> 1 decomposition_g0_pth_power(f2)[Integer(0)] + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(x)[?7h[?12l[?25h[?25l[?7lsage: p +[?7h[?12l[?25h[?2004l[?7h5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0, A = decomposition_g0_pth_power(fct)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g0, A = decomposition_g0_pth_power(f1) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0, A = decomposition_g0_pth_power(f1)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: g0 +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: A +[?7h[?12l[?25h[?2004l[?7h((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA0, A1 = decomposition_g0_pth_power(A)[?7h[?12l[?25h[?25l[?7lsage: A0, A1 = decomposition_g0_pth_power(A) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [72], in () +----> 1 A0, A1 = decomposition_g0_pth_power(A) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA0, A1 = decomposition_g0_pth_power(A)[?7h[?12l[?25h[?25l[?7lsage: A +[?7h[?12l[?25h[?2004l[?7h((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.leading_coefficient()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.diffn().regular_form() +[?7h[?12l[?25h[?2004l[?7h((3*x^145 + 3*x^141 + 3*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + 3*x^127 + 4*x^125 + x^123 + 2*x^121 + x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 3*x^109 + x^107 + 3*x^103 + 2*x^101 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 3*x^87 + 2*x^85 + 4*x^83 + 2*x^81 + 3*x^77 + x^75 + x^73 + 4*x^69 + 2*x^67 + 4*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 4*x^57 + 4*x^55 + 4*x^53 + 2*x^51 + 2*x^47 + 3*x^45 + x^43 + 2*x^41 + x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^25 + 3*x^23 + 2*x^15 + 2*x^13 + x^11 + x^5 + x^3 + 2*x)*y) dx + (2*x^150 + 2*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 2*x^126 + 2*x^124 + x^122 + 3*x^118 + x^116 + 2*x^114 + 4*x^106 + 3*x^104 + 3*x^100 + 2*x^98 + x^96 + 2*x^94 + x^92 + 2*x^88 + 2*x^84 + 2*x^82 + 4*x^80 + 4*x^78 + 3*x^76 + 4*x^74 + 3*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^50 + 2*x^46 + 4*x^44 + x^42 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + 2*x^32 + x^30 + 4*x^28 + x^26 + 3*x^22 + 3*x^20 + 4*x^18 + x^16 + 3*x^14 + x^12 + 2*x^10 + x^8 + 3*x^6 + 3*x^4 + x^2 + 3) dy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = fct.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn().regular_form()[?7h[?12l[?25h[?25l[?7l.difn().regular_form()[?7h[?12l[?25h[?25l[?7l.difn().regular_form()[?7h[?12l[?25h[?25l[?7l.difn().regular_form()[?7h[?12l[?25h[?25l[?7l .difn().regular_form()[?7h[?12l[?25h[?25l[?7lA.difn().regular_form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega = A.diffn().regular_form() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0 = omega.int()[?7h[?12l[?25h[?25l[?7lsage: g0 = omega.int() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [77], in () +----> 1 g0 = omega.int() + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = A.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega.int() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [78], in () +----> 1 omega.int() + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega +[?7h[?12l[?25h[?2004l[?7h((3*x^145 + 3*x^141 + 3*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + 3*x^127 + 4*x^125 + x^123 + 2*x^121 + x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 3*x^109 + x^107 + 3*x^103 + 2*x^101 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 3*x^87 + 2*x^85 + 4*x^83 + 2*x^81 + 3*x^77 + x^75 + x^73 + 4*x^69 + 2*x^67 + 4*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 4*x^57 + 4*x^55 + 4*x^53 + 2*x^51 + 2*x^47 + 3*x^45 + x^43 + 2*x^41 + x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^25 + 3*x^23 + 2*x^15 + 2*x^13 + x^11 + x^5 + x^3 + 2*x)*y) dx + (2*x^150 + 2*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 2*x^126 + 2*x^124 + x^122 + 3*x^118 + x^116 + 2*x^114 + 4*x^106 + 3*x^104 + 3*x^100 + 2*x^98 + x^96 + 2*x^94 + x^92 + 2*x^88 + 2*x^84 + 2*x^82 + 4*x^80 + 4*x^78 + 3*x^76 + 4*x^74 + 3*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^50 + 2*x^46 + 4*x^44 + x^42 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + 2*x^32 + x^30 + 4*x^28 + x^26 + 3*x^22 + 3*x^20 + 4*x^18 + x^16 + 3*x^14 + x^12 + 2*x^10 + x^8 + 3*x^6 + 3*x^4 + x^2 + 3) dy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^I^Ireturn 0*C.x +....: ^I#which = random.choice([0, 1]) +....: ^IP = self.dx.function +....: ^IQ = self.dy.function +....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px +....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I print('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l....: ^I^Ireturn 0*C.x +....: ^I#which = random.choice([0, 1]) +....: ^IP = self.dx.function +....: ^IQ = self.dy.function +....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px +....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I print('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +[?7h[?12l[?25h[?2004l Input In [80] + W += Rx(numerator/f.derivative()) + ^ +TabError: inconsistent use of tabs and spaces in indentation + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^I^Ireturn 0*C.x +....: ^I#which = random.choice([0, 1]) +....: ^IP = self.dx.function +....: ^IQ = self.dy.function +....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px +....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l#which = random.choice([0, 1]) +P = self.dx.function +Qy +Py,Px = P.quo_rem(y) #P = y*Py + Px +QQQ +resultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +numerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Id = .degree() +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^I#which = random.choice([0, 1]) +....: ^IP = self.dx.function +....: ^IQ = self.dy.function +....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px +....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li, j = (x^6*y^7).exponents()[0][?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: int(omega) +[?7h[?12l[?25h[?2004lnumerator 2*x^10 + 2*x^6 + x^2 + 2 +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [82], in () +----> 1 int(omega) + +Input In [81], in int(self) + 32 if a < Integer(0): + 33 print('numerator', numerator) +---> 34 W += Rx(numerator/f.derivative()) + 35 numerator = Rx(Integer(0)) + 36 result = result + superelliptic_function(C, y*W) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*x^10 + 2*x^6 + x^2 + 2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*x^10 + 2*x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^10 + 2*x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l1x^10 + 2*x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l.x^10 + 2*x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l1x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l.x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l1x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l.x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*/C1.y*C.dx[?7h[?12l[?25h[?25l[?7lC/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l1/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l./C1.y*C.dx[?7h[?12l[?25h[?25l[?7lo/C1.y*C.dx[?7h[?12l[?25h[?25l[?7ln/C1.y*C.dx[?7h[?12l[?25h[?25l[?7le/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l()/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega1 = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1 = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: omega1 +[?7h[?12l[?25h[?2004l[?7h((2*x^10 + 2*x^6 + x^2 + 2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1.int() +[?7h[?12l[?25h[?2004l[?7h((2*x^32 + 4*x^30 + 2*x^28 + 3*x^24 + 2*x^20 + 4*x^18 + 2*x^16 + 4*x^12 + x^10 + x^8 + 4*x^4 + 3*x^2 + 4)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega1 = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C1.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1 = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C1.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1.int() +[?7h[?12l[?25h[?2004l[?7h((2*x^32 + 4*x^30 + 2*x^28 + 3*x^24 + 2*x^20 + 4*x^18 + 2*x^16 + 4*x^12 + x^10 + x^8 + 4*x^4 + 3*x^2 + 4)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l1 = suerelliptic(x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C1 +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1.regular_form() +[?7h[?12l[?25h[?2004l[?7h((x^15 + 2*x^7 + x^5 + 2*x^3 + 4*x)*y) dx + (4*x^20 + x^16 + 3*x^12 + 3*x^6 + 2*x^4 + 2*x^2 + 1) dy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: omega1 +[?7h[?12l[?25h[?2004l[?7h((2*x^10 + 2*x^6 + x^2 + 2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1 +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C1.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1 == 2*C1.y.diffn() +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1 == 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l@[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1, 2*C1.diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [93], in () +----> 1 omega1, Integer(2)*C1.diffn() + +AttributeError: 'superelliptic' object has no attribute 'diffn' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1, 2*C1.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lydifn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega1, 2*C1.y.diffn() +[?7h[?12l[?25h[?2004l[?7h(((2*x^10 + 2*x^6 + x^2 + 2)/y) dx, ((2*x^10 + x^6 + 2*x^2 - 1)/y) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C1.dx[?7h[?12l[?25h[?25l[?7l()C1.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(C[?7h[?12l[?25h[?25l[?7l1C1.dx[?7h[?12l[?25h[?25l[?7l.C1.dx[?7h[?12l[?25h[?25l[?7lyC1.dx[?7h[?12l[?25h[?25l[?7l()C1.dx[?7h[?12l[?25h[?25l[?7l()^C1.dx[?7h[?12l[?25h[?25l[?7l(C1.dx[?7h[?12l[?25h[?25l[?7l-C1.dx[?7h[?12l[?25h[?25l[?7l1C1.dx[?7h[?12l[?25h[?25l[?7l()C1.dx[?7h[?12l[?25h[?25l[?7l()*C1.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la(C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7lu(C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7lx(C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7l (C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7l=(C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7l (C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = (C1.y)^(-1)*C1.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = (C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.omegacartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.int() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [96], in () +----> 1 aux.int() + +File :198, in int(self) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral() + 3992 cdef Py_ssize_t n + 3993 zero = Q.zero() +-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv) + 3995 if self.get_unsafe(n) else zero for n in range(self.degree() + 1)] + 3996 return S(p) + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 5) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.int()[?7h[?12l[?25h[?25l[?7l = (C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7lomega1, 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 2*C1.y.difn()[?7h[?12l[?25h[?25l[?7l- 2*C1.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega1- 2*C1.y.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^6 - x^2 - 2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1- 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(omega1- 2*C1.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (omega1- 2*C1.y.diffn()).int() +[?7h[?12l[?25h[?2004l[?7h((3*x^28 + 4*x^26 + 4*x^24 + x^22 + 4*x^20 + 4*x^16 + x^14 + 2*x^12 + 2*x^10 + 4*x^8 + 3*x^6 + 4*x^4 + 2*x^2 + 4)/(x^36 + 3*x^34 + 2*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 3*x^12 + 4*x^10 + 4*x^6 + x^2 + 1))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1- 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1.int() +[?7h[?12l[?25h[?2004l[?7h((2*x^32 + 4*x^30 + 2*x^28 + 3*x^24 + 2*x^20 + 4*x^18 + 2*x^16 + 4*x^12 + x^10 + x^8 + 4*x^4 + 3*x^2 + 4)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1.int()[?7h[?12l[?25h[?25l[?7l(omega1- 2*C1.y.diffn()).int()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7leint()[?7h[?12l[?25h[?25l[?7lgint()[?7h[?12l[?25h[?25l[?7luint()[?7h[?12l[?25h[?25l[?7llint()[?7h[?12l[?25h[?25l[?7laint()[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7l_int()[?7h[?12l[?25h[?25l[?7lfint()[?7h[?12l[?25h[?25l[?7loint()[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7lmint()[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (omega1- 2*C1.y.diffn()).regular_form.int() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [100], in () +----> 1 (omega1- Integer(2)*C1.y.diffn()).regular_form.int() + +AttributeError: 'function' object has no attribute 'int' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(omega1- 2*C1.y.diffn()).regular_form.int()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(.int()[?7h[?12l[?25h[?25l[?7l().int()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (omega1- 2*C1.y.diffn()).regular_form().int() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [101], in () +----> 1 (omega1- Integer(2)*C1.y.diffn()).regular_form().int() + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: omega1 +[?7h[?12l[?25h[?2004l[?7h((2*x^10 + 2*x^6 + x^2 + 2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1 +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(omega)[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: int(omega) +[?7h[?12l[?25h[?2004lnumerator 2*x^10 + 2*x^6 + x^2 + 2 +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [104], in () +----> 1 int(omega) + +Input In [81], in int(self) + 32 if a < Integer(0): + 33 print('numerator', numerator) +---> 34 W += Rx(numerator/f.derivative()) + 35 numerator = Rx(Integer(0)) + 36 result = result + superelliptic_function(C, y*W) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1 +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.polynomial.derivative() +[?7h[?12l[?25h[?2004l[?7h2*x^10 + x^6 + 2*x^2 + 4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: omega1 +[?7h[?12l[?25h[?2004l[?7h((2*x^10 + 2*x^6 + x^2 + 2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B1[0].omega0.regular_form() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [108], in () +----> 1 B1[Integer(0)].omega0.regular_form() + +File :83, in regular_drw_form(omega) + +File :12, in decomposition_g0_p2th_power(fct) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=B1[0].omega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB1[0].omega0[?7h[?12l[?25h[?25l[?7lsage: OM = B1[0].omega0 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM = B1[0].omega0[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: OM +[?7h[?12l[?25h[?2004l[?7h[(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^114 + 3*x^110 + x^108 + 2*x^106 + 3*x^104 + x^100 + x^90 + 3*x^88 + 2*x^84 + 3*x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 2*x^70 + x^66 + 3*x^64 + 4*x^62 + x^60 + x^58 + 3*x^56 + 2*x^48 + 3*x^44 + 3*x^42 + 2*x^36 + x^34 + 2*x^32 + 4*x^30 + 2*x^28 + 4*x^26 + 2*x^24 + 3*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = B1[0].omega0[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l- de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lsage: OM - de_rham_witt_lift_form0(om) +[?7h[?12l[?25h[?2004l[?7hV(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laOM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7luOM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7lxOM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7l OM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7l=OM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7l OM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = OM - de_rham_witt_lift_form0(om) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = OM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lomega.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = OM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = OM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aom = aux.omega +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laom = aux.omega[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: aom +[?7h[?12l[?25h[?2004l[?7h((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laom[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: aom.is_regular_on_U + aom.is_regular_on_U0  + aom.is_regular_on_Uinfty + + + [?7h[?12l[?25h[?25l[?7l0 + aom.is_regular_on_U0  + + [?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aom.is_regular_on_U0() +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7laom.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef int(self):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_pth_power(f2)[0][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition + decomposition decomposition_g0_pth_power decomposition_omega0_hpdh  + decomposition_g0_g8 decomposition_g8_p2th_power decomposition_omega0_omega8 +  decomposition_g0_p2th_power decomposition_g8_pth_power decomposition_omega8_hpdh  + + [?7h[?12l[?25h[?25l[?7l + decomposition  + + + [?7h[?12l[?25h[?25l[?7l_g0_pth_power + decomposition  decomposition_g0_pth_power [?7h[?12l[?25h[?25l[?7lomega0hpdh + decomposition_g0_pth_power  decomposition_omega0_hpdh [?7h[?12l[?25h[?25l[?7l( + + + +[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laom)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladecomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7lodecomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7lmdecomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l0decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l,decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7lhdecomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l=decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aom0, h = decomposition_omega0_hpdh(aom) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7laom0, h = decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm0, h = decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmh.difn()[?7h[?12l[?25h[?25l[?7luh.difn()[?7h[?12l[?25h[?25l[?7llh.difn()[?7h[?12l[?25h[?25l[?7lth.difn()[?7h[?12l[?25h[?25l[?7l_h.difn()[?7h[?12l[?25h[?25l[?7lbh.difn()[?7h[?12l[?25h[?25l[?7lyh.difn()[?7h[?12l[?25h[?25l[?7l_h.difn()[?7h[?12l[?25h[?25l[?7lph.difn()[?7h[?12l[?25h[?25l[?7l(h.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: aom.verschiebung() == aom0.verschiebung() + mult_by_p(h.diffn()) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7laom.verschiebung() == aom0.verschiebung() + mult_by_p(h.diffn())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7l()mult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7l(mult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7l()mult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7l(mult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(h.diffn()) == (0*C.dx).verschiebung() +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(h.diffn()) == (0*C.dx).verschiebung()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt_by_p(h.diffn()) == (0*C.dx).verschiebung()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(h.diffn()) == (h^(p-1)*h.diffn()).verschiebung() +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(h.diffn()) == (h^(p-1)*h.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(h.diffn()) == (h^p).verschiebung().diffn() +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: h1 = h^p +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef int(self):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_pth_power(f2)[0][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_pth_power(f2)[0] + decomposition decomposition_g0_pth_power decomposition_omega0_hpdh  + decomposition_g0_g8 decomposition_g8_p2th_power decomposition_omega0_omega8 + decomposition_g0_p2th_power decomposition_g8_pth_power decomposition_omega8_hpdh  + + [?7h[?12l[?25h[?25l[?7l + decomposition  + + + [?7h[?12l[?25h[?25l[?7l_g0_pth_power + decomposition  decomposition_g0_pth_power [?7h[?12l[?25h[?25l[?7l82th_power + decomposition_g0_pth_power  + decomposition_g8_p2th_power[?7h[?12l[?25h[?25l[?7l0th_power + decomposition_g0_pth_power  + decomposition_g8_p2th_power[?7h[?12l[?25h[?25l[?7l + decomposition  decomposition_g0_pth_power [?7h[?12l[?25h[?25l[?7l_g0_g8 + decomposition  + decomposition_g0_g8 [?7h[?12l[?25h[?25l[?7lp2th_power + + decomposition_g0_g8  + decomposition_g0_p2th_power[?7h[?12l[?25h[?25l[?7l(f2)[0] + + + +[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_p2th_power(h1) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [122], in () +----> 1 decomposition_g0_p2th_power(h1) + +File :12, in decomposition_g0_p2th_power(fct) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh1 = h^p[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: h1 +[?7h[?12l[?25h[?2004l[?7h((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh1[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh1.diffn()[?7h[?12l[?25h[?25l[?7lsage: h1.diffn().regular_form().form() == h1.diffn() +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh1.diffn().regular_form().form() == h1.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: h1.diffn().regular_form().int() +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_p2th_power(h1)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_p2th_power(h1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lth_power(h1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_pth_power(h1) +[?7h[?12l[?25h[?2004l[?7h(0, + ((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAdecomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l1decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l,decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7lAdecomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l=decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1, A = decomposition_g0_pth_power(h1) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A = decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l.diffn().regular_frm()[?7h[?12l[?25h[?25l[?7ldiffn().regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn()[?7h[?12l[?25h[?25l[?7l().regular_form()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.diffn().int() +[?7h[?12l[?25h[?2004l[?7h((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn().int()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7leint()[?7h[?12l[?25h[?25l[?7lgint()[?7h[?12l[?25h[?25l[?7luint()[?7h[?12l[?25h[?25l[?7llint()[?7h[?12l[?25h[?25l[?7laint()[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7l_int()[?7h[?12l[?25h[?25l[?7lfint()[?7h[?12l[?25h[?25l[?7loint()[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7lmint()[?7h[?12l[?25h[?25l[?7l(int()[?7h[?12l[?25h[?25l[?7l()int()[?7h[?12l[?25h[?25l[?7l().int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.diffn().regular_form().int() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [130], in () +----> 1 A.diffn().regular_form().int() + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liA.difn().regular_form()[?7h[?12l[?25h[?25l[?7lnA.difn().regular_form()[?7h[?12l[?25h[?25l[?7ltA.difn().regular_form()[?7h[?12l[?25h[?25l[?7lint(A.difn().regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator 2*x^10 + 2*x^6 + x^2 + 2 +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [131], in () +----> 1 int(A.diffn().regular_form()) + +Input In [81], in int(self) + 32 if a < Integer(0): + 33 print('numerator', numerator) +---> 34 W += Rx(numerator/f.derivative()) + 35 numerator = Rx(Integer(0)) + 36 result = result + superelliptic_function(C, y*W) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lintA.difn().regular_form()[?7h[?12l[?25h[?25l[?7lA.difn().regular_form()[?7h[?12l[?25h[?25l[?7lA.difn().regular_form()[?7h[?12l[?25h[?25l[?7lA.difn().regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.diffn().regular_form() +[?7h[?12l[?25h[?2004l[?7h((3*x^145 + 3*x^141 + 3*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + 3*x^127 + 4*x^125 + x^123 + 2*x^121 + x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 3*x^109 + x^107 + 3*x^103 + 2*x^101 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 3*x^87 + 2*x^85 + 4*x^83 + 2*x^81 + 3*x^77 + x^75 + x^73 + 4*x^69 + 2*x^67 + 4*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 4*x^57 + 4*x^55 + 4*x^53 + 2*x^51 + 2*x^47 + 3*x^45 + x^43 + 2*x^41 + x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^25 + 3*x^23 + 2*x^15 + 2*x^13 + x^11 + x^5 + x^3 + 2*x)*y) dx + (2*x^150 + 2*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 2*x^126 + 2*x^124 + x^122 + 3*x^118 + x^116 + 2*x^114 + 4*x^106 + 3*x^104 + 3*x^100 + 2*x^98 + x^96 + 2*x^94 + x^92 + 2*x^88 + 2*x^84 + 2*x^82 + 4*x^80 + 4*x^78 + 3*x^76 + 4*x^74 + 3*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^50 + 2*x^46 + 4*x^44 + x^42 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + 2*x^32 + x^30 + 4*x^28 + x^26 + 3*x^22 + 3*x^20 + 4*x^18 + x^16 + 3*x^14 + x^12 + 2*x^10 + x^8 + 3*x^6 + 3*x^4 + x^2 + 3) dy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IP = self.dx.function +....: ^IQ = self.dy.function +....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px +....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lQy +Py,Px = P.quo_rem(y) #P = y*Py + Px +QQQ +resultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +numerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Iprint('numerator: ', numerator) +W: ', W) +d = numerator.degree() +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^IQ = self.dy.function +....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px +....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: 0 +numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 +numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 +numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 +numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 +numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 +numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 +numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 +numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 +numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 +numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 +numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 +numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 +numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 +numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 +numerator: 4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 +numerator: 4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 +numerator: 2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 +numerator: 2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 +numerator: 3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 +numerator: 4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 +numerator: 4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 +numerator: 4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 +numerator: 3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 +numerator: 4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^42 + 2*x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 +numerator: 3*x^48 + 2*x^46 + 3*x^44 + x^40 + 2*x^38 + 2*x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 +numerator: 2*x^46 + x^40 + 4*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 +numerator: x^40 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 +numerator: 3*x^36 + x^32 + 3*x^28 + x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 +numerator: x^32 + 2*x^28 + 3*x^26 + 2*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 +numerator: 3*x^28 + 3*x^26 + 3*x^24 + x^22 + 4*x^20 + x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 +numerator: 3*x^26 + x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 +numerator: x^22 + 4*x^20 + 2*x^18 + 3*x^16 + 2*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 +numerator: 4*x^20 + 3*x^18 + 3*x^16 + 3*x^14 + 4*x^12 + x^10 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 +numerator: 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 2*x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 +numerator: x^16 + 2*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 +numerator: 2*x^10 + 2*x^6 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 + 4*x^2 +numerator 2*x^10 + 2*x^6 + x^2 + 2 +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [134], in () +----> 1 int(A.diffn().regular_form()) + +Input In [133], in int(self) + 34 if a < Integer(0): + 35 print('numerator', numerator) +---> 36 W += Rx(numerator/f.derivative()) + 37 numerator = Rx(Integer(0)) + 38 result = result + superelliptic_function(C, y*W) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self == (C.y*W1).diffn() + n1) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lresultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +numerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Iprint('numerator: ', numerator) +W: ', W) +W1 = superelliptic_function(C, W) +norm(C, numerator/y) +print(self == (C.y*W1).diff() + n1) +d = numerator.degree( +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self == (C.y*W1).diffn() + n1) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self == (C.y*W1).diffn() + n1) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7lsage:  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: 0 +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [136], in () +----> 1 int(A.diffn().regular_form()) + +Input In [135], in int(self) + 24 W1 = superelliptic_function(C, W) + 25 n1 = superelliptic_form(C, numerator/y) +---> 26 print(self == (C.y*W1).diffn() + n1) + 27 d = numerator.degree() + 28 r = f.degree() + +File :12, in __eq__(self, other) + +AttributeError: 'superelliptic_regular_form' object has no attribute 'reduce' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + [?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lresultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +numerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Iprint('numerator: ', numerator) +W: ', W) +W1 = superelliptic_function(C, W) +norm(C, numerator/y) +print(self.form() == (C.y*W1).diffn() + n1) +d = numerator.degree() +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: 0 +False +numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 +False +numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 +False +numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 +False +numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 +False +numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 +False +numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 +False +numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 +False +numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 +False +numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 +False +numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 +False +numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 +False +numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 +False +numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 +False +numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 +False +numerator: 4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 +False +numerator: 4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 +False +numerator: 2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 +False +numerator: 2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 +False +numerator: 3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 +False +numerator: 4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [138], in () +----> 1 int(A.diffn().regular_form()) + +Input In [137], in int(self) + 24 W1 = superelliptic_function(C, W) + 25 n1 = superelliptic_form(C, numerator/y) +---> 26 print(self.form() == (C.y*W1).diffn() + n1) + 27 d = numerator.degree() + 28 r = f.degree() + +File :95, in diffn(self) + +File :7, in __init__(self, C, g) + +File :296, in reduction_form(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 112 FieldElement.__init__(self, parent) + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + 116 else: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1001 + 1002 try: +-> 1003 return self(str(element)) + 1004 except TypeError: + 1005 pass + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lresultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +numerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Iprint('numerator: ', numerator) +W: ', W) +W1 = superelliptic_function(C, W) +norm(C, numerator/y) +print(self.form(), (C.y*W1).diffn() + n1) +d = numerator.degree() +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: 0 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + x^136 + x^130 - 2*x^128 - x^126 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 + x^130 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 + 2*x^128 + 2*x^124 + 2*x^120 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + 2*x^120 + 2*x^118 - 2*x^116 - x^114 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 + x^118 - 2*x^116 - 2*x^114 - x^112 - x^110 + x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 - 2*x^116 - x^112 - x^110 - 2*x^108 - x^104 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 - 2*x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - 2*x^102 - 2*x^98 + 2*x^96 - 2*x^94 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 + 2*x^98 + 2*x^96 + 2*x^94 - x^90 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 + 2*x^96 - x^90 - 2*x^88 - x^86 - 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 - x^90 + 2*x^88 + x^86 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^86 - x^82 + 2*x^80 - x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^86 + x^84 - x^82 + 2*x^80 + x^76 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 - x^82 + 2*x^80 - 2*x^78 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 + 2*x^80 + x^78 + x^74 + 2*x^72 - x^70 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 + x^78 - x^76 + x^74 + 2*x^70 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + 2*x^70 - 2*x^68 - x^66 + x^64 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 - 2*x^68 + x^66 + x^64 - x^62 - 2*x^58 - 2*x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - x^62 + 2*x^58 - 2*x^54 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 + x^58 + 2*x^54 + x^52 + 2*x^50 - x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 + x^58 - x^56 + 2*x^54 - x^52 - x^48 + 2*x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 - x^56 - x^52 + 2*x^48 + x^46 + 2*x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [140], in () +----> 1 int(A.diffn().regular_form()) + +Input In [139], in int(self) + 24 W1 = superelliptic_function(C, W) + 25 n1 = superelliptic_form(C, numerator/y) +---> 26 print(self.form(), (C.y*W1).diffn() + n1) + 27 d = numerator.degree() + 28 r = f.degree() + +File :17, in form(self) + +File :95, in diffn(self) + +File :7, in __init__(self, C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 112 FieldElement.__init__(self, parent) + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + 116 else: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1001 + 1002 try: +-> 1003 return self(str(element)) + 1004 except TypeError: + 1005 pass + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 986 try: + 987 if '/' in element: +--> 988 element = sage_eval(element,d) + 989 else: + 990 element = element.replace("^","**") + +File /ext/sage/9.7/src/sage/misc/sage_eval.py:192, in sage_eval(source, locals, cmds, preparse) + 190 else: + 191 if preparse: +--> 192 source = preparser.preparse(source) + 194 if cmds: + 195 exec(cmd_seq, sage.all.__dict__, locals) + +File /ext/sage/9.7/src/sage/repl/preparse.py:1816, in preparse(line, reset, do_time, ignore_prompts, numeric_literals) + 1811 L = implicit_mul(L, level = implicit_mul_level) + 1813 if numeric_literals: + 1814 # Wrapping + 1815 # 1 + 0.5 -> Integer(1) + RealNumber('0.5') +-> 1816 L = preparse_numeric_literals(L, quotes=quote_state.safe_delimiter()) + 1818 # Generators + 1819 # R.0 -> R.gen(0) + 1820 L = re.sub(r'(\b[^\W\d]\w*|[)\]])\.(\d+)', r'\1.gen(\2)', L) + +File /ext/sage/9.7/src/sage/repl/preparse.py:1286, in preparse_numeric_literals(code, extract, quotes) + 1283 all_num_regex = re.compile(all_num, re.I) + 1285 for m in all_num_regex.finditer(code): +-> 1286 start, end = m.start(), m.end() + 1287 num = m.group(1) + 1288 postfix = m.groups()[-1].upper() + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lresultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +numerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Iprint('numerator: ', numerator) +W: ', W) +W1 = superelliptic_function(C, W) +norm(C, numerator/y) +print(self.form() == (2*.y*W1).diffn( + n1) +d = numerator.degree() +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7lsage:  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: 0 +False +numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 +False +numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 +False +numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 +False +numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 +False +numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 +False +numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 +False +numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 +False +numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 +False +numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 +False +numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 +False +numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 +False +numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 +False +numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 +False +numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [142], in () +----> 1 int(A.diffn().regular_form()) + +Input In [141], in int(self) + 23 print('W: ', W) + 24 W1 = superelliptic_function(C, W) +---> 25 n1 = superelliptic_form(C, numerator/y) + 26 print(self.form() == (Integer(2)*C.y*W1).diffn() + n1) + 27 d = numerator.degree() + +File :7, in __init__(self, C, g) + +File :296, in reduction_form(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 112 FieldElement.__init__(self, parent) + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + 116 else: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1007 try: + 1008 # now try calling the base ring's __call__ methods +-> 1009 element = self.base_ring()(element) + 1010 _p = p_NSet(sa2si(element,_ring), _ring) + 1011 return new_MP(self,_p) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) + 1143 """ + 1144 TESTS:: + 1145 + (...) + 1182  True + 1183 """ + 1184 try: +-> 1185 return integer_mod.IntegerMod(self, x) + 1186 except (NotImplementedError, PariError): + 1187 raise TypeError("error coercing to finite field") + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() + 199 return a + 200 t = modulus.element_class() +--> 201 return t(parent, value) + 202 + 203 + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 378 else: + 379 try: +--> 380 z = integer_ring.Z(value) + 381 except (TypeError, ValueError): + 382 from sage.structure.element import Expression + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_() + 285 raise TypeError("Cannot coerce {} to {}".format(x, C)) + 286 cdef Map m +--> 287 cdef Element e = method(C) + 288 if e is None: + 289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x))) + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:831, in sage.rings.fraction_field_element.FractionFieldElement._conversion() + 829 return R(self.__numerator) + 830 else: +--> 831 self.reduce() + 832 num = R(self.__numerator) + 833 inv_den = R(self.__denominator).inverse_of_unit() + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce() + 1237 if self._is_reduced: + 1238 return +-> 1239 super(self.__class__, self).reduce() + 1240 self.normalize_leading_coefficients() + 1241 + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce() + 162 return codomain.coerce(nnum/nden) + 163 +--> 164 cpdef reduce(self): + 165 """ + 166 Reduce this fraction. + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce() + 195 return + 196 try: +--> 197 g = self.__numerator.gcd(self.__denominator) + 198 if not g.is_unit(): + 199 self.__numerator //= g + +File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method() + 4492 def new_method(self, other, *args, **kwargs): + 4493 if have_same_parent(self, other): +-> 4494 return method(self, other, *args, **kwargs) + 4495 else: + 4496 a, b = coercion_model.canonical_coercion(self, other) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd() + 4911 raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base) + 4912 else: +-> 4913 return doit(self, other) + 4914 + 4915 @coerce_binop + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g) + 944 f1 = Num(f.numerator()) + 945 g1 = Num(g.numerator()) +--> 946 return Pol(f1.gcd(g1)).monic() + +File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method() + 4492 def new_method(self, other, *args, **kwargs): + 4493 if have_same_parent(self, other): +-> 4494 return method(self, other, *args, **kwargs) + 4495 else: + 4496 a, b = coercion_model.canonical_coercion(self, other) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4906, in sage.rings.polynomial.polynomial_element.Polynomial.gcd() + 4904 tgt = flatten.codomain() + 4905 if tgt.ngens() > 1 and tgt._has_singular: +-> 4906 g = flatten(self).gcd(flatten(other)) + 4907 return flatten.section()(g) + 4908 try: + +File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__() + 767 if P is D: # we certainly want to call _call_/with_args + 768 if not args and not kwds: +--> 769 return self._call_(x) + 770 return self._call_with_args(x, args, kwds) + 771 # Is there coercion? + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:220, in FlatteningMorphism._call_(self, p) + 218 for mon, pp in p.items(): + 219 assert pp.parent() is ring +--> 220 for i, j in pp.dict().items(): + 221 new_p[(i,)+(mon)] = j + 222 elif is_MPolynomialRing(ring): + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result) +....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lnumerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Iprint('numerator: ', numerator) +W: ', W) +W1 = superelliptic_function(C, W) +norm(C, numerator/y) +print(self.form() == (2*.y*W1).diffn( + n1 + result) +, (2*C.y*W1).diffn() +n1 +result) +d = numerator.degree() +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result) +....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: 0 +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [144], in () +----> 1 int(A.diffn().regular_form()) + +Input In [143], in int(self) + 24 W1 = superelliptic_function(C, W) + 25 n1 = superelliptic_form(C, numerator/y) +---> 26 print(self.form() == (Integer(2)*C.y*W1).diffn() + n1 + result) + 27 print(self.form(), (Integer(2)*C.y*W1).diffn() + n1 + result) + 28 d = numerator.degree() + +File :19, in __add__(self, other) + +AttributeError: 'superelliptic_function' object has no attribute 'form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lnumerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Iprint('numerator: ', numerator) +W: ', W) +W1 = superelliptic_function(C, W) +norm(C, numerator/y) +print(self.form() == (2*.y*W1).diffn( + n1 + result.diffn()) +, (2*C.y*W1).diffn() +n1 +result.diffn()) +d = numerator.degree() +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7lsage:  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7lregular_drw_form(OM)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: 0 +False +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 +False +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 +False +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 +False +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 +False +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 +False +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [146], in () +----> 1 int(A.diffn().regular_form()) + +Input In [145], in int(self) + 25 n1 = superelliptic_form(C, numerator/y) + 26 print(self.form() == (Integer(2)*C.y*W1).diffn() + n1 + result.diffn()) +---> 27 print(self.form(), (Integer(2)*C.y*W1).diffn() + n1 + result.diffn()) + 28 d = numerator.degree() + 29 r = f.degree() + +File :95, in diffn(self) + +File :7, in __init__(self, C, g) + +File :282, in reduction_form(C, g) + +File :263, in reduction(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:974, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 972 if isinstance(element, (SingularElement, cypari2.gen.Gen)): + 973 element = str(element) +--> 974 elif is_Macaulay2Element(element): + 975 element = element.external_string() + 976 + +File /ext/sage/9.7/src/sage/interfaces/macaulay2.py:1835, in is_Macaulay2Element(x) + 1823 """ + 1824  EXAMPLES:: + 1825 + (...) + 1828  -- code for method: resolution(Matrix)... + 1829  """ + 1830 return self._obj.parent().eval( + 1831 'code select(methods %s, m->instance(%s, m#1))' + 1832 % (self._name, self._obj._name)) +-> 1835 def is_Macaulay2Element(x): + 1836 """ + 1837  EXAMPLES:: + 1838 + (...) + 1843  True + 1844  """ + 1845 return isinstance(x, Macaulay2Element) + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lnumerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Iprint('numerator: ', numerator) +W: ', W) +W1 = superelliptic_function(C, W) +norm(C, numerator/y) +print(self.form() == (C.y*W1).diffn() + n1 + result.diffn()) +, (C.y*W1).diffn() +n1 +result.diffn()) +d = numerator.degree() +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/y) +....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lsage:  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: 0 +False +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 +False +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + x^136 + x^130 - 2*x^128 - x^126 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 +False +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 + x^130 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 +False +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 + 2*x^128 + 2*x^124 + 2*x^120 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx +numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 +False +^C--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File :58, in __mul__(self, other) + +AttributeError: 'superelliptic_form' object has no attribute 'function' + +During handling of the above exception, another exception occurred: + +KeyboardInterrupt Traceback (most recent call last) +Input In [148], in () +----> 1 int(A.diffn().regular_form()) + +Input In [147], in int(self) + 25 n1 = superelliptic_form(C, numerator/y) + 26 print(self.form() == (C.y*W1).diffn() + n1 + result.diffn()) +---> 27 print(self.form(), (C.y*W1).diffn() + n1 + result.diffn()) + 28 d = numerator.degree() + 29 r = f.degree() + +File :17, in form(self) + +File :65, in __mul__(self, other) + +File :7, in __init__(self, C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 112 FieldElement.__init__(self, parent) + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + 116 else: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1001 + 1002 try: +-> 1003 return self(str(element)) + 1004 except TypeError: + 1005 pass + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 986 try: + 987 if '/' in element: +--> 988 element = sage_eval(element,d) + 989 else: + 990 element = element.replace("^","**") + +File /ext/sage/9.7/src/sage/misc/sage_eval.py:186, in sage_eval(source, locals, cmds, preparse) + 183 locals = {} + 185 import sage.all +--> 186 if cmds: + 187 cmd_seq = cmds + '\n_sage_eval_returnval_ = ' + source + 188 if preparse: + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/(2*y)) +....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lnumerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Iprint('numerator: ', numerator) +W: ', W) +W1 = superelliptic_function(C, W) +norm(C, numerator/(2*y)) +print(self.form() == (C.y*W1).diffn() + n1 + result.diffn()) +, (C.y*W1).diffn() +n1 +result.diffn()) +d = numerator.degree() +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/(2*y)) +....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn()) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: 0 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^42 + 2*x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^48 + 2*x^46 + 3*x^44 + x^40 + 2*x^38 + 2*x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 2*x^46 + x^40 + 4*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: x^40 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^36 + x^32 + 3*x^28 + x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: x^32 + 2*x^28 + 3*x^26 + 2*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^28 + 3*x^26 + 3*x^24 + x^22 + 4*x^20 + x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^26 + x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: x^22 + 4*x^20 + 2*x^18 + 3*x^16 + 2*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 4*x^20 + 3*x^18 + 3*x^16 + 3*x^14 + 4*x^12 + x^10 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 2*x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: x^16 + 2*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator: 2*x^10 + 2*x^6 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 + 4*x^2 +True +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx +numerator 2*x^10 + 2*x^6 + x^2 + 2 +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [150], in () +----> 1 int(A.diffn().regular_form()) + +Input In [149], in int(self) + 38 if a < Integer(0): + 39 print('numerator', numerator) +---> 40 W += Rx(numerator/f.derivative()) + 41 numerator = Rx(Integer(0)) + 42 result = result + superelliptic_function(C, y*W) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y) +....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/(2*y)) +....: ^I^Iprint((C.y*W1).diffn()) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lresultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +numerator = Rx(2*f*Py + f.derivative()*Qx) +# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +W = Rx(0) +while(numerator != 0): +^Iprint('numerator: ', numerator) +W: ', W) +W1 = superelliptic_function(C, W) +norm(C, numerator/(2*y)) +print((C.y*W1).dffn()) +d = numerator.degree +rf.dgree() +n_lead = numerator.leading_coefficient() +fRx(f).leading_coefficient() +a = d - (r-1) +if a >=0: +^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) + += W_coeff*Rx(x^a) +numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() += Rx(numerator) +if a < 0: +^Iprint('numerator', numerator) +W += Rx(numerator/f.derivative()) +numerator = Rx(0) +result = result+ superelliptic_function(C, y*W) +returnresult +[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral()) +....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx) +....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y. +....: ^IW = Rx(0) +....: ^Iwhile(numerator != 0): +....: ^I^Iprint('numerator: ', numerator) +....: ^I^Iprint('W: ', W) +....: ^I^IW1 = superelliptic_function(C, W) +....: ^I^In1 = superelliptic_form(C, numerator/(2*y)) +....: ^I^Iprint((C.y*W1).diffn()) +....: ^I^Id = numerator.degree() +....: ^I^Ir = f.degree() +....: ^I^In_lead = numerator.leading_coefficient() +....: ^I^If_lead = Rx(f).leading_coefficient() +....: ^I^Ia = d - (r-1) +....: ^I^Iif a >= 0: +....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1)) +....: ^I^I^IW += W_coeff*Rx(x^a) +....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative() +....: ^I^I^Inumerator = Rx(numerator) +....: ^I^Iif a < 0: +....: ^I^I^Iprint('numerator', numerator) +....: ^I^I^IW += Rx(numerator/f.derivative()) +....: ^I^I^Inumerator = Rx(0) +....: ^Iresult = result + superelliptic_function(C, y*W) +....: ^Ireturn result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form()) +[?7h[?12l[?25h[?2004lnumerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: 0 +0 dx +numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 +((x^140 - 2*x^136 + x^132 + x^130 + x^126)/y) dx +numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 +((x^140 + 2*x^136 + x^132 + x^130 - 2*x^128 - 2*x^124)/y) dx +numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 +((x^140 + 2*x^136 - 2*x^132 + x^130 + x^128 + x^124 + 2*x^122 + 2*x^120 + x^118)/y) dx +numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + 2*x^122 + 2*x^120 - x^118 - x^116 + x^114)/y) dx +numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - x^116 + 2*x^114 - x^112 - x^110 + 2*x^108)/y) dx +numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 - x^116 - x^112 - x^110 - x^106 + x^104)/y) dx +numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + x^106)/y) dx +numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 + 2*x^98 + x^96 + 2*x^94)/y) dx +numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - 2*x^98 + x^96 - 2*x^94 - x^92 - x^90 + 2*x^88)/y) dx +numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 + x^96 - x^92 - x^90 - x^88 + x^86 - x^84)/y) dx +numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 - x^92 - x^90 - x^86)/y) dx +numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + 2*x^88 - x^86 + 2*x^84 - 2*x^82 - 2*x^80 - x^78)/y) dx +numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 - x^86 + x^84 - 2*x^82 - 2*x^80 - 2*x^78 + 2*x^76 - 2*x^74)/y) dx +numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 - 2*x^82 - 2*x^80 - 2*x^76)/y) dx +numerator: 4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - 2*x^80 + 2*x^78 - 2*x^76 + 2*x^74 - 2*x^72 - 2*x^70 - x^68)/y) dx +numerator: 4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 + 2*x^78 - x^76 + 2*x^74 - x^68 + 2*x^66)/y) dx +numerator: 2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^68 - 2*x^66 - x^64)/y) dx +numerator: 2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + x^68 + x^66 - x^64 + x^62 + x^60 + x^56)/y) dx +numerator: 3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 + x^62 + x^60 + x^58 - x^56 + 2*x^54)/y) dx +numerator: 4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 + x^60 + 2*x^58 - x^56 - 2*x^54 - x^52 - x^50 + 2*x^48)/y) dx +numerator: 4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 + 2*x^58 - 2*x^54 + x^52 + x^50 + 2*x^48 + 2*x^46)/y) dx +numerator: 4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + x^52 + x^50 - x^48 - 2*x^46 - x^44)/y) dx +numerator: 3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 + x^52 + x^50 - 2*x^48 - 2*x^44)/y) dx +numerator: 4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^42 + 2*x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 + x^50 - x^48 - x^44 - x^42 - x^40 + 2*x^38)/y) dx +numerator: 3*x^48 + 2*x^46 + 3*x^44 + x^40 + 2*x^38 + 2*x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - x^48 + x^46 - x^44 + x^42 + x^40 + 2*x^38 + 2*x^36)/y) dx +numerator: 2*x^46 + x^40 + 4*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + x^46 - 2*x^44 + x^42 + x^40 + x^38 - x^36 - 2*x^34)/y) dx +numerator: x^40 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 + x^40 - 2*x^38)/y) dx +numerator: 3*x^36 + x^32 + 3*x^28 + x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - x^36 - 2*x^32 - 2*x^30 - 2*x^26)/y) dx +numerator: x^32 + 2*x^28 + 3*x^26 + 2*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 - 2*x^32 - 2*x^30 - 2*x^28 + 2*x^26 - 2*x^24)/y) dx +numerator: 3*x^28 + 3*x^26 + 3*x^24 + x^22 + 4*x^20 + x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 + 2*x^26 - 2*x^22 - 2*x^20 - x^18)/y) dx +numerator: 3*x^26 + x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + 2*x^26 - x^24 - 2*x^22 - 2*x^20 - 2*x^18 + 2*x^16 - 2*x^14)/y) dx +numerator: x^22 + 4*x^20 + 2*x^18 + 3*x^16 + 2*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 - 2*x^22 - 2*x^20 + x^18 + x^16 + x^14)/y) dx +numerator: 4*x^20 + 3*x^18 + 3*x^16 + 3*x^14 + 4*x^12 + x^10 + x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 - 2*x^20 - 2*x^18 + x^16 - 2*x^14 - 2*x^12 - 2*x^10 - x^8)/y) dx +numerator: 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 2*x^6 + 3*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 - 2*x^18 + 2*x^16 - 2*x^14 - x^8 + 2*x^6)/y) dx +numerator: x^16 + 2*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^16 + 2*x^14 - 2*x^8 - x^6 - 2*x^4)/y) dx +numerator: 2*x^10 + 2*x^6 + x^2 + 2 +W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 + 4*x^2 +((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 - x^8 + 2*x^6 - x^4)/y) dx +numerator 2*x^10 + 2*x^6 + x^2 + 2 +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [152], in () +----> 1 int(A.diffn().regular_form()) + +Input In [151], in int(self) + 37 if a < Integer(0): + 38 print('numerator', numerator) +---> 39 W += Rx(numerator/f.derivative()) + 40 numerator = Rx(Integer(0)) + 41 result = result + superelliptic_function(C, y*W) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l1, A = decompositin_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1 = C1.x^126 + 2*C1.x^122 + 4*C1.x^118 + 2*C1.x^114 + 3*C1.x^108 + 2*C1.x^104 + C1.x^102 + 3*C1.x^92 + 3*C1.x^88 + 3*C1.x^84 + 4*C1.x^82 + C1.x^78 + C1.x^7 4 +....:  + 3*C1.x^72 + C1.x^68 + 2*C1.x^66 + 3*C1.x^64 + C1.x^56 + 4*C1.x^54 + 3*C1.x^48 + 2*C1.x^46 + 3*C1.x^44 + C1.x^42 + 3*C1.x^38 + 2*C1.x^36 + C1.x^34 + 3*C1. x +....: ^32 + 3*C1.x^26 + 2*C1.x^22 + C1.x^18 + C1.x^14 + 2*C1.x^12 + C1.x^8 + 2*C1.x^6 + C1.x^4 + 4*C1.x^2[?7h[?12l[?25h[?25l[?7lsage: A1 = C1.x^126 + 2*C1.x^122 + 4*C1.x^118 + 2*C1.x^114 + 3*C1.x^108 + 2*C1.x^104 + C1.x^102 + 3*C1.x^92 + 3*C1.x^88 + 3*C1.x^84 + 4*C1.x^82 + C1.x^78 + C1.x^7 4 +....:  + 3*C1.x^72 + C1.x^68 + 2*C1.x^66 + 3*C1.x^64 + C1.x^56 + 4*C1.x^54 + 3*C1.x^48 + 2*C1.x^46 + 3*C1.x^44 + C1.x^42 + 3*C1.x^38 + 2*C1.x^36 + C1.x^34 + 3*C1. x +....: ^32 + 3*C1.x^26 + 2*C1.x^22 + C1.x^18 + C1.x^14 + 2*C1.x^12 + C1.x^8 + 2*C1.x^6 + C1.x^4 + 4*C1.x^2 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1 = C1.x^126 + 2*C1.x^122 + 4*C1.x^118 + 2*C1.x^114 + 3*C1.x^108 + 2*C1.x^104 + C1.x^102 + 3*C1.x^92 + 3*C1.x^88 + 3*C1.x^84 + 4*C1.x^82 + C1.x^78 + C1.x^7 4 +....:  + 3*C1.x^72 + C1.x^68 + 2*C1.x^66 + 3*C1.x^64 + C1.x^56 + 4*C1.x^54 + 3*C1.x^48 + 2*C1.x^46 + 3*C1.x^44 + C1.x^42 + 3*C1.x^38 + 2*C1.x^36 + C1.x^34 + 3*C1. x +....: ^32 + 3*C1.x^26 + 2*C1.x^22 + C1.x^18 + C1.x^14 + 2*C1.x^12 + C1.x^8 + 2*C1.x^6 + C1.x^4 + 4*C1.x^2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA +  + [?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: A1 = A1 * C1.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lA1 = A1 * C1.y[?7h[?12l[?25h[?25l[?7l = Rx(A)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (A - A1).diffn() +[?7h[?12l[?25h[?2004l[?7h((x^10 + x^6 - 2*x^2 + 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1 = A1 * C1.y[?7h[?12l[?25h[?25l[?7l = Rx(A)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: A - A1 +[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + x^32 + 2*x^30 + x^28 + 2*x^26 + 3*x^24 + 2*x^22 + x^20 + 2*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + 3*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.polynomial.derivative()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lpolynomial.derivative()[?7h[?12l[?25h[?25l[?7lsage: C1.polynomial.derivative() +[?7h[?12l[?25h[?2004l[?7h2*x^10 + x^6 + 2*x^2 + 4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA - A1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y/2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - C.y/2).diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [158], in () +----> 1 (A - A1 - C.y/Integer(2)).diffn() + +File :75, in __truediv__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y/2).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1C.y).difn()[?7h[?12l[?25h[?25l[?7l1.C.y).difn()[?7h[?12l[?25h[?25l[?7l2C.y).difn()[?7h[?12l[?25h[?25l[?7l*C.y).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l12*C.y).difn()[?7h[?12l[?25h[?25l[?7l/2*C.y).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - 1/2*C.y).diffn() +[?7h[?12l[?25h[?2004l[?7h((-2*x^10 + 2*x^6)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - 1/2*C.y).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - C.y).diffn() +[?7h[?12l[?25h[?2004l[?7h((-2*x^6 + 2*x^2 - 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y).diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - C.y) +[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y)[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA(A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l2(A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l=(A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A2 = (A - A1 - C.y)/C.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: A2 +[?7h[?12l[?25h[?2004l[?7h(x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA2.function.numerator()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldnumerator()[?7h[?12l[?25h[?25l[?7lenumerator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lerator()[?7h[?12l[?25h[?25l[?7lerator()[?7h[?12l[?25h[?25l[?7loerator()[?7h[?12l[?25h[?25l[?7lmerator()[?7h[?12l[?25h[?25l[?7lierator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lator()[?7h[?12l[?25h[?25l[?7lnator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A2.function.numerator().quo_rem(A2.function.denominator()) +[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4), + 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2.function.numerator().quo_rem(A2.function.denominator())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A2.function.numerator() +[?7h[?12l[?25h[?2004l[?7hx^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2.function.numerator()[?7h[?12l[?25h[?25l[?7l().quo_rem(A2.function.denominator())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()).quo_rem(A2.function.denominator()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A2.function.numerator().quo_rem(A2.function.denominator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (A2.function.numerator()).quo_rem(A2.function.denominator()) +[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4), + 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxt. = PolynomialRing(Rx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFF[?7h[?12l[?25h[?25l[?7lxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7ly, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C.fct_field +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C1.fct_field +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7l(A2.function.numeraor()).quo_rem(A2.function.denominator())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(A2.function.numerator()).quo_rem(A2.function.denominator()[?7h[?12l[?25h[?25l[?7lx(A2.function.numerator()).quo_rem(A2.function.denominator()[?7h[?12l[?25h[?25l[?7ly(A2.function.numerator()).quo_rem(A2.function.denominator()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A2.function.denominator()[?7h[?12l[?25h[?25l[?7lA2.function.denominator()[?7h[?12l[?25h[?25l[?7lRA2.function.denominator()[?7h[?12l[?25h[?25l[?7lxA2.function.denominator()[?7h[?12l[?25h[?25l[?7lyA2.function.denominator()[?7h[?12l[?25h[?25l[?7l(A2.function.denominator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: Rxy(A2.function.numerator()).quo_rem(Rxy(A2.function.denominator())) +[?7h[?12l[?25h[?2004l[?7h(x^110 - x^106 + 2*x^100 + 2*x^96 + 2*x^92 - x^90 + 2*x^88 + 2*x^84 + x^82 + x^76 - 2*x^72 + x^70 - 2*x^68 - 2*x^66 - 2*x^64 - 2*x^62 - x^58 + x^56 - x^54 + x^52 + x^50 - x^48 + x^46 - x^44 - x^42 + 2*x^40 + 2*x^38 - 2*x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 - x^26 - 2*x^24 + 2*x^22 - 2*x^18 + x^16 - 2*x^14 - x^12 + 2*x^10 - 2*x^6 + 2, + x^32 + 2*x^30 + 2*x^22 - x^20 + 2*x^18 - x^16 - 2*x^14 + 2*x^12 + x^10 - x^6 + x^4 - 2*x^2) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1 = om.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lega1[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: omega1 +[?7h[?12l[?25h[?2004l[?7h((2*x^10 + 2*x^6 + x^2 + 2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.polynomial.derivative()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.y.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^10 - 2*x^6 + x^2 + 2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loC1.y.difn()[?7h[?12l[?25h[?25l[?7lmC1.y.difn()[?7h[?12l[?25h[?25l[?7leC1.y.difn()[?7h[?12l[?25h[?25l[?7lgC1.y.difn()[?7h[?12l[?25h[?25l[?7laC1.y.difn()[?7h[?12l[?25h[?25l[?7l2C1.y.difn()[?7h[?12l[?25h[?25l[?7l =C1y.diffn()[?7h[?12l[?25h[?25l[?7l C1.y.difn()[?7h[?12l[?25h[?25l[?7loC1.y.difn()[?7h[?12l[?25h[?25l[?7lmC1.y.difn()[?7h[?12l[?25h[?25l[?7leC1.y.difn()[?7h[?12l[?25h[?25l[?7lgC1.y.difn()[?7h[?12l[?25h[?25l[?7laC1.y.difn()[?7h[?12l[?25h[?25l[?7l1C1.y.difn()[?7h[?12l[?25h[?25l[?7l C1.y.difn()[?7h[?12l[?25h[?25l[?7l-C1.y.difn()[?7h[?12l[?25h[?25l[?7l C1.y.difn()[?7h[?12l[?25h[?25l[?7l2C1.y.difn()[?7h[?12l[?25h[?25l[?7l*C1.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega2 = omega1 - 2*C1.y.diffn() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega2 = omega1 - 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: omega2 +[?7h[?12l[?25h[?2004l[?7h((x^6 - x^2 - 2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega2[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega2.regular_form() +[?7h[?12l[?25h[?2004l[?7h((3*x^11 + 4*x^7 + 4*x^5 + 3*x^3 + x)*y) dx + (2*x^16 + 4*x^12 + x^10 + x^8 + x^6 + 3*x^4 + 3*x^2 + 4) dy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega2.regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega2.int() +[?7h[?12l[?25h[?2004l[?7h((3*x^28 + 4*x^26 + 4*x^24 + x^22 + 4*x^20 + 4*x^16 + x^14 + 2*x^12 + 2*x^10 + 4*x^8 + 3*x^6 + 4*x^4 + 2*x^2 + 4)/(x^36 + 3*x^34 + 2*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 3*x^12 + 4*x^10 + 4*x^6 + x^2 + 1))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.y.diffn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.y.diffn()[?7h[?12l[?25h[?25l[?7lsage: C1 +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.y.diffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.is_smooth() +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2.function.numerator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega2.int()[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = omega1 - 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7lC1.y.diffn()[?7h[?12l[?25h[?25l[?7lomega1[?7h[?12l[?25h[?25l[?7lRxy(A2.function.numerator()).quo_rem(Rxy(A2.function.denominator()))[?7h[?12l[?25h[?25l[?7lF, Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7l(A2.function.numeraor()).quo_rem(A2.function.denominator())[?7h[?12l[?25h[?25l[?7lA2.function.numerator()[?7h[?12l[?25h[?25l[?7l().quo_rem(A2.function.denominator())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7lsage: A2 = (A - A1 - C.y)/C.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l - A1[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - C.y).diffn() +[?7h[?12l[?25h[?2004l[?7h((-2*x^6 + 2*x^2 - 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l - A1[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: A - A1 - C.y +[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy(A2.function.numerator()).quo_rem(Rxy(A2.function.denominator()))[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: Rx +[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4).factor() +[?7h[?12l[?25h[?2004l[?7h(x - 1)^3 * (x + 1)^3 * (x^5 - x + 2)^3 * (x^5 - x - 2)^3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4).factor()[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lA - A1 - C.y[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.y).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - C1.y).diffn() +[?7h[?12l[?25h[?2004l[?7h((-2*x^6 + 2*x^2 - 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C1.y).diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA - A1 - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA1 - C.y[?7h[?12l[?25h[?25l[?7lsage: A - A1 - C.y +[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.is_smooth()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 3 +....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54 +....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 4 +....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 + +....:  2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y +....: print(A.diffn()) +....: print(A.diffn().is_regular_on_U0())[?7h[?12l[?25h[?25l[?7lsage: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 3 +....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54 +....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 4 +....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 + +....:  2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y +....: print(A.diffn()) +....: print(A.diffn().is_regular_on_U0()) +[?7h[?12l[?25h[?2004l((-2*x^6 + 2*x^2 - 1)/y) dx +True +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 3 +....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54   +....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 4 +....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 + +....:  2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7l.diffn().regular_form() +  +  +  + [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion + A.expansion  + A.expansion_at_infty + +  + [?7h[?12l[?25h[?25l[?7l + A.expansion  + + [?7h[?12l[?25h[?25l[?7l_at_infty + A.expansion  + A.expansion_at_infty[?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-235 + 3*t^-195 + 2*t^-175 + 2*t^-155 + 3*t^-95 + 3*t^-55 + 3*t^-35 + 4*t + 2*t^9 + 4*t^13 + 4*t^25 + 4*t^29 + 2*t^33 + 4*t^37 + 2*t^41 + 3*t^49 + 2*t^65 + t^69 + 3*t^73 + 4*t^77 + 4*t^81 + t^85 + 4*t^93 + 4*t^97 + 2*t^105 + t^109 + 3*t^117 + 3*t^125 + 2*t^129 + t^137 + t^145 + 4*t^149 + 2*t^165 + 4*t^173 + 4*t^177 + 2*t^181 + 3*t^185 + t^197 + 2*t^201 + 3*t^205 + t^209 + 2*t^213 + 3*t^217 + 3*t^221 + 2*t^225 + 2*t^229 + 4*t^237 + t^245 + 4*t^249 + O(t^265) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7ldef int(self):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_pth_power(A) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [187], in () +----> 1 decomposition_g0_pth_power(A) + +File :5, in decomposition_g0_pth_power(fct) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_() + 1329 normalize(x._numer, x._denom, self.p) + 1330 if nmod_poly_degree(x._denom) != 0: +-> 1331 raise ValueError("not integral") + 1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint) + 1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1: + +ValueError: not integral +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: A +[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1 = A1 * C1.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldiff().regular_form()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.diffn() +[?7h[?12l[?25h[?2004l[?7h((-2*x^6 + 2*x^2 - 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 3 +....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54 +....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 4 +....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 + +....:  2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y +....: print(A.diffn()) +....: print(A.diffn().is_regular_on_U0()) +....: print(decomposition_g0_pth_power(A))[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() + + + + + +A =((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 3 +*C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86+ 2*C1.x^84 + C1.x^82 +4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54  ++ 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 4 +*C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36+ 2*C1.x^34+ 2*C1.x^32+ 2*C1.x^30+ 2*C1.x^28+ 4*C1.x^26+ C1.x^24+ + 2*C1.x^22+ 3*C1.x^20+ 2*C1.x^18 + C1.x^14+ 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^44one))*C1.y +print(A.diffn()) +.is_regular_on_U0()) +  + [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l + + + + +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7lom1= ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 +4*C1.x^136 + 3*C1.x^134+ 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 3 +*C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54  ++ 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 +4*C1.x^28 +3*C1.x^26 +2*C1.x^24 +3*C1.x^20 +2*C1.x^16 +C1.x^14 +4 +*C1.x^12 +3*C1.x^10 +2*C1.x^8 + 3*C1.x^6 +2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^362x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 + + 2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y +() +....: print(A.diffn().is_regular_on_U0()) +....: print(decomposition_g0_pth_power(A))[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l() +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +( + + +)[?7h[?12l[?25h[?25l[?7l( + + +) + +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7limport itertools +....: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: N = 5 +....: lista = [GF(p) for _ in range(N)] +....: for a in itertools.product(*lista): +....:  polynom = sum(a[i] * x^i for i in range(N)) +....: ^Ipolynom = superelliptic_function(C1, polynom) +....: ^Iif polynom.diffn() == om1: +....: ^I print(polynom)[?7h[?12l[?25h[?25l[?7lsage: import itertools +....: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: N = 5 +....: lista = [GF(p) for _ in range(N)] +....: for a in itertools.product(*lista): +....:  polynom = sum(a[i] * x^i for i in range(N)) +....: ^Ipolynom = superelliptic_function(C1, polynom) +....: ^Iif polynom.diffn() == om1: +....: ^I print(polynom) +[?7h[?12l[?25h[?2004l Input In [190] + polynom = superelliptic_function(C1, polynom) + ^ +TabError: inconsistent use of tabs and spaces in indentation + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools +....: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: N = 5 +....: lista = [GF(p) for _ in range(N)] +....: for a in itertools.product(*lista): +....:  polynom = sum(a[i] * x^i for i in range(N)) +....: ^Ipolynom = superelliptic_function(C1, polynom) +....: ^Iif polynom.diffn() == om1: +....: ^I^Iprint(polynom)[?7h[?12l[?25h[?25l[?7lsage: import itertools +....: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: N = 5 +....: lista = [GF(p) for _ in range(N)] +....: for a in itertools.product(*lista): +....:  polynom = sum(a[i] * x^i for i in range(N)) +....: ^Ipolynom = superelliptic_function(C1, polynom) +....: ^Iif polynom.diffn() == om1: +....: ^I^Iprint(polynom) +[?7h[?12l[?25h[?2004l Input In [191] + polynom = superelliptic_function(C1, polynom) + ^ +TabError: inconsistent use of tabs and spaces in indentation + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools +....: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: N = 5 +....: lista = [GF(p) for _ in range(N)] +....: for a in itertools.product(*lista): +....: ^Ipolynom = sum(a[i] * x^i for i in range(N)) +....: ^Ipolynom = superelliptic_function(C1, polynom) +....: ^Iif polynom.diffn() == om1: +....: ^I^Iprint(polynom)[?7h[?12l[?25h[?25l[?7l....: ^I^Iprint(polynom) +....: [?7h[?12l[?25h[?25l[?7lsage: import itertools +....: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: N = 5 +....: lista = [GF(p) for _ in range(N)] +....: for a in itertools.product(*lista): +....: ^Ipolynom = sum(a[i] * x^i for i in range(N)) +....: ^Ipolynom = superelliptic_function(C1, polynom) +....: ^Iif polynom.diffn() == om1: +....: ^I^Iprint(polynom) +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools +....: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: N = 7 +....: lista = [GF(p) for _ in range(N)] +....: for a in itertools.product(*lista): +....: ^Ipolynom = sum(a[i] * x^i for i in range(N)) +....: ^Ipolynom = superelliptic_function(C1, polynom) +....: ^Iif polynom.diffn() == om1: +....: ^I^Iprint(polynom)[?7h[?12l[?25h[?25l[?7l....: ^I^Iprint(polynom) +....: [?7h[?12l[?25h[?25l[?7lsage: import itertools +....: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: N = 7 +....: lista = [GF(p) for _ in range(N)] +....: for a in itertools.product(*lista): +....: ^Ipolynom = sum(a[i] * x^i for i in range(N)) +....: ^Ipolynom = superelliptic_function(C1, polynom) +....: ^Iif polynom.diffn() == om1: +....: ^I^Iprint(polynom) +....:  +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +KeyError Traceback (most recent call last) +File /ext/sage/9.7/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category() + 838 try: +--> 839 return self.__cached_methods[name] + 840 except KeyError: + +KeyError: '_mpoly_base_ring' + +During handling of the above exception, another exception occurred: + +AttributeError Traceback (most recent call last) +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:1114, in PolynomialRing_general._mpoly_base_ring(self, variables) + 1113 try: +-> 1114 return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)]) + 1115 except AttributeError: + +File /ext/sage/9.7/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__() + 832 """ +--> 833 return self.getattr_from_category(name) + 834 + +File /ext/sage/9.7/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category() + 847 +--> 848 attr = getattr_from_other_class(self, cls, name) + 849 self.__cached_methods[name] = attr + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class() + 355 dummy_error_message.name = name +--> 356 raise AttributeError(dummy_error_message) + 357 cdef PyObject* attr = instance_getattr(cls, name) + +AttributeError: 'FpT_with_category' object has no attribute '_mpoly_base_ring' + +During handling of the above exception, another exception occurred: + +KeyboardInterrupt Traceback (most recent call last) +Input In [193], in () + 15 polynom = sum(a[i] * x**i for i in range(N)) + 16 polynom = superelliptic_function(C1, polynom) +---> 17 if polynom.diffn() == om1: + 18 print(polynom) + +File :12, in __eq__(self, other) + +File :161, in reduce(self) + +File :263, in reduction(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:921, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 919 + 920 elif isinstance(element, polynomial_element.Polynomial): +--> 921 if base_ring.has_coerce_map_from(element.parent()._mpoly_base_ring(self.variable_names())): + 922 return self(element._mpoly_dict_recursive(self.variable_names(), base_ring)) + 923 + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:1114, in PolynomialRing_general._mpoly_base_ring(self, variables) + 1112 else: + 1113 try: +-> 1114 return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)]) + 1115 except AttributeError: + 1116 return self.base_ring() + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools +....: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: N = 7 +....: lista = [GF(p) for _ in range(N)] +....: for a in itertools.product(*lista): +....: ^Ipolynom = sum(a[i] * x^i for i in range(N)) +....: ^Ipolynom = C1.y*superelliptic_function(C1, polynom) +....: ^Iif polynom.diffn() == om1: +....: ^I^Iprint(polynom)[?7h[?12l[?25h[?25l[?7l....: ^I^Iprint(polynom) +....: [?7h[?12l[?25h[?25l[?7lsage: import itertools +....: p = 5 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: #f = (x^3 - x)^3 + x^3 - x +....: f = x^3 + x +....: f1 = f(x = x^5 - x) +....: C = superelliptic(f, m) +....: C1 = superelliptic(f1, m, prec = 500) +....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx +....: N = 7 +....: lista = [GF(p) for _ in range(N)] +....: for a in itertools.product(*lista): +....: ^Ipolynom = sum(a[i] * x^i for i in range(N)) +....: ^Ipolynom = C1.y*superelliptic_function(C1, polynom) +....: ^Iif polynom.diffn() == om1: +....: ^I^Iprint(polynom) +....:  +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [194], in () + 15 polynom = sum(a[i] * x**i for i in range(N)) + 16 polynom = C1.y*superelliptic_function(C1, polynom) +---> 17 if polynom.diffn() == om1: + 18 print(polynom) + +File :12, in __eq__(self, other) + +File :162, in reduce(self) + +File :7, in __init__(self, C, g) + +File :296, in reduction_form(C, g) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + 1518 cdef long value + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op() + 1198 # Now coerce to a common parent and do the operation there + 1199 try: +-> 1200 xy = self.canonical_coercion(x, y) + 1201 except TypeError: + 1202 self._record_exception() + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion() + 1313 x_elt = x + 1314 if y_map is not None: +-> 1315 y_elt = (y_map)._call_(y) + 1316 else: + 1317 y_elt = y + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:432, in sage.structure.coerce_maps.CallableConvertMap._call_() + 430 y = self._func(C, x) + 431 else: +--> 432 y = self._func(x) + 433 except Exception: + 434 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:324, in FractionField_generic._coerce_map_from_..wrapper(x) + 323 def wrapper(x): +--> 324 return self._element_class(self, x.numerator(), x.denominator()) + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1167, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__() + 1165 1/2/x + 1166 """ +-> 1167 FractionFieldElement.__init__(self, parent, numerator, denominator, + 1168 coerce, reduce) + 1169 if not reduce: + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:121, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 119 if reduce and parent.is_exact(): + 120 try: +--> 121 self.reduce() + 122 except ArithmeticError: + 123 pass + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce() + 1237 if self._is_reduced: + 1238 return +-> 1239 super(self.__class__, self).reduce() + 1240 self.normalize_leading_coefficients() + 1241 + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce() + 162 return codomain.coerce(nnum/nden) + 163 +--> 164 cpdef reduce(self): + 165 """ + 166 Reduce this fraction. + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce() + 195 return + 196 try: +--> 197 g = self.__numerator.gcd(self.__denominator) + 198 if not g.is_unit(): + 199 self.__numerator //= g + +File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method() + 4492 def new_method(self, other, *args, **kwargs): + 4493 if have_same_parent(self, other): +-> 4494 return method(self, other, *args, **kwargs) + 4495 else: + 4496 a, b = coercion_model.canonical_coercion(self, other) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd() + 4911 raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base) + 4912 else: +-> 4913 return doit(self, other) + 4914 + 4915 @coerce_binop + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g) + 944 f1 = Num(f.numerator()) + 945 g1 = Num(g.numerator()) +--> 946 return Pol(f1.gcd(g1)).monic() + +File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method() + 4492 def new_method(self, other, *args, **kwargs): + 4493 if have_same_parent(self, other): +-> 4494 return method(self, other, *args, **kwargs) + 4495 else: + 4496 a, b = coercion_model.canonical_coercion(self, other) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4907, in sage.rings.polynomial.polynomial_element.Polynomial.gcd() + 4905 if tgt.ngens() > 1 and tgt._has_singular: + 4906 g = flatten(self).gcd(flatten(other)) +-> 4907 return flatten.section()(g) + 4908 try: + 4909 doit = self._parent._base._gcd_univariate_polynomial + +File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__() + 767 if P is D: # we certainly want to call _call_/with_args + 768 if not args and not kwds: +--> 769 return self._call_(x) + 770 return self._call_with_args(x, args, kwds) + 771 # Is there coercion? + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:362, in UnflatteningMorphism._call_(self, p) + 359 Morphism.__init__(self, hom) + 360 self._repr_type_str = 'Unflattening' +--> 362 def _call_(self, p): + 363 """ + 364  Evaluate an unflattening morphism. + 365 + (...) + 377  ....: assert z == g(f(z)) + 378  """ + 379 index = [0] + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1 +[?7h[?12l[?25h[?2004l[?7h((-2*x^6 + 2*x^2 - 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.cartier().cartier().inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.cartier() +[?7h[?12l[?25h[?2004l[?7h0 dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7linv_catier().inv_cartier()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint().diffn[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.int() +[?7h[?12l[?25h[?2004l[?7h((4*x^28 + 2*x^26 + 2*x^24 + 3*x^22 + 2*x^20 + 2*x^16 + 3*x^14 + x^12 + x^10 + 2*x^8 + 4*x^6 + 2*x^4 + x^2 + 2)/(x^36 + 3*x^34 + 2*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 3*x^12 + 4*x^10 + 4*x^6 + x^2 + 1))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: om1.curve +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.genus() +[?7h[?12l[?25h[?2004l[?7h7 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = [GF(p) for _ in range(N)][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [200], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :11, in  + +File :44, in crystalline_cohomology_basis(self, prec, info) + +File :26, in de_rham_witt_lift(cech_class, prec) + +File :90, in diffn(self, dy_w) + +File :99, in diffn(self, dy_w) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :149, in auxilliary_derivative(P) + +File :55, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :55, in __rmul__(self, other) + +File :84, in __add__(self, other) + +File :65, in __mul__(self, other) + +File :94, in diffn(self) + +File /ext/sage/9.7/src/sage/categories/quotient_fields.py:610, in QuotientFields.ElementMethods.derivative(self, *args) + 580 r""" + 581 The derivative of this rational function, with respect to variables + 582 supplied in args. + (...) + 607  2/(x^3 + 3*x^2*y + 3*x*y^2 + y^3) + 608 """ + 609 from sage.misc.derivative import multi_derivative +--> 610 return multi_derivative(self, args) + +File /ext/sage/9.7/src/sage/misc/derivative.pyx:222, in sage.misc.derivative.multi_derivative() + 220 + 221 for arg in derivative_parse(args): +--> 222 F = F._derivative(arg) + 223 return F + 224 + +File /ext/sage/9.7/src/sage/categories/quotient_fields.py:671, in QuotientFields.ElementMethods._derivative(self, var) + 613 r""" + 614 Returns the derivative of this rational function with respect to the + 615 variable ``var``. + (...) + 668  (-t + 1)/(t^3 + 3*t^2 + 3*t + 1) + 669 """ + 670 R = self.parent() +--> 671 if var in R.gens(): + 672 var = R.ring()(var) + 674 num = self.numerator() + +File /ext/sage/9.7/src/sage/structure/element.pyx:1112, in sage.structure.element.Element.__richcmp__() + 1110 return (self)._richcmp_(other, op) + 1111 else: +-> 1112 return coercion_model.richcmp(self, other, op) + 1113 + 1114 cpdef _richcmp_(left, right, int op): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp() + 1971 # Coerce to a common parent + 1972 try: +-> 1973 x, y = self.canonical_coercion(x, y) + 1974 except (TypeError, NotImplementedError): + 1975 pass + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion() + 1313 x_elt = x + 1314 if y_map is not None: +-> 1315 y_elt = (y_map)._call_(y) + 1316 else: + 1317 y_elt = y + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[([(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^18 + 4*x^16 + 4*x^14 + x^8 + x^6 + x^4)/(x^4 + 2*x^2 + 1))*y]), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y), [(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^2 + 1)/(x^4 + 2*x^2 + 1))*y])), + ([(1/(x^2 + 1))*y] d[x] + V(((-2*x^7 - 2*x^5 - 2*x^3 + x)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^23 + 4*x^21 + 4*x^19 + x^13 + x^11 + x^9)/(x^4 + 2*x^2 + 1))*y]), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y), [(1/(x^4 + x^2))*y] d[x] + V(((-2*x^6 + x^4 - 2*x^2 - 2)/(x^7*y + 2*x^5*y + x^3*y)) dx) + dV([(3*x/(x^4 + 2*x^2 + 1))*y]))] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laom.verschiebung() == aom0.verschiebung() + mult_by_p(h.diffn())[?7h[?12l[?25h[?25l[?7lux = OM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7ltom(B1[0]).coordinaes(basis = B1)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[4]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[0]).coordinates(basis=B) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [203], in () +----> 1 autom(B[Integer(0)]).coordinates(basis=B) + +File :109, in coordinates(self, basis, prec, info) + +File :59, in coordinates(self) + +File :93, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lC1.genus()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[0]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lutom(B[0]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[0]).coordinates(basis=B) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [206], in () +----> 1 autom(B[Integer(0)]).coordinates(basis=B) + +File :117, in coordinates(self, basis, prec, info) + +File :88, in div_by_p(self, info) + +TypeError: cannot unpack non-iterable superelliptic_function object +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[0]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lutom(B[0]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[0]).coordinates(basis=B) +[?7h[?12l[?25h[?2004l[?7h[4, 6] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +Computing 2. basis element +Computing 3. basis element +Computing 4. basis element +Computing 5. basis element +Computing 6. basis element +Computing 7. basis element +Computing 8. basis element +Computing 9. basis element +Computing 10. basis element +Computing 11. basis element +Computing 12. basis element +Computing 13. basis element +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [209], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :13, in  + +File :91, in regular_drw_cech(cocycle) + +File :83, in regular_drw_form(omega) + +AttributeError: 'superelliptic_drw_form' object has no attribute 'omega0' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....:  C = omega.curve +....:  omega_aux = omega.r() +....:  omega_aux = omega_aux.regular_form() +....:  aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....:  aux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....:  aux.h2 += fct^p +....:  aux.h2, A = decomposition_g0_pth_power(aux.h2) +....:  aux.omega += (A.diffn()).inv_cartier() +....:  result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....:  return result[?7h[?12l[?25h[?25l[?7l....:  return result +....: [?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....:  C = omega.curve +....:  omega_aux = omega.r() +....:  omega_aux = omega_aux.regular_form() +....:  aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....:  aux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....:  aux.h2 += fct^p +....:  aux.h2, A = decomposition_g0_pth_power(aux.h2) +....:  aux.omega += (A.diffn()).inv_cartier() +....:  result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....:  return result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_drw_form(OM)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr_drw_form(OM)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: regular_drw_form(B[0].omega0) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +File :59, in __mul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + +TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5' + +During handling of the above exception, another exception occurred: + +AttributeError Traceback (most recent call last) +Input In [211], in () +----> 1 regular_drw_form(B[Integer(0)].omega0) + +Input In [210], in regular_drw_form(omega) + 3 omega_aux = omega.r() + 4 omega_aux = omega_aux.regular_form() +----> 5 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() + 6 aux.omega, fct = decomposition_omega0_hpdh(aux.omega) + 7 aux.h2 += fct**p + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__() + 2412 return x + 2413 +-> 2414 return coercion_model.bin_op(left, right, operator.mul) + 2415 + 2416 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :48, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + + [... skipping similar frames: __rmul__ at line 43 (2 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (2 times), sage.structure.element.Element.__mul__ at line 1528 (2 times)] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File :31, in __add__(self, other) + +File :63, in __mul__(self, other) + +AttributeError: 'superelliptic_function' object has no attribute 'form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[0].regular_form()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[0] +[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].regular_form()[?7h[?12l[?25h[?25l[?7lomega0.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0 +[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....:  C = omega.curve +....:  p = C.characteristic +....:  omega_aux = omega.r() +....:  omega_aux = omega_aux.regular_form() +....:  aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....:  aux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....:  aux.h2 += fct^p +....:  aux.h2, A = decomposition_g0_pth_power(aux.h2) +....:  aux.omega += (A.diffn()).inv_cartier() +....:  result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....:  return result[?7h[?12l[?25h[?25l[?7l....:  return result +....: [?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....:  C = omega.curve +....:  p = C.characteristic +....:  omega_aux = omega.r() +....:  omega_aux = omega_aux.regular_form() +....:  aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....:  aux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....:  aux.h2 += fct^p +....:  aux.h2, A = decomposition_g0_pth_power(aux.h2) +....:  aux.omega += (A.diffn()).inv_cartier() +....:  result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....:  return result +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega): +....:  C = omega.curve +....:  p = C.characteristic +....:  omega_aux = omega.r() +....:  omega_aux = omega_aux.regular_form() +....:  aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +....:  aux.omega, fct = decomposition_omega0_hpdh(aux.omega) +....:  aux.h2 += fct^p +....:  aux.h2, A = decomposition_g0_pth_power(aux.h2) +....:  aux.omega += (A.diffn()).inv_cartier() +....:  result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) +....:  return result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l() +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_drw_form(B[0].omega0)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7llar_drw_form(B[0].omega0)[?7h[?12l[?25h[?25l[?7lsage: regular_drw_form(B[0].omega0) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +File :59, in __mul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + +TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5' + +During handling of the above exception, another exception occurred: + +AttributeError Traceback (most recent call last) +Input In [215], in () +----> 1 regular_drw_form(B[Integer(0)].omega0) + +Input In [214], in regular_drw_form(omega) + 4 omega_aux = omega.r() + 5 omega_aux = omega_aux.regular_form() +----> 6 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() + 7 aux.omega, fct = decomposition_omega0_hpdh(aux.omega) + 8 aux.h2 += fct**p + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__() + 2412 return x + 2413 +-> 2414 return coercion_model.bin_op(left, right, operator.mul) + 2415 + 2416 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :48, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + + [... skipping similar frames: __rmul__ at line 43 (2 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (2 times), sage.structure.element.Element.__mul__ at line 1528 (2 times)] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File :31, in __add__(self, other) + +File :63, in __mul__(self, other) + +AttributeError: 'superelliptic_function' object has no attribute 'form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx.diffn().expnson_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx.diffn().expnson_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller().diffn() +[?7h[?12l[?25h[?2004l[?7h[1] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOB[0].omega0[?7h[?12l[?25h[?25l[?7lMB[0].omega0[?7h[?12l[?25h[?25l[?7l B[0].omega0[?7h[?12l[?25h[?25l[?7l=B[0].omega0[?7h[?12l[?25h[?25l[?7l B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7lo = B[0].omega0[?7h[?12l[?25h[?25l[?7lm = B[0].omega0[?7h[?12l[?25h[?25l[?7le = B[0].omega0[?7h[?12l[?25h[?25l[?7lg = B[0].omega0[?7h[?12l[?25h[?25l[?7la = B[0].omega0[?7h[?12l[?25h[?25l[?7lsage: omega = B[0].omega0 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux = omega.r()[?7h[?12l[?25h[?25l[?7lsage: omega_aux = omega.r() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux = omega_aux.regular_form()[?7h[?12l[?25h[?25l[?7lsage: omega_aux = omega_aux.regular_form() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File :58, in __mul__(self, other) + +AttributeError: 'superelliptic_form' object has no attribute 'function' + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Input In [220], in () +----> 1 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() + +File :65, in __mul__(self, other) + +File :64, in __mul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + 1518 cdef long value + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1246 # We should really include the underlying error. + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + 1250 cpdef canonical_coercion(self, x, y): + +TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l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omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File :58, in __mul__(self, other) + +AttributeError: 'superelliptic_form' object has no attribute 'function' + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Input In [221], in () +----> 1 omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() + +File :65, in __mul__(self, other) + +File :64, in __mul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + 1518 cdef long value + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1246 # We should really include the underlying error. + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + 1250 cpdef canonical_coercion(self, x, y): + +TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7laux.dx.teichmuller()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega_aux.dx.teichmuller() +[?7h[?12l[?25h[?2004l[?7h[0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpomega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7laomega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7lromega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7leomega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7lnomega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7ltomega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7l(omega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: parent(omega_aux.dx.teichmuller()) +[?7h[?12l[?25h[?2004l[?7h +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(omega_aux.dx.teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(omega_aux.dx.teichmuller().t.function) +[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega +[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = omga_ax.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lomega_aux.regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = omga_ax.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lomega_aux.regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lparent(omega_aux.dx.teichmuller().t.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7l()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.xteichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File :58, in __mul__(self, other) + +AttributeError: 'superelliptic_form' object has no attribute 'function' + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Input In [226], in () +----> 1 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() + +File :65, in __mul__(self, other) + +File :64, in __mul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + 1518 cdef long value + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1246 # We should really include the underlying error. + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + 1250 cpdef canonical_coercion(self, x, y): + +TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lparent(omega_aux.dx.teichmuller().t.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7l()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.xteichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lomega_aux =omega_ux.regular_form()[?7h[?12l[?25h[?25l[?7lsage: omega_aux = omega_aux.regular_form() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [227], in () +----> 1 omega_aux = omega_aux.regular_form() + +AttributeError: 'superelliptic_regular_form' object has no attribute 'regular_form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux = omega_aux.regular_form()[?7h[?12l[?25h[?25l[?7laux = omega- omeg_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lparent(omega_aux.dx.teichmuller().t.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7l()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.xteichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lomega_aux =omega_ux.regular_form()[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l_aux = omega.r()[?7h[?12l[?25h[?25l[?7lsage: omega_aux = omega.r() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpamega_aux.function[?7h[?12l[?25h[?25l[?7lamega_aux.function[?7h[?12l[?25h[?25l[?7lramega_aux.function[?7h[?12l[?25h[?25l[?7leamega_aux.function[?7h[?12l[?25h[?25l[?7lnamega_aux.function[?7h[?12l[?25h[?25l[?7ltamega_aux.function[?7h[?12l[?25h[?25l[?7l(amega_aux.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmega_aux.function[?7h[?12l[?25h[?25l[?7lomega_aux.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(omega_aux.function) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [229], in () +----> 1 parent(omega_aux.function) + +AttributeError: 'superelliptic_form' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(omega_aux.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lfor)[?7h[?12l[?25h[?25l[?7lform)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(omega_aux.form) +[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux = omega.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: omega.curve +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.xpansion_at_inty[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lrham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, (1/(x*y)) dx)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn()[?7h[?12l[?25h[?25l[?7lsage: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 3 +....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54   +....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 4 +....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 + +....:  2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC +  +  +  + [?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A = C.de_rham_basis[0] +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [234], in () +----> 1 A = C.de_rham_basis[Integer(0)] + +TypeError: 'method' object is not subscriptable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C.de_rham_basis[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = C.de_rham_basis()[0] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: A = A.omega0 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = A.omega0[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpA.form[?7h[?12l[?25h[?25l[?7laA.form[?7h[?12l[?25h[?25l[?7lrA.form[?7h[?12l[?25h[?25l[?7leA.form[?7h[?12l[?25h[?25l[?7lnA.form[?7h[?12l[?25h[?25l[?7ltA.form[?7h[?12l[?25h[?25l[?7l(A.form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(A.form) +[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0].omega0[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7laB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7lrB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7leB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7lnB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7ltB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7l(B[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(B[0].omega0.omega.form) +[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef regular_drw_form(omega):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift + de_rham_witt_lift  + de_rham_witt_lift_form0 + de_rham_witt_lift_form8 + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + de_rham_witt_lift  + + + [?7h[?12l[?25h[?25l[?7l_form0 + de_rham_witt_lift  + de_rham_witt_lift_form0[?7h[?12l[?25h[?25l[?7l( + + + +[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift_form0(C.dx) +[?7h[?12l[?25h[?2004l[?7h[1] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAde_rham_wit_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = de_rham_witt_lift_form0(C.dx) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7lA = de_rham_witt_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpA.omega.form)[?7h[?12l[?25h[?25l[?7laA.omega.form)[?7h[?12l[?25h[?25l[?7lrA.omega.form)[?7h[?12l[?25h[?25l[?7leA.omega.form)[?7h[?12l[?25h[?25l[?7lnA.omega.form)[?7h[?12l[?25h[?25l[?7ltA.omega.form)[?7h[?12l[?25h[?25l[?7l(A.omega.form)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(A.omega.form) +[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A.omega.form)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.form)[?7h[?12l[?25h[?25l[?7l.form)[?7h[?12l[?25h[?25l[?7l.form)[?7h[?12l[?25h[?25l[?7l.form)[?7h[?12l[?25h[?25l[?7l.form)[?7h[?12l[?25h[?25l[?7lh.form)[?7h[?12l[?25h[?25l[?7l1.form)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lfor)[?7h[?12l[?25h[?25l[?7lfo)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(A.h1.function) +[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A.h1.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.function)[?7h[?12l[?25h[?25l[?7l2.function)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(A.h2.function) +[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() +[?7h[?12l[?25h[?2004l +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12, in  + +NameError: name 'C1' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +Computing 2. basis element +Computing 3. basis element +Computing 4. basis element +Computing 5. basis element +Computing 6. basis element +Computing 7. basis element +Computing 8. basis element +Computing 9. basis element +Computing 10. basis element +Computing 11. basis element +Computing 12. basis element +Computing 13. basis element +( [(3*x^5 + 2*x)*y] d[x] + [2*x^10 + x^6 + 2*x^2 + 3] d[y] + V(((2*x^215 + 2*x^211 + 2*x^207 + 3*x^205 + 2*x^203 + 4*x^201 + 3*x^197 + 4*x^189 + 3*x^185 + x^181 + 4*x^179 + 4*x^177 + 2*x^175 + 2*x^173 + 4*x^171 + 2*x^169 + x^167 + 4*x^165 + 2*x^163 + 3*x^161 + x^159 + x^155 + 2*x^151 + 4*x^149 + 3*x^147 + 4*x^145 + 3*x^143 + 2*x^141 + 3*x^137 + 4*x^135 + 4*x^133 + 2*x^131 + 4*x^129 + x^127 + x^125 + 4*x^123 + 2*x^121 + x^117 + 4*x^115 + x^113 + 2*x^111 + x^109 + 2*x^105 + x^103 + 2*x^99 + 3*x^97 + 2*x^95 + 4*x^93 + 4*x^91 + 2*x^89 + x^87 + x^85 + x^83 + x^81 + x^79 + 3*x^77 + 4*x^75 + 4*x^71 + 3*x^69 + x^67 + 2*x^63 + 3*x^61 + x^59 + x^57 + x^55 + 3*x^51 + 3*x^47 + x^43 + x^41 + 4*x^37 + 4*x^33 + 4*x^31 + 4*x^29 + 4*x^25 + 2*x^23 + 2*x^21 + x^19 + 4*x^17 + 3*x^13 + 3*x^11 + x^9 + 3*x^7 + 2*x^3)*y) dx + (3*x^220 + 4*x^210 + 3*x^206 + 2*x^204 + 2*x^202 + 3*x^200 + x^198 + 2*x^196 + 4*x^194 + 4*x^190 + 4*x^180 + x^176 + 2*x^174 + 2*x^170 + 3*x^168 + 4*x^166 + 2*x^164 + 2*x^162 + x^158 + 2*x^156 + 3*x^154 + 2*x^152 + 3*x^150 + 3*x^148 + 2*x^146 + 2*x^142 + 2*x^140 + x^134 + 2*x^132 + 3*x^130 + 2*x^128 + x^126 + 3*x^124 + 4*x^122 + x^120 + 2*x^118 + 4*x^116 + 2*x^114 + 3*x^108 + 4*x^104 + 2*x^100 + 3*x^98 + 3*x^94 + 3*x^92 + 4*x^90 + 4*x^88 + 2*x^86 + x^84 + x^82 + 4*x^80 + 2*x^78 + 3*x^76 + 2*x^74 + 4*x^72 + 2*x^70 + x^62 + 4*x^60 + 2*x^58 + 2*x^54 + 3*x^52 + 3*x^50 + 4*x^44 + x^42 + 3*x^40 + 2*x^32 + x^26 + 2*x^24 + 2*x^22 + x^20 + 2*x^18 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 2*x^4 + 3*x^2) dy) + dV(0), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +Computing 0. basis element +Computing 1. basis element +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12, in  + +File :44, in crystalline_cohomology_basis(self, prec, info) + +File :25, in de_rham_witt_lift(cech_class, prec) + +File :15, in de_rham_witt_lift_form8(omega) + +File :90, in diffn(self, dy_w) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :149, in auxilliary_derivative(P) + +File :149, in auxilliary_derivative(P) + + [... skipping similar frames: auxilliary_derivative at line 149 (1 times)] + +File :149, in auxilliary_derivative(P) + +File :55, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :55, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + + [... skipping similar frames: __rmul__ at line 55 (2 times), sage.rings.integer.Integer.__mul__ at line 1964 (2 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (2 times)] + +File :55, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :53, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :44, in __rmul__(self, constant) + +File :7, in __init__(self, C, g) + +File :296, in reduction_form(C, g) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + 1518 cdef long value + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__() + 1512 cdef int cl = classify_elements(left, right) + 1513 if HAVE_SAME_PARENT(cl): +-> 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): + 1516 return coercion_model.bin_op(left, right, mul) + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:669, in sage.rings.fraction_field_element.FractionFieldElement._mul_() + 667 try: + 668 d1 = rnum.gcd(sden) +--> 669 d2 = snum.gcd(rden) + 670 if not d1.is_unit(): + 671 rnum = rnum // d1 + +File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method() + 4492 def new_method(self, other, *args, **kwargs): + 4493 if have_same_parent(self, other): +-> 4494 return method(self, other, *args, **kwargs) + 4495 else: + 4496 a, b = coercion_model.canonical_coercion(self, other) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd() + 4911 raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base) + 4912 else: +-> 4913 return doit(self, other) + 4914 + 4915 @coerce_binop + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g) + 944 f1 = Num(f.numerator()) + 945 g1 = Num(g.numerator()) +--> 946 return Pol(f1.gcd(g1)).monic() + +File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method() + 4492 def new_method(self, other, *args, **kwargs): + 4493 if have_same_parent(self, other): +-> 4494 return method(self, other, *args, **kwargs) + 4495 else: + 4496 a, b = coercion_model.canonical_coercion(self, other) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4907, in sage.rings.polynomial.polynomial_element.Polynomial.gcd() + 4905 if tgt.ngens() > 1 and tgt._has_singular: + 4906 g = flatten(self).gcd(flatten(other)) +-> 4907 return flatten.section()(g) + 4908 try: + 4909 doit = self._parent._base._gcd_univariate_polynomial + +File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__() + 767 if P is D: # we certainly want to call _call_/with_args + 768 if not args and not kwds: +--> 769 return self._call_(x) + 770 return self._call_with_args(x, args, kwds) + 771 # Is there coercion? + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:380, in UnflatteningMorphism._call_(self, p) + 363 """ + 364 Evaluate an unflattening morphism. + 365 + (...) + 377  ....: assert z == g(f(z)) + 378 """ + 379 index = [0] +--> 380 for R, _ in reversed(self._intermediate_rings): + 381 index.append(index[-1] + len(R.gens())) + 382 newpol = [{} for _ in self._intermediate_rings] + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +Computing 0. basis element +Computing 1. basis element +Computing 2. basis element +Computing 3. basis element +Computing 4. basis element +Computing 5. basis element +Computing 6. basis element +Computing 7. basis element +Computing 8. basis element +Computing 9. basis element +Computing 10. basis element +Computing 11. basis element +Computing 12. basis element +Computing 13. basis element +( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((x^37 + 2*x^35 + x^33 + 4*x^29 + 4*x^27 + x^25 + x^23 + 2*x^19 + 4*x^17 + 2*x^15 + 4*x^9 + x^7 + 3*x^3)*y) dx + (x^38 + x^36 + 4*x^34 + 4*x^32 + 4*x^30 + 2*x^26 + 4*x^22 + 2*x^20 + 2*x^18 + 3*x^16 + 3*x^14 + 4*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) ) +( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((x^42 + 2*x^40 + x^38 + 4*x^34 + 4*x^32 + x^30 + x^28 + 2*x^24 + 3*x^22 + 4*x^18)*y) dx + (x^43 + x^41 + 4*x^39 + 4*x^37 + 4*x^35 + 2*x^31 + 4*x^27 + 2*x^25 + x^23 + 2*x^21 + 4*x^19 + x^17) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) ) +( [(3*x^5 + 2*x)*y] d[x] + [2*x^10 + x^6 + 2*x^2 + 3] d[y] + V(((2*x^215 + 2*x^211 + 2*x^207 + 3*x^205 + 2*x^203 + 4*x^201 + 3*x^197 + 4*x^189 + 3*x^185 + x^181 + 4*x^179 + 4*x^177 + 2*x^175 + 2*x^173 + 4*x^171 + 2*x^169 + x^167 + 4*x^165 + 2*x^163 + 3*x^161 + x^159 + x^155 + 2*x^151 + 4*x^149 + 3*x^147 + 4*x^145 + 3*x^143 + 2*x^141 + 3*x^137 + 4*x^135 + 4*x^133 + 2*x^131 + 4*x^129 + x^127 + x^125 + 4*x^123 + 2*x^121 + x^117 + 4*x^115 + x^113 + 2*x^111 + x^109 + 2*x^105 + x^103 + 2*x^99 + 3*x^97 + 2*x^95 + 4*x^93 + 4*x^91 + 2*x^89 + x^87 + x^85 + x^83 + x^81 + x^79 + 3*x^77 + 4*x^75 + 4*x^71 + 3*x^69 + x^67 + 2*x^63 + 3*x^61 + x^59 + x^57 + x^55 + 3*x^51 + 3*x^47 + x^43 + x^41 + 4*x^37 + 4*x^33 + 4*x^31 + 4*x^29 + 4*x^25 + 2*x^23 + 2*x^21 + x^19 + 4*x^17 + 3*x^13 + 3*x^11 + x^9 + 3*x^7 + 2*x^3)*y) dx + (3*x^220 + 4*x^210 + 3*x^206 + 2*x^204 + 2*x^202 + 3*x^200 + x^198 + 2*x^196 + 4*x^194 + 4*x^190 + 4*x^180 + x^176 + 2*x^174 + 2*x^170 + 3*x^168 + 4*x^166 + 2*x^164 + 2*x^162 + x^158 + 2*x^156 + 3*x^154 + 2*x^152 + 3*x^150 + 3*x^148 + 2*x^146 + 2*x^142 + 2*x^140 + x^134 + 2*x^132 + 3*x^130 + 2*x^128 + x^126 + 3*x^124 + 4*x^122 + x^120 + 2*x^118 + 4*x^116 + 2*x^114 + 3*x^108 + 4*x^104 + 2*x^100 + 3*x^98 + 3*x^94 + 3*x^92 + 4*x^90 + 4*x^88 + 2*x^86 + x^84 + x^82 + 4*x^80 + 2*x^78 + 3*x^76 + 2*x^74 + 4*x^72 + 2*x^70 + x^62 + 4*x^60 + 2*x^58 + 2*x^54 + 3*x^52 + 3*x^50 + 4*x^44 + x^42 + 3*x^40 + 2*x^32 + x^26 + 2*x^24 + 2*x^22 + x^20 + 2*x^18 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 2*x^4 + 3*x^2) dy) + dV(0), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y) ) +( [(3*x^6 + 2*x^2)*y] d[x] + [2*x^11 + x^7 + 2*x^3 + 3*x] d[y] + V(((2*x^220 + 2*x^216 + 2*x^212 + 4*x^210 + 2*x^208 + 4*x^202 + 4*x^200 + x^198 + 2*x^196 + 4*x^194 + 4*x^192 + 3*x^190 + x^186 + x^184 + 4*x^182 + 2*x^180 + 2*x^178 + 3*x^176 + 4*x^174 + 4*x^172 + 2*x^170 + 4*x^168 + 2*x^164 + x^160 + 4*x^158 + 3*x^156 + 4*x^154 + x^152 + 2*x^150 + 4*x^148 + x^138 + x^136 + 3*x^134 + 3*x^128 + 3*x^126 + 4*x^124 + 3*x^122 + x^120 + 3*x^118 + 3*x^116 + 3*x^114 + 2*x^110 + 3*x^108 + 4*x^106 + 4*x^104 + 2*x^102 + 4*x^98 + 2*x^94 + 4*x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + x^76 + 4*x^74 + 2*x^72 + x^70 + 3*x^68 + 3*x^66 + 2*x^64 + 3*x^58 + x^56 + 2*x^50 + x^48 + 2*x^46 + x^44 + 4*x^42 + 2*x^40 + x^38 + 4*x^36 + x^32 + 4*x^30 + 2*x^28 + x^26 + 4*x^24 + 3*x^22 + 4*x^18 + 3*x^16 + x^14 + 3*x^12 + 2*x^8)*y) dx + (3*x^225 + 3*x^215 + 3*x^211 + 2*x^209 + 2*x^207 + x^203 + x^201 + x^197 + 3*x^195 + 3*x^193 + x^191 + 2*x^189 + x^181 + 2*x^179 + 3*x^175 + 3*x^173 + x^171 + 4*x^169 + 3*x^167 + 3*x^163 + 2*x^161 + 4*x^159 + x^157 + 2*x^155 + x^149 + 4*x^147 + 4*x^145 + 2*x^143 + 3*x^141 + x^139 + x^135 + 2*x^133 + x^131 + 2*x^129 + 4*x^127 + x^125 + 2*x^123 + 4*x^121 + x^119 + 2*x^117 + 3*x^115 + 4*x^113 + 3*x^111 + 4*x^109 + 2*x^107 + x^105 + x^103 + x^101 + 4*x^99 + 3*x^97 + 2*x^91 + 4*x^89 + 4*x^87 + 3*x^85 + 3*x^83 + 3*x^81 + 3*x^77 + x^75 + x^73 + 2*x^71 + 2*x^69 + 4*x^67 + 4*x^65 + x^63 + 4*x^61 + 4*x^59 + x^57 + 4*x^55 + 2*x^53 + 2*x^51 + 3*x^49 + 4*x^45 + x^43 + 4*x^37 + 2*x^35 + x^33 + 3*x^31 + 4*x^27 + 2*x^23 + 4*x^21 + 3*x^15 + 2*x^9 + 3*x^7) dy) + dV(0), V(((2*x^88 + 4*x^84 + x^82 + 3*x^80 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + x^58 + 3*x^56 + 2*x^54 + 3*x^52 + x^50 + 4*x^46 + 3*x^44 + x^42 + 2*x^40 + x^38 + 3*x^36 + 2*x^34 + 4*x^28 + x^26 + 2*x^24 + 4*x^22 + x^20 + x^18 + 4*x^16 + 2*x^14 + 4*x^12 + 3*x^8 + 3*x^4 + 4*x^2 + 3)/x^7)*y) ) +( [(3*x^7 + 2*x^3)*y] d[x] + [2*x^12 + x^8 + 2*x^4 + 3*x^2] d[y] + V(((2*x^225 + 2*x^221 + 2*x^217 + 2*x^213 + x^211 + 3*x^205 + 2*x^203 + 4*x^201 + 4*x^199 + 3*x^197 + 3*x^195 + x^191 + 3*x^189 + 4*x^187 + 2*x^185 + 2*x^183 + 2*x^181 + x^179 + 2*x^177 + x^173 + 2*x^171 + 3*x^169 + x^165 + 3*x^163 + 4*x^161 + 4*x^159 + 4*x^157 + 3*x^151 + 2*x^147 + x^145 + 3*x^143 + 2*x^139 + 4*x^137 + 4*x^135 + 2*x^133 + 4*x^131 + 3*x^129 + 4*x^125 + x^117 + x^115 + x^113 + x^109 + 2*x^105 + 4*x^103 + 4*x^99 + 3*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 4*x^87 + 2*x^85 + 2*x^83 + x^81 + 4*x^79 + 2*x^77 + 4*x^75 + x^73 + x^71 + 4*x^69 + x^67 + 2*x^65 + 4*x^61 + 3*x^59 + 4*x^57 + 2*x^55 + x^49 + 4*x^47 + x^45 + x^43 + 3*x^41 + 4*x^39 + x^37 + 4*x^35 + 3*x^33 + x^31 + 2*x^29 + x^27 + 2*x^25 + 2*x^23 + 4*x^21 + 4*x^19 + x^13 + 4*x^11 + 3*x^9 + 4*x^7 + x^3)*y) dx + (3*x^230 + 2*x^220 + 3*x^216 + 2*x^214 + 2*x^212 + 2*x^210 + x^208 + x^204 + 2*x^202 + 2*x^200 + x^198 + 2*x^196 + 4*x^194 + x^190 + x^186 + 2*x^184 + 4*x^180 + 3*x^178 + 3*x^176 + x^174 + 4*x^172 + 2*x^166 + x^160 + 2*x^158 + 3*x^156 + 2*x^154 + x^152 + x^150 + 4*x^148 + x^146 + x^144 + 3*x^142 + 4*x^140 + 2*x^138 + x^136 + x^134 + 4*x^132 + 2*x^128 + 4*x^126 + 4*x^122 + 3*x^120 + 2*x^108 + 3*x^106 + 2*x^104 + 3*x^102 + x^100 + x^98 + 3*x^96 + x^94 + x^92 + 4*x^90 + x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + x^74 + 4*x^72 + x^68 + 2*x^66 + x^64 + 2*x^60 + 4*x^58 + 2*x^56 + 2*x^54 + 2*x^48 + 3*x^46 + 2*x^44 + x^42 + x^40 + 3*x^38 + 2*x^36 + 3*x^30 + 2*x^28 + 2*x^26 + 3*x^24 + 4*x^22 + x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + 4*x^10 + x^4 + 4*x^2) dy) + dV(0), V(((2*x^92 + 4*x^88 + x^86 + 3*x^84 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 4*x^50 + 3*x^48 + x^46 + 2*x^44 + x^42 + 3*x^40 + 2*x^38 + 4*x^32 + x^30 + 2*x^28 + 4*x^26 + x^24 + x^22 + 4*x^20 + 2*x^18 + 4*x^16 + 3*x^12 + 3*x^8 + 4*x^6 + 3*x^4 + 3)/x^6)*y) ) +( [(3*x^8 + 2*x^4)*y] d[x] + [2*x^13 + x^9 + 2*x^5 + 3*x^3] d[y] + V(((2*x^230 + 2*x^226 + 2*x^222 + x^220 + 2*x^218 + 2*x^216 + x^212 + 2*x^210 + 3*x^208 + x^206 + 4*x^204 + 2*x^202 + 3*x^200 + x^196 + 4*x^192 + 2*x^190 + 2*x^188 + x^186 + 3*x^184 + 3*x^180 + 3*x^178 + 4*x^176 + 4*x^174 + x^170 + 2*x^168 + 4*x^164 + 2*x^162 + 3*x^160 + x^158 + x^156 + 4*x^152 + 2*x^150 + 4*x^146 + x^144 + 3*x^142 + 3*x^140 + x^138 + 2*x^134 + 2*x^132 + 3*x^130 + 2*x^128 + 3*x^126 + 2*x^124 + 3*x^122 + x^120 + 3*x^114 + 4*x^112 + 4*x^110 + x^108 + x^106 + 3*x^104 + x^102 + 4*x^100 + 4*x^98 + x^96 + 4*x^94 + 3*x^92 + 4*x^88 + 4*x^86 + 3*x^84 + 3*x^82 + 4*x^80 + 3*x^78 + x^76 + 4*x^74 + 2*x^72 + 3*x^70 + 2*x^68 + x^66 + 2*x^64 + 4*x^62 + 2*x^54 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + 4*x^44 + 3*x^40 + 3*x^38 + 4*x^36 + 4*x^34 + 3*x^30 + 3*x^28 + 4*x^24 + 4*x^22 + x^16 + 2*x^14 + x^12 + 4*x^8)*y) dx + (3*x^235 + x^225 + 3*x^221 + 2*x^219 + 2*x^217 + 4*x^215 + x^213 + 4*x^211 + 2*x^209 + 3*x^207 + x^205 + 4*x^203 + 3*x^201 + x^199 + 2*x^195 + x^191 + 2*x^189 + 3*x^183 + 3*x^179 + 2*x^173 + 2*x^171 + x^169 + 4*x^167 + 4*x^163 + x^161 + 3*x^159 + 3*x^157 + 3*x^155 + x^153 + 4*x^151 + x^149 + x^147 + 2*x^145 + 2*x^143 + x^141 + 4*x^137 + 3*x^135 + 2*x^133 + 4*x^131 + 4*x^129 + x^127 + 3*x^125 + x^123 + x^121 + 2*x^119 + 4*x^117 + x^113 + 4*x^111 + 4*x^109 + 4*x^105 + 3*x^103 + 4*x^101 + 4*x^99 + 2*x^95 + x^89 + 3*x^87 + 4*x^85 + x^83 + 2*x^81 + 3*x^79 + x^77 + 4*x^75 + x^71 + 4*x^69 + 3*x^67 + 4*x^65 + 2*x^63 + 3*x^61 + 3*x^59 + 3*x^57 + x^55 + 4*x^53 + 2*x^51 + 2*x^49 + 3*x^47 + x^45 + 3*x^43 + 3*x^41 + 4*x^39 + 3*x^37 + 4*x^35 + 4*x^33 + 3*x^27 + 3*x^25 + 4*x^23 + 3*x^21 + 2*x^19 + 3*x^17 + x^15 + 4*x^9 + x^7) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^7)*y) ) +( [(3*x^9 + 2*x^5)*y] d[x] + [2*x^14 + x^10 + 2*x^6 + 3*x^4] d[y] + V(((2*x^235 + 2*x^231 + 2*x^227 + 2*x^225 + 2*x^223 + 3*x^221 + 2*x^217 + x^215 + 4*x^213 + 3*x^211 + 4*x^209 + x^207 + 3*x^205 + x^201 + 2*x^199 + 4*x^197 + 2*x^195 + 2*x^193 + 3*x^187 + x^185 + x^181 + x^175 + x^173 + x^171 + 4*x^169 + x^165 + 2*x^163 + 4*x^161 + x^157 + 3*x^155 + 2*x^153 + 3*x^151 + 2*x^147 + 2*x^145 + x^141 + x^139 + 4*x^137 + 2*x^135 + 4*x^133 + x^131 + 4*x^129 + 4*x^123 + 4*x^121 + 2*x^117 + x^115 + 2*x^113 + 4*x^111 + 2*x^109 + 4*x^107 + 4*x^105 + 4*x^101 + x^99 + 2*x^95 + 3*x^93 + 3*x^91 + 3*x^89 + 3*x^85 + 4*x^83 + 2*x^77 + 4*x^75 + x^73 + x^69 + x^65 + 2*x^61 + 3*x^59 + 2*x^57 + 4*x^55 + x^53 + x^51 + 4*x^49 + 2*x^47 + x^45 + 4*x^43 + 3*x^41 + 2*x^37 + x^35 + x^33 + x^31 + 4*x^29 + 3*x^27 + x^25 + 3*x^23 + 3*x^19 + 3*x^17 + 2*x^11 + 4*x^9 + 2*x^7 + 3*x^3)*y) dx + (3*x^240 + 3*x^226 + 2*x^224 + 2*x^222 + x^220 + x^218 + 3*x^216 + 3*x^214 + 4*x^212 + 2*x^208 + 4*x^206 + 3*x^204 + 3*x^200 + x^196 + 2*x^194 + x^190 + 3*x^188 + 2*x^186 + x^182 + 4*x^178 + 2*x^176 + 2*x^174 + 3*x^172 + 4*x^170 + x^168 + 4*x^166 + 4*x^164 + 3*x^158 + 2*x^156 + x^154 + 4*x^152 + 2*x^148 + x^146 + 4*x^144 + 4*x^142 + x^140 + 2*x^138 + 4*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 2*x^128 + 2*x^126 + 4*x^124 + 3*x^122 + 4*x^120 + x^116 + x^112 + 4*x^110 + 2*x^108 + 4*x^104 + 3*x^102 + 3*x^100 + x^98 + 2*x^96 + x^92 + 2*x^90 + 2*x^88 + 3*x^86 + 3*x^84 + 3*x^82 + 3*x^80 + x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 2*x^66 + 3*x^64 + 3*x^62 + x^60 + 4*x^58 + 2*x^56 + 3*x^54 + 3*x^50 + 4*x^46 + 4*x^42 + x^40 + 3*x^38 + 4*x^34 + x^30 + 3*x^28 + 2*x^24 + 4*x^22 + x^20 + 3*x^18 + x^16 + 4*x^14 + x^12 + 2*x^10 + 3*x^4 + 2*x^2) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^2)*y) ) +( [(3*x^10 + 2*x^6)*y] d[x] + [2*x^15 + x^11 + 2*x^7 + 3*x^5] d[y] + V(((2*x^240 + 2*x^236 + 2*x^232 + 3*x^230 + 2*x^228 + 4*x^226 + 3*x^222 + 4*x^214 + 3*x^210 + x^206 + 4*x^204 + 4*x^202 + 2*x^200 + 2*x^198 + 4*x^196 + 2*x^194 + x^192 + 4*x^190 + 2*x^188 + 3*x^186 + x^184 + x^180 + 2*x^176 + 4*x^174 + 3*x^172 + 4*x^170 + 3*x^168 + 2*x^166 + 3*x^162 + 4*x^160 + 4*x^158 + 2*x^156 + 4*x^154 + x^152 + x^150 + 4*x^148 + 2*x^146 + x^142 + x^140 + x^138 + 4*x^136 + x^134 + 2*x^132 + 4*x^130 + 3*x^128 + 3*x^126 + 2*x^124 + 4*x^120 + 3*x^118 + 3*x^116 + x^114 + 3*x^112 + x^110 + 2*x^108 + 2*x^106 + 3*x^104 + 4*x^102 + 4*x^100 + x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 4*x^84 + 4*x^82 + 4*x^78 + x^76 + 3*x^74 + 2*x^72 + 2*x^70 + 4*x^68 + x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^58 + 4*x^54 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 3*x^42 + 3*x^38 + 2*x^36 + 3*x^34 + x^32 + x^30 + 2*x^28 + 3*x^26 + 4*x^24 + x^22 + 2*x^18 + 2*x^16 + 4*x^14 + 2*x^12 + 3*x^8)*y) dx + (3*x^245 + 4*x^235 + 3*x^231 + 2*x^229 + 2*x^227 + 3*x^225 + x^223 + 2*x^221 + 4*x^219 + 4*x^215 + 4*x^205 + x^201 + 2*x^199 + 2*x^195 + 3*x^193 + 4*x^191 + 2*x^189 + 2*x^187 + x^183 + 2*x^181 + 3*x^179 + 2*x^177 + 3*x^175 + 3*x^173 + 2*x^171 + 2*x^167 + 2*x^165 + x^159 + 2*x^157 + 3*x^155 + 2*x^153 + x^151 + 3*x^149 + 4*x^147 + 4*x^145 + 2*x^143 + 4*x^141 + 2*x^139 + 3*x^133 + 3*x^131 + x^129 + 2*x^127 + 2*x^125 + 4*x^123 + 3*x^121 + x^119 + 2*x^117 + 3*x^115 + x^113 + 2*x^107 + x^105 + 2*x^101 + 4*x^99 + 2*x^97 + 2*x^95 + 2*x^93 + 4*x^91 + 2*x^89 + 3*x^87 + 3*x^85 + 4*x^83 + 4*x^81 + 4*x^79 + 3*x^77 + 4*x^75 + x^73 + 3*x^69 + 4*x^67 + 4*x^65 + 4*x^63 + 2*x^59 + 4*x^57 + 4*x^55 + x^53 + 4*x^51 + 3*x^49 + 3*x^45 + 4*x^43 + 3*x^41 + 4*x^39 + 4*x^37 + x^35 + 4*x^31 + 2*x^29 + 4*x^27 + 4*x^25 + 3*x^23 + x^21 + x^19 + 4*x^17 + 2*x^15 + 3*x^9 + 2*x^7) dy) + dV(0), V(((2*x^106 + 4*x^102 + x^100 + 3*x^98 + 4*x^94 + 2*x^92 + 4*x^90 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^78 + x^76 + 3*x^74 + 2*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + x^60 + 2*x^58 + x^56 + 3*x^54 + 2*x^52 + 4*x^46 + x^44 + 2*x^42 + 4*x^40 + x^38 + x^36 + 4*x^34 + 2*x^32 + 4*x^30 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + 3*x^14 + 2*x^12 + 3*x^10 + 4*x^8 + 3*x^2 + 3)/x^5)*y) ) +( [(3*x^11 + 2*x^7)*y] d[x] + [2*x^16 + x^12 + 2*x^8 + 3*x^6] d[y] + V(((2*x^245 + 2*x^241 + 2*x^237 + 4*x^235 + 2*x^233 + 4*x^227 + 4*x^225 + x^223 + 2*x^221 + 4*x^219 + 4*x^217 + 3*x^215 + x^211 + x^209 + 4*x^207 + 2*x^205 + 2*x^203 + 3*x^201 + 4*x^199 + 4*x^197 + 2*x^195 + 4*x^193 + 2*x^189 + x^185 + 4*x^183 + 3*x^181 + 4*x^179 + x^177 + 2*x^175 + 4*x^173 + x^163 + x^161 + 3*x^159 + 3*x^153 + 3*x^151 + 4*x^149 + 3*x^147 + 3*x^143 + 2*x^141 + 3*x^139 + 4*x^137 + 3*x^135 + 2*x^133 + 2*x^131 + 4*x^129 + 3*x^127 + 2*x^125 + 4*x^123 + 2*x^121 + 2*x^117 + 4*x^115 + 4*x^113 + x^111 + 4*x^107 + x^105 + 3*x^103 + 2*x^101 + 2*x^99 + 4*x^97 + 3*x^95 + 3*x^93 + 4*x^91 + 4*x^85 + 2*x^83 + 4*x^81 + 4*x^79 + 4*x^75 + 3*x^73 + 3*x^71 + 4*x^69 + 4*x^65 + 4*x^63 + 3*x^61 + x^59 + x^53 + x^51 + 3*x^49 + x^45 + 2*x^41 + 4*x^39 + 2*x^37 + 2*x^35 + x^33 + 4*x^29 + 4*x^27 + 2*x^25 + 3*x^23 + x^19 + x^17 + 4*x^11 + 3*x^9 + 4*x^7 + x^3)*y) dx + (3*x^250 + 3*x^240 + 3*x^236 + 2*x^234 + 2*x^232 + x^228 + x^226 + x^222 + 3*x^220 + 3*x^218 + x^216 + 2*x^214 + x^206 + 2*x^204 + 3*x^200 + 3*x^198 + x^196 + 4*x^194 + 3*x^192 + 3*x^188 + 2*x^186 + 4*x^184 + x^182 + 2*x^180 + x^174 + 4*x^172 + 4*x^170 + 2*x^168 + 3*x^166 + x^164 + x^160 + 2*x^158 + x^156 + 2*x^154 + 4*x^152 + 2*x^150 + 2*x^148 + 4*x^146 + x^144 + 2*x^142 + x^140 + 4*x^138 + 4*x^136 + 3*x^134 + x^132 + 3*x^128 + 2*x^124 + 3*x^122 + x^120 + x^114 + x^112 + 4*x^108 + x^106 + 4*x^104 + 4*x^102 + 3*x^100 + 4*x^94 + 4*x^92 + x^88 + 3*x^86 + x^84 + 2*x^82 + 2*x^80 + 2*x^78 + 2*x^76 + 3*x^74 + 4*x^72 + 3*x^70 + 2*x^66 + x^64 + 4*x^62 + 3*x^60 + 4*x^58 + 4*x^56 + 4*x^54 + x^52 + 3*x^50 + x^48 + x^46 + 2*x^42 + 2*x^40 + 3*x^38 + 4*x^36 + 3*x^34 + x^28 + x^24 + x^22 + 2*x^20 + x^18 + 2*x^16 + 3*x^14 + 2*x^12 + 4*x^10 + x^4 + 4*x^2) dy) + dV(0), V(((2*x^112 + 4*x^108 + x^106 + 3*x^104 + 4*x^100 + 2*x^98 + 4*x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 3*x^76 + x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + x^62 + 3*x^60 + 2*x^58 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + x^44 + x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 3*x^32 + 3*x^28 + 4*x^26 + 3*x^24 + 3*x^20 + 2*x^18 + 3*x^16 + 4*x^14 + 3*x^8 + 3*x^6 + 4*x^2 + 3)/x^6)*y) ) +( [(4*x^18 + x^10 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [x^23 + 4*x^19 + 4*x^15 + 4*x^11 + 2*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((x^280 + x^276 + x^272 + 3*x^270 + x^268 + x^266 + 3*x^262 + x^260 + 4*x^258 + 3*x^256 + 2*x^254 + x^252 + 3*x^250 + 2*x^246 + x^242 + 4*x^236 + 4*x^234 + 4*x^232 + x^230 + 2*x^228 + 3*x^226 + 2*x^222 + 3*x^220 + x^218 + x^216 + x^214 + 3*x^212 + 4*x^210 + x^208 + x^206 + 4*x^202 + x^196 + x^194 + x^192 + 3*x^190 + 2*x^188 + x^186 + 2*x^184 + x^180 + 2*x^178 + 4*x^174 + 4*x^172 + 2*x^170 + 2*x^168 + 2*x^166 + x^164 + 2*x^162 + 3*x^160 + x^158 + x^156 + x^150 + 3*x^148 + 4*x^144 + x^142 + x^138 + 4*x^136 + 4*x^132 + 4*x^130 + 2*x^128 + x^126 + x^124 + x^122 + 3*x^120 + 3*x^118 + x^116 + 2*x^112 + 3*x^110 + x^108 + 2*x^106 + 4*x^104 + 2*x^102 + 3*x^100 + 4*x^98 + 4*x^96 + 2*x^92 + x^88 + 3*x^86 + 2*x^84 + x^82 + x^80 + 4*x^78 + 3*x^74 + 3*x^70 + 3*x^68 + 2*x^66 + 4*x^64 + 3*x^62 + 4*x^60 + 4*x^58 + x^56 + 3*x^54 + x^48 + 3*x^46 + 2*x^44 + 4*x^42 + 3*x^40 + 4*x^38 + x^36 + 4*x^34 + 3*x^32 + 2*x^30 + 2*x^28 + 2*x^26 + 3*x^22 + 3*x^18 + 4*x^16 + 3*x^14 + 4*x^12 + x^8)*y) dx + (4*x^285 + 3*x^275 + 4*x^271 + x^269 + x^267 + 2*x^265 + 3*x^263 + 2*x^261 + x^259 + 4*x^257 + 4*x^255 + 2*x^253 + 4*x^251 + 3*x^249 + x^245 + 4*x^241 + 4*x^237 + 2*x^235 + x^233 + x^231 + 3*x^227 + x^225 + 4*x^221 + 4*x^219 + 2*x^217 + 4*x^215 + 2*x^213 + x^211 + 2*x^209 + 3*x^207 + x^203 + x^199 + 4*x^193 + x^189 + 4*x^183 + x^181 + x^179 + x^177 + x^175 + 4*x^173 + 4*x^171 + 2*x^169 + 3*x^167 + x^165 + x^163 + 2*x^161 + 2*x^159 + 3*x^157 + 3*x^155 + x^151 + 2*x^149 + 4*x^147 + 3*x^145 + 3*x^143 + 3*x^139 + 3*x^135 + 3*x^133 + 4*x^131 + 2*x^129 + 3*x^125 + 3*x^121 + x^119 + x^117 + 3*x^115 + x^113 + 3*x^111 + 2*x^109 + 4*x^107 + 4*x^105 + 3*x^103 + 4*x^101 + 3*x^99 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 2*x^85 + x^83 + 2*x^79 + 2*x^75 + x^73 + 3*x^71 + x^69 + x^67 + 4*x^63 + x^57 + x^55 + 3*x^53 + x^51 + x^49 + 3*x^47 + x^45 + 2*x^41 + 2*x^39 + 2*x^37 + 2*x^35 + 4*x^33 + x^31 + 4*x^29 + 3*x^27 + 4*x^25 + x^23 + 2*x^21 + x^19 + 4*x^17 + 4*x^15 + x^9 + 4*x^7) dy) + dV(0), [2/x*y] + V(((x^146 + 2*x^142 + 3*x^140 + 4*x^138 + 2*x^134 + x^132 + 2*x^130 + 2*x^126 + 3*x^124 + x^122 + x^120 + 3*x^118 + 3*x^116 + x^114 + 2*x^112 + x^110 + 3*x^108 + x^106 + 3*x^102 + x^100 + 2*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + 2*x^76 + 4*x^72 + x^70 + 4*x^68 + 2*x^66 + x^64 + 3*x^62 + 2*x^60 + 2*x^58 + 2*x^56 + 4*x^52 + x^50 + 2*x^48 + 2*x^46 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + x^26 + x^24 + 3*x^18 + 4*x^14 + x^12 + 4*x^10 + 2*x^8 + 3*x^6 + 4*x^4 + 3*x^2 + 1)/x^5)*y) ) +( [(3*x^17 + 4*x^13 + 3*x^7 + x^5 + 2*x^3 + 2*x)*y] d[x] + [2*x^22 + 4*x^18 + 4*x^14 + 4*x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3] d[y] + V(((2*x^275 + 2*x^271 + 2*x^267 + 2*x^263 + x^261 + 4*x^255 + 2*x^253 + 4*x^249 + 4*x^247 + 2*x^245 + x^243 + 3*x^241 + 3*x^239 + 3*x^237 + x^235 + 2*x^233 + x^231 + 3*x^229 + x^227 + 2*x^225 + x^215 + x^213 + x^211 + 3*x^209 + x^207 + 2*x^205 + 2*x^203 + x^201 + 4*x^197 + 3*x^195 + 2*x^193 + 2*x^191 + 4*x^189 + x^187 + 4*x^185 + 4*x^183 + 3*x^181 + 4*x^179 + x^177 + 3*x^175 + x^173 + 3*x^171 + x^169 + 3*x^167 + x^165 + x^163 + 3*x^161 + 4*x^159 + 4*x^157 + 4*x^153 + 2*x^151 + 3*x^149 + 3*x^143 + 2*x^139 + 4*x^135 + 3*x^133 + 2*x^131 + 3*x^129 + 3*x^127 + x^123 + 4*x^121 + 2*x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 4*x^109 + 4*x^107 + 4*x^105 + 3*x^103 + x^101 + 2*x^99 + 4*x^97 + 2*x^95 + 3*x^89 + x^87 + 2*x^85 + 4*x^79 + 2*x^77 + 4*x^75 + 2*x^73 + 4*x^71 + x^67 + 4*x^65 + x^61 + 4*x^59 + x^57 + 3*x^53 + 4*x^49 + 2*x^45 + 2*x^43 + 4*x^39 + 4*x^37 + 3*x^31 + 2*x^29 + 4*x^27 + 4*x^25 + 3*x^23 + 2*x^21 + x^19 + 4*x^17 + 3*x^13 + 3*x^11 + x^9 + 3*x^7 + 2*x^3)*y) dx + (3*x^280 + 2*x^270 + 3*x^266 + 2*x^264 + 2*x^262 + x^260 + x^258 + x^254 + 2*x^252 + 4*x^250 + x^248 + x^246 + x^242 + x^240 + 3*x^238 + 2*x^236 + 4*x^234 + 2*x^230 + 3*x^228 + 4*x^226 + 3*x^222 + x^220 + 2*x^218 + 2*x^216 + x^214 + 2*x^212 + 2*x^208 + x^206 + 3*x^204 + 3*x^202 + x^194 + 4*x^192 + x^190 + 2*x^188 + 4*x^186 + 4*x^184 + x^182 + 4*x^180 + 3*x^178 + x^176 + 2*x^174 + 2*x^172 + x^166 + x^164 + 4*x^160 + 2*x^158 + x^156 + 2*x^154 + 4*x^152 + 4*x^150 + 3*x^148 + 3*x^146 + 3*x^142 + 2*x^140 + 3*x^138 + x^136 + 3*x^134 + 3*x^132 + 4*x^128 + 4*x^124 + 2*x^122 + 2*x^118 + 2*x^116 + x^114 + 3*x^112 + 2*x^110 + 4*x^108 + 4*x^106 + 3*x^104 + 2*x^102 + x^100 + 2*x^98 + 4*x^96 + 2*x^94 + 3*x^90 + 2*x^88 + 4*x^86 + x^82 + x^80 + 3*x^78 + x^76 + 4*x^74 + x^72 + 2*x^70 + x^68 + 3*x^66 + x^64 + x^62 + 3*x^60 + 4*x^58 + 4*x^54 + x^52 + 2*x^50 + 2*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + 2*x^36 + 4*x^34 + 3*x^32 + 4*x^30 + x^26 + 3*x^24 + x^22 + x^20 + 2*x^18 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 2*x^4 + 3*x^2) dy) + dV(0), [2/x^2*y] + V(((2*x^142 + 4*x^138 + x^136 + 3*x^134 + 4*x^130 + 2*x^128 + 4*x^126 + x^120 + 4*x^118 + x^112 + 4*x^110 + 4*x^106 + x^104 + x^102 + 3*x^100 + x^98 + 4*x^96 + x^94 + 2*x^92 + x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + 2*x^76 + 4*x^74 + x^72 + 3*x^70 + 3*x^68 + x^66 + 2*x^64 + 2*x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 2*x^44 + 4*x^42 + x^40 + 3*x^38 + x^36 + 3*x^34 + 3*x^32 + 4*x^28 + 3*x^26 + 3*x^24 + 3*x^22 + x^18 + 3*x^16 + 4*x^14 + 4*x^6 + 3*x^4 + 4)/x^6)*y) ) +( [(2*x^16 + 3*x^12 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [3*x^21 + 4*x^17 + 4*x^13 + 3*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((3*x^270 + 3*x^266 + 3*x^262 + x^260 + 3*x^258 + x^252 + x^250 + 4*x^248 + 3*x^246 + x^244 + x^242 + x^240 + 3*x^236 + 4*x^234 + 4*x^230 + 2*x^228 + x^224 + 2*x^222 + 3*x^220 + x^218 + x^214 + x^208 + 4*x^206 + 4*x^204 + 2*x^202 + 3*x^200 + 4*x^196 + 4*x^194 + 3*x^192 + x^190 + 4*x^188 + x^186 + 4*x^184 + 3*x^182 + 4*x^180 + x^178 + x^174 + 4*x^170 + 4*x^168 + 2*x^164 + x^162 + 4*x^160 + 2*x^156 + 2*x^152 + 3*x^150 + 4*x^148 + 2*x^142 + x^138 + 2*x^136 + 3*x^134 + x^132 + 4*x^130 + 2*x^128 + 2*x^124 + 3*x^122 + 3*x^120 + 3*x^118 + 3*x^116 + 3*x^114 + 2*x^112 + 4*x^106 + 4*x^104 + 3*x^102 + 2*x^96 + x^94 + 3*x^92 + 3*x^90 + 3*x^86 + 4*x^84 + 3*x^82 + 3*x^80 + 3*x^76 + 4*x^74 + 2*x^72 + 2*x^70 + 2*x^68 + x^66 + 4*x^64 + 4*x^62 + x^60 + 3*x^58 + x^56 + 3*x^54 + x^50 + 4*x^44 + 4*x^42 + 3*x^40 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^30 + 2*x^26 + 3*x^22 + 3*x^18 + 4*x^16 + 3*x^14 + 4*x^12 + x^8)*y) dx + (2*x^275 + 2*x^265 + 2*x^261 + 3*x^259 + 3*x^257 + 4*x^253 + 4*x^251 + 4*x^247 + 3*x^245 + 2*x^243 + 4*x^241 + 3*x^239 + 3*x^235 + 2*x^229 + 4*x^227 + 3*x^225 + 4*x^223 + 3*x^221 + 4*x^219 + 2*x^217 + 3*x^215 + 2*x^213 + 3*x^211 + x^209 + 4*x^207 + 2*x^201 + 3*x^199 + x^197 + 3*x^195 + 4*x^193 + 4*x^191 + 4*x^189 + 3*x^183 + 4*x^177 + x^175 + x^173 + 3*x^171 + 3*x^169 + 3*x^167 + 3*x^165 + 4*x^163 + 2*x^161 + x^157 + x^155 + 4*x^153 + 4*x^151 + x^147 + 4*x^145 + 3*x^143 + 2*x^141 + 2*x^137 + x^135 + x^133 + 3*x^131 + 2*x^127 + 3*x^125 + 2*x^123 + 4*x^121 + 4*x^119 + 3*x^117 + 2*x^113 + x^111 + 4*x^109 + 3*x^107 + 2*x^105 + 4*x^97 + 4*x^95 + 3*x^93 + 3*x^91 + 2*x^89 + x^87 + 4*x^83 + 2*x^81 + x^79 + x^77 + 2*x^71 + 2*x^69 + 4*x^65 + x^63 + 2*x^61 + 4*x^59 + 2*x^57 + 2*x^55 + 4*x^53 + 2*x^51 + 3*x^49 + 2*x^47 + 4*x^45 + 3*x^43 + 3*x^41 + 4*x^39 + 4*x^35 + 4*x^33 + x^31 + 2*x^29 + 4*x^25 + x^23 + 2*x^21 + x^19 + 4*x^17 + 4*x^15 + x^9 + 4*x^7) dy) + dV(0), [2/x^3*y] + V(((3*x^138 + x^134 + 4*x^132 + 2*x^130 + x^126 + 3*x^124 + x^122 + 3*x^118 + 4*x^116 + 2*x^114 + 4*x^112 + 2*x^110 + 4*x^108 + 2*x^106 + 3*x^104 + 2*x^102 + 4*x^100 + x^98 + x^96 + 4*x^94 + 2*x^92 + 2*x^90 + 2*x^88 + 4*x^86 + x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 3*x^70 + 4*x^66 + x^64 + 4*x^62 + x^58 + 4*x^56 + 4*x^54 + x^52 + 2*x^50 + 3*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + x^34 + 4*x^32 + 3*x^30 + 3*x^26 + 2*x^22 + 3*x^20 + 3*x^18 + x^16 + x^14 + 4*x^12 + 2*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2 + 4)/x^7)*y) ) +( [(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x)*y] d[x] + [4*x^20 + 4*x^16 + 4*x^12 + 4*x^8 + 4*x^4 + 1] d[y] + V(((4*x^265 + 4*x^261 + 4*x^257 + x^255 + 4*x^253 + 3*x^251 + x^247 + 2*x^245 + 2*x^241 + 3*x^239 + 2*x^237 + 3*x^235 + 2*x^233 + 3*x^229 + 3*x^223 + x^221 + 3*x^219 + 3*x^217 + x^215 + 4*x^213 + 2*x^211 + 4*x^209 + 4*x^207 + 2*x^205 + 2*x^203 + 2*x^201 + 3*x^199 + 2*x^197 + 3*x^195 + 4*x^193 + 3*x^191 + x^185 + x^183 + 3*x^181 + 3*x^179 + 4*x^177 + x^175 + 4*x^173 + x^165 + 2*x^163 + 3*x^161 + 2*x^159 + 4*x^157 + x^153 + x^151 + 4*x^149 + 4*x^147 + x^145 + 2*x^143 + 3*x^141 + 2*x^139 + 4*x^137 + 4*x^133 + 2*x^131 + 4*x^129 + 3*x^127 + 4*x^123 + 2*x^121 + 3*x^119 + 3*x^117 + x^115 + x^113 + 4*x^111 + 4*x^103 + 4*x^101 + x^99 + 2*x^97 + x^95 + 3*x^93 + x^91 + x^89 + 3*x^87 + 3*x^85 + 2*x^81 + 2*x^77 + 3*x^75 + 3*x^73 + 3*x^71 + 3*x^67 + 2*x^65 + 3*x^61 + 2*x^59 + 3*x^57 + 2*x^55 + 4*x^53 + x^51 + 3*x^47 + 3*x^45 + 2*x^43 + 2*x^41 + 2*x^39 + 3*x^35 + x^31 + 4*x^27 + x^25 + 3*x^23 + 4*x^21 + x^19 + 2*x^17 + x^13 + 2*x^11 + 4*x^9 + 2*x^7 + 3*x^3)*y) dx + (x^270 + 3*x^260 + x^256 + 4*x^254 + 4*x^252 + 4*x^250 + 2*x^248 + 4*x^246 + 3*x^244 + 3*x^240 + 3*x^236 + 2*x^234 + 2*x^232 + 4*x^230 + x^228 + 2*x^224 + 4*x^222 + 4*x^220 + 3*x^218 + 2*x^216 + 2*x^214 + 4*x^212 + 2*x^208 + 3*x^204 + 4*x^202 + x^200 + 4*x^198 + 3*x^196 + 3*x^194 + 3*x^192 + x^190 + 3*x^188 + 3*x^186 + 2*x^184 + 4*x^182 + 2*x^180 + x^178 + 4*x^176 + 3*x^174 + 2*x^172 + 4*x^170 + 4*x^168 + 3*x^166 + x^164 + 4*x^162 + 4*x^160 + 4*x^156 + x^154 + x^152 + 2*x^150 + 2*x^148 + 3*x^146 + 4*x^144 + 3*x^142 + 2*x^140 + x^138 + x^136 + 3*x^134 + x^132 + 2*x^130 + 3*x^126 + x^124 + 2*x^122 + 2*x^120 + 4*x^118 + 4*x^116 + x^114 + 4*x^112 + x^110 + 2*x^108 + x^106 + 4*x^104 + 2*x^102 + x^100 + 3*x^98 + 2*x^94 + 4*x^90 + 3*x^88 + 3*x^86 + x^84 + x^80 + 4*x^78 + x^76 + 3*x^74 + 3*x^72 + x^70 + 4*x^68 + 4*x^64 + 4*x^62 + 3*x^60 + 3*x^58 + 2*x^56 + 2*x^52 + 4*x^48 + 3*x^44 + 4*x^42 + 4*x^38 + x^34 + 3*x^30 + 4*x^28 + 2*x^26 + x^22 + 3*x^18 + x^16 + 2*x^10 + 3*x^4 + 2*x^2) dy) + dV(0), [2/x^4*y] + V(((4*x^132 + 3*x^128 + 2*x^126 + x^124 + 3*x^120 + 4*x^118 + 3*x^116 + x^112 + 2*x^110 + 3*x^106 + 4*x^104 + 2*x^102 + x^98 + 2*x^94 + x^92 + 4*x^90 + 2*x^88 + 3*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + 3*x^76 + 2*x^74 + 2*x^72 + x^70 + 2*x^68 + 4*x^66 + 4*x^62 + 4*x^60 + x^58 + x^56 + 3*x^54 + 2*x^52 + 3*x^48 + 3*x^44 + 3*x^42 + 4*x^40 + x^38 + 2*x^36 + 2*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + x^4 + 2)/x^6)*y) ) +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [2], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File :92, in regular_drw_cech(cocycle) + +File :81, in regular_drw_form(omega) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :149, in auxilliary_derivative(P) + +File :55, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :55, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :55, in __rmul__(self, other) + +File :84, in __add__(self, other) + +File :65, in __mul__(self, other) + +File :95, in diffn(self) + +File :7, in __init__(self, C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 112 FieldElement.__init__(self, parent) + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + 116 else: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1001 + 1002 try: +-> 1003 return self(str(element)) + 1004 except TypeError: + 1005 pass + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 192 except AttributeError: + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + 196 return result + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:482, in sage.rings.fraction_field_element.FractionFieldElement._repr_() + 480 if self.is_zero(): + 481 return "0" +--> 482 s = "%s" % self.__numerator + 483 if self.__denominator != 1: + 484 denom_string = str( self.__denominator ) + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 192 except AttributeError: + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + 196 return result + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_() + 2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3 + 2689 """ +-> 2690 return self._repr() + 2691 + 2692 def _latex_(self, name=None): + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr() + 2654 if n != m-1: + 2655 s += " + " +-> 2656 x = y = repr(x) + 2657 if y.find("-") == 0: + 2658 y = y[1:] + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTraceback (most recent call last): + + File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code + exec(code_obj, self.user_global_ns, self.user_ns) + + Input In [3] in  + load('init.sage') + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :21 in  + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :40 + C = omega.curve + ^ +IndentationError: unexpected indent + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +Computing 0. basis element +Computing 1. basis element +Computing 2. basis element +Computing 3. basis element +Computing 4. basis element +Computing 5. basis element +Computing 6. basis element +Computing 7. basis element +Computing 8. basis element +Computing 9. basis element +Computing 10. basis element +Computing 11. basis element +Computing 12. basis element +Computing 13. basis element +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [4], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :25, in  + +File :92, in regular_drw_cech(cocycle) + +File :84, in regular_drw_form(omega) + +File :5, in decomposition_g0_pth_power(fct) + +AttributeError: 'superelliptic_function' object has no attribute 'fucntion' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(elliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/superelliptic_drw_auxilliaries.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in itertools.product(*lista):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lbB1:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: for b in B: +....: [?7h[?12l[?25h[?25l[?7lp = C.characteristic[?7h[?12l[?25h[?25l[?7lrint(b.regula_form())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(b.regular_form())[?7h[?12l[?25h[?25l[?7l....:  print(b.regular_form()) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in B: +....:  print(b.regular_form()) +....:  +[?7h[?12l[?25h[?2004l( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) ) +( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in B: +....:  print(b.regular_form())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(b.regular_form()) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in B1: +....:  print(b.regular_form()) +....:  +[?7h[?12l[?25h[?2004l( [(3*x^5 + 2*x)*y] d[x] + [2*x^10 + x^6 + 2*x^2 + 3] d[y] + V(((x^99 + 2*x^91 + 3*x^89 + 3*x^87 + 2*x^85 + 2*x^83 + 2*x^79 + x^77 + 4*x^75 + x^73 + 2*x^71 + 2*x^69 + 3*x^67 + 3*x^65 + x^63 + 3*x^61 + x^55 + 2*x^53 + 4*x^51 + x^49 + 2*x^47 + 4*x^45 + 4*x^43 + 3*x^35 + 2*x^33 + 2*x^31 + 2*x^29 + 3*x^25 + x^23 + 3*x^21 + 3*x^19 + 3*x^15 + x^13 + 4*x^11 + 2*x^7 + 4*x^5 + x^3 + 3*x)*y) dx + (4*x^104 + x^100 + 3*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + x^88 + 3*x^84 + 3*x^80 + 3*x^78 + 2*x^76 + 4*x^74 + 3*x^70 + 4*x^68 + x^66 + 2*x^62 + x^60 + 3*x^58 + 2*x^56 + x^54 + 2*x^52 + 3*x^50 + 4*x^46 + 2*x^44 + 2*x^42 + 4*x^40 + 4*x^38 + 3*x^36 + x^34 + 4*x^32 + 3*x^30 + 3*x^28 + x^26 + 4*x^24 + 4*x^22 + 4*x^20 + x^18 + x^16 + x^14 + 4*x^12 + 4*x^10 + 4*x^8 + 3*x^6 + 4*x^4 + 2*x^2 + 2) dy) + dV(0), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y) ) +( [(3*x^6 + 2*x^2)*y] d[x] + [2*x^11 + x^7 + 2*x^3 + 3*x] d[y] + V(((x^104 + x^100 + x^94 + x^90 + x^88 + 4*x^86 + x^84 + x^82 + 4*x^80 + 4*x^78 + 4*x^76 + x^74 + 4*x^72 + 2*x^70 + 2*x^66 + 4*x^64 + 2*x^60 + 4*x^58 + 3*x^56 + 3*x^54 + 4*x^52 + 2*x^50 + 4*x^48 + x^44 + 2*x^42 + 3*x^40 + 3*x^38 + 3*x^36 + 4*x^34 + x^32 + 3*x^30 + 3*x^28 + 4*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 4*x^18 + x^16 + 2*x^14 + 4*x^12 + 4*x^10 + 4*x^8 + x^4 + 2*x^2)*y) dx + (4*x^109 + x^101 + 2*x^95 + 4*x^93 + 4*x^91 + x^89 + 4*x^85 + x^81 + 2*x^79 + 2*x^77 + 2*x^75 + 2*x^71 + 3*x^69 + 3*x^67 + x^65 + 2*x^63 + x^59 + 3*x^55 + 2*x^51 + x^49 + 2*x^47 + 3*x^45 + 2*x^43 + 3*x^39 + 4*x^37 + 3*x^35 + 3*x^33 + 4*x^31 + 3*x^29 + 3*x^27 + 4*x^25 + 2*x^23 + 2*x^21 + 3*x^15 + 2*x^13 + 2*x^9 + 3*x^7 + 4*x^5 + x^3 + 3*x) dy) + dV(0), V(((2*x^88 + 4*x^84 + x^82 + 3*x^80 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + x^58 + 3*x^56 + 2*x^54 + 3*x^52 + x^50 + 4*x^46 + 3*x^44 + x^42 + 2*x^40 + x^38 + 3*x^36 + 2*x^34 + 4*x^28 + x^26 + 2*x^24 + 4*x^22 + x^20 + x^18 + 4*x^16 + 2*x^14 + 4*x^12 + 3*x^8 + 3*x^4 + 4*x^2 + 3)/x^7)*y) ) +( [(3*x^7 + 2*x^3)*y] d[x] + [2*x^12 + x^8 + 2*x^4 + 3*x^2] d[y] + V(((x^109 + 2*x^105 + 3*x^101 + 4*x^99 + 2*x^97 + 3*x^91 + x^87 + 4*x^85 + 2*x^83 + x^81 + x^75 + 4*x^73 + x^71 + 3*x^69 + 3*x^65 + x^63 + 2*x^61 + x^57 + 4*x^53 + 2*x^49 + 4*x^47 + 3*x^45 + 4*x^43 + 4*x^41 + x^39 + 2*x^37 + 3*x^35 + 4*x^27 + x^25 + 2*x^23 + 3*x^21 + 4*x^19 + x^17 + 4*x^15 + 3*x^13 + x^11 + 2*x^7 + 2*x^5 + 3*x^3 + 4*x)*y) dx + (4*x^114 + 4*x^110 + 4*x^106 + 2*x^104 + x^102 + 2*x^100 + 2*x^98 + 3*x^96 + 4*x^94 + 2*x^88 + 4*x^82 + x^80 + x^78 + 3*x^76 + x^74 + 4*x^72 + x^70 + x^68 + 3*x^66 + x^64 + 3*x^62 + 3*x^60 + 2*x^52 + 2*x^50 + 2*x^46 + 4*x^42 + 3*x^40 + 3*x^38 + 2*x^36 + 2*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + 3*x^26 + 4*x^24 + x^22 + 2*x^20 + 4*x^18 + 3*x^16 + 3*x^14 + 2*x^10 + 3*x^8 + 3*x^6 + 2*x^4 + x^2 + 1) dy) + dV(0), V(((2*x^92 + 4*x^88 + x^86 + 3*x^84 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 4*x^50 + 3*x^48 + x^46 + 2*x^44 + x^42 + 3*x^40 + 2*x^38 + 4*x^32 + x^30 + 2*x^28 + 4*x^26 + x^24 + x^22 + 4*x^20 + 2*x^18 + 4*x^16 + 3*x^12 + 3*x^8 + 4*x^6 + 3*x^4 + 3)/x^6)*y) ) +( [(3*x^8 + 2*x^4)*y] d[x] + [2*x^13 + x^9 + 2*x^5 + 3*x^3] d[y] + V(((x^114 + 3*x^110 + x^106 + 2*x^104 + 4*x^102 + 4*x^100 + 4*x^98 + 2*x^96 + 4*x^94 + x^92 + 4*x^90 + 3*x^86 + 4*x^84 + x^82 + 3*x^78 + 2*x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + 3*x^62 + 3*x^60 + 4*x^58 + 3*x^54 + x^52 + 3*x^50 + 3*x^44 + 3*x^42 + 3*x^40 + 2*x^38 + x^36 + x^34 + x^32 + x^24 + 3*x^22 + 4*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + 2*x^12 + 4*x^10 + x^8 + x^6 + 4*x^2)*y) dx + (4*x^119 + 3*x^115 + 2*x^111 + 4*x^109 + 2*x^107 + 2*x^105 + 2*x^101 + 2*x^99 + x^95 + 4*x^93 + 4*x^91 + 3*x^89 + x^87 + 2*x^83 + 4*x^81 + 4*x^79 + x^75 + x^71 + x^69 + x^67 + 3*x^65 + 3*x^61 + 4*x^59 + 2*x^57 + x^55 + 3*x^53 + 4*x^51 + 2*x^49 + 4*x^47 + 3*x^45 + 3*x^43 + x^39 + x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^29 + 2*x^27 + x^25 + x^23 + x^21 + x^19 + 2*x^17 + 3*x^15 + 2*x^9 + x^7 + 4*x^3 + x) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^7)*y) ) +( [(3*x^9 + 2*x^5)*y] d[x] + [2*x^14 + x^10 + 2*x^6 + 3*x^4] d[y] + V(((x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^83 + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 + 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x)*y) dx + (4*x^124 + 2*x^120 + x^114 + 3*x^112 + 2*x^110 + 3*x^108 + x^106 + 2*x^100 + x^98 + 3*x^96 + x^94 + 3*x^92 + 4*x^90 + 3*x^88 + 2*x^84 + x^82 + x^80 + 4*x^78 + 4*x^76 + x^74 + 4*x^72 + 3*x^70 + x^66 + 3*x^64 + 2*x^62 + x^58 + x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 4*x^40 + 2*x^34 + 3*x^32 + 3*x^28 + 4*x^26 + 4*x^24 + 4*x^22 + 4*x^20 + 2*x^14 + 4*x^10 + 3*x^8 + 2*x^6 + 4*x^4 + 4*x^2 + 1) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^2)*y) ) +( [(3*x^10 + 2*x^6)*y] d[x] + [2*x^15 + x^11 + 2*x^7 + 3*x^5] d[y] + V(((x^124 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^110 + 2*x^108 + 2*x^104 + x^102 + 4*x^100 + x^98 + 2*x^96 + 2*x^94 + 3*x^92 + 3*x^90 + x^88 + 3*x^86 + x^80 + 2*x^78 + 4*x^76 + x^74 + 2*x^72 + 4*x^70 + 4*x^68 + 3*x^60 + 2*x^58 + 2*x^56 + 2*x^54 + 3*x^50 + x^48 + 3*x^46 + 3*x^44 + 3*x^40 + x^38 + 4*x^36 + 2*x^32 + 4*x^30 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + x^18 + 4*x^16 + 4*x^14 + 3*x^12 + 2*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 3*x^2)*y) dx + (4*x^129 + x^125 + 3*x^121 + 3*x^119 + 4*x^117 + 2*x^115 + x^113 + 3*x^109 + 3*x^105 + 3*x^103 + 2*x^101 + 4*x^99 + 3*x^95 + 4*x^93 + x^91 + 2*x^87 + x^85 + 3*x^83 + 2*x^81 + x^79 + 2*x^77 + 3*x^75 + 4*x^71 + 2*x^69 + 2*x^67 + 4*x^65 + 4*x^63 + 3*x^61 + x^59 + 4*x^57 + 3*x^55 + 3*x^53 + x^51 + 4*x^49 + 4*x^47 + 4*x^45 + x^43 + x^41 + x^39 + 4*x^37 + 4*x^35 + 2*x^31 + 2*x^29 + x^27 + 2*x^19 + 4*x^17 + 2*x^11 + 2*x^9 + 4*x^7 + 3*x^5 + 2*x) dy) + dV(0), V(((2*x^106 + 4*x^102 + x^100 + 3*x^98 + 4*x^94 + 2*x^92 + 4*x^90 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^78 + x^76 + 3*x^74 + 2*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + x^60 + 2*x^58 + x^56 + 3*x^54 + 2*x^52 + 4*x^46 + x^44 + 2*x^42 + 4*x^40 + x^38 + x^36 + 4*x^34 + 2*x^32 + 4*x^30 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + 3*x^14 + 2*x^12 + 3*x^10 + 4*x^8 + 3*x^2 + 3)/x^5)*y) ) +( [(3*x^11 + 2*x^7)*y] d[x] + [2*x^16 + x^12 + 2*x^8 + 3*x^6] d[y] + V(((x^129 + x^125 + x^119 + x^115 + x^113 + 4*x^111 + x^109 + x^107 + 4*x^105 + 4*x^103 + 4*x^101 + x^99 + 4*x^97 + 2*x^95 + 2*x^91 + 4*x^89 + 2*x^85 + 4*x^83 + 3*x^81 + 3*x^79 + 4*x^77 + 2*x^75 + 4*x^73 + x^69 + 2*x^67 + 3*x^65 + 3*x^63 + 3*x^61 + 4*x^59 + x^57 + 3*x^55 + 3*x^53 + 4*x^51 + 4*x^49 + 2*x^47 + 2*x^45 + 4*x^43 + x^41 + 2*x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 3*x^29 + 2*x^27 + x^23 + 3*x^21 + x^19 + 2*x^15 + x^13 + x^9 + x^7 + 3*x)*y) dx + (4*x^134 + x^126 + 2*x^120 + 4*x^118 + 4*x^116 + x^114 + 4*x^110 + x^106 + 2*x^104 + 2*x^102 + 2*x^100 + 2*x^96 + 3*x^94 + 3*x^92 + x^90 + 2*x^88 + x^84 + 3*x^80 + 2*x^76 + x^74 + 2*x^72 + 3*x^70 + 2*x^68 + 3*x^64 + 4*x^62 + 3*x^60 + 3*x^58 + 4*x^56 + 3*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + 2*x^46 + 3*x^40 + 2*x^38 + 3*x^32 + x^30 + 2*x^24 + 3*x^22 + x^20 + 2*x^16 + 2*x^14 + 4*x^12 + 2*x^8 + x^6 + 2*x^4 + 3*x^2 + 2) dy) + dV(0), V(((2*x^112 + 4*x^108 + x^106 + 3*x^104 + 4*x^100 + 2*x^98 + 4*x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 3*x^76 + x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + x^62 + 3*x^60 + 2*x^58 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + x^44 + x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 3*x^32 + 3*x^28 + 4*x^26 + 3*x^24 + 3*x^20 + 2*x^18 + 3*x^16 + 4*x^14 + 3*x^8 + 3*x^6 + 4*x^2 + 3)/x^6)*y) ) +( [(4*x^18 + x^10 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [x^23 + 4*x^19 + 4*x^15 + 4*x^11 + 2*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((3*x^164 + 4*x^160 + x^156 + x^154 + 3*x^152 + x^150 + 4*x^148 + x^146 + 2*x^144 + 3*x^140 + 2*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + 2*x^126 + 4*x^124 + 4*x^122 + 2*x^120 + 3*x^118 + 4*x^116 + 4*x^114 + 2*x^110 + x^108 + 4*x^106 + 2*x^100 + 2*x^98 + 2*x^96 + x^94 + 3*x^92 + 2*x^90 + 4*x^88 + x^86 + 4*x^84 + 2*x^82 + 4*x^80 + 2*x^78 + 3*x^72 + x^70 + x^68 + x^64 + x^60 + x^58 + 2*x^56 + 2*x^54 + 3*x^52 + 3*x^50 + x^48 + 3*x^46 + 3*x^44 + x^40 + 4*x^36 + 3*x^34 + 3*x^32 + 3*x^30 + x^28 + 4*x^26 + 2*x^24 + 3*x^22 + 2*x^20 + x^18 + 4*x^16 + 2*x^12 + 2*x^10 + x^6 + 2*x^4 + x^2)*y) dx + (2*x^169 + 4*x^165 + 3*x^161 + 2*x^159 + 3*x^157 + 2*x^155 + 4*x^153 + 3*x^151 + 3*x^149 + 2*x^147 + x^145 + 3*x^143 + x^141 + 3*x^139 + x^137 + 4*x^135 + 4*x^129 + 3*x^121 + 2*x^119 + 3*x^117 + 2*x^115 + x^113 + 2*x^111 + 2*x^109 + 3*x^107 + x^105 + 3*x^103 + 2*x^101 + x^99 + x^97 + x^95 + 3*x^93 + x^87 + 2*x^85 + x^83 + 2*x^81 + 2*x^79 + 2*x^77 + 3*x^75 + 4*x^73 + 2*x^69 + 2*x^67 + 3*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 2*x^57 + 4*x^55 + x^53 + 2*x^51 + 4*x^49 + 3*x^47 + x^45 + x^43 + 4*x^41 + x^39 + 3*x^37 + 4*x^33 + 3*x^31 + 4*x^29 + 3*x^27 + 3*x^25 + x^19 + 2*x^17 + 3*x^13 + 2*x^11 + 4*x^9 + 3*x^7 + 4*x^3 + 4*x) dy) + dV(0), [2/x*y] + V(((x^146 + 2*x^142 + 3*x^140 + 4*x^138 + 2*x^134 + x^132 + 2*x^130 + 2*x^126 + 3*x^124 + x^122 + x^120 + 3*x^118 + 3*x^116 + x^114 + 2*x^112 + x^110 + 3*x^108 + x^106 + 3*x^102 + x^100 + 2*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + 2*x^76 + 4*x^72 + x^70 + 4*x^68 + 2*x^66 + x^64 + 3*x^62 + 2*x^60 + 2*x^58 + 2*x^56 + 4*x^52 + x^50 + 2*x^48 + 2*x^46 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + x^26 + x^24 + 3*x^18 + 4*x^14 + x^12 + 4*x^10 + 2*x^8 + 3*x^6 + 4*x^4 + 3*x^2 + 1)/x^5)*y) ) +( [(3*x^17 + 4*x^13 + 3*x^7 + x^5 + 2*x^3 + 2*x)*y] d[x] + [2*x^22 + 4*x^18 + 4*x^14 + 4*x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3] d[y] + V(((x^159 + 2*x^155 + 2*x^151 + 4*x^149 + x^147 + 2*x^145 + 3*x^143 + x^141 + 3*x^139 + 4*x^137 + 2*x^135 + 2*x^133 + x^131 + x^129 + 4*x^127 + x^125 + 3*x^123 + 2*x^121 + 3*x^119 + 3*x^115 + 2*x^111 + 3*x^107 + 4*x^103 + 2*x^101 + 2*x^99 + 3*x^97 + 4*x^95 + 3*x^93 + 4*x^91 + x^89 + 4*x^87 + 4*x^85 + x^83 + 2*x^77 + 2*x^69 + 3*x^67 + 3*x^63 + 4*x^61 + 4*x^59 + x^55 + 3*x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 3*x^41 + 2*x^39 + x^37 + 2*x^33 + 2*x^31 + x^29 + 4*x^27 + x^25 + 2*x^23 + x^19 + 4*x^17 + x^15 + x^13 + 4*x^11 + 4*x^7 + x^5 + 3*x^3 + 2*x)*y) dx + (4*x^164 + 4*x^160 + 2*x^154 + x^152 + 3*x^148 + x^146 + 4*x^144 + 3*x^142 + 2*x^140 + x^138 + 3*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 4*x^126 + 4*x^124 + x^122 + 2*x^118 + 3*x^116 + x^112 + 3*x^110 + x^108 + 3*x^106 + 4*x^104 + 2*x^102 + 2*x^98 + 4*x^96 + x^94 + 2*x^92 + 3*x^88 + x^86 + 2*x^84 + 4*x^82 + 4*x^78 + 4*x^72 + 4*x^70 + 2*x^68 + 3*x^66 + 3*x^64 + 4*x^62 + 2*x^60 + 3*x^56 + x^48 + 4*x^46 + 3*x^44 + x^40 + x^38 + x^32 + 4*x^30 + 2*x^28 + 2*x^26 + 2*x^24 + x^22 + 2*x^20 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 3*x^8 + 2*x^6 + 4*x^2 + 3) dy) + dV(0), [2/x^2*y] + V(((2*x^142 + 4*x^138 + x^136 + 3*x^134 + 4*x^130 + 2*x^128 + 4*x^126 + x^120 + 4*x^118 + x^112 + 4*x^110 + 4*x^106 + x^104 + x^102 + 3*x^100 + x^98 + 4*x^96 + x^94 + 2*x^92 + x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + 2*x^76 + 4*x^74 + x^72 + 3*x^70 + 3*x^68 + x^66 + 2*x^64 + 2*x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 2*x^44 + 4*x^42 + x^40 + 3*x^38 + x^36 + 3*x^34 + 3*x^32 + 4*x^28 + 3*x^26 + 3*x^24 + 3*x^22 + x^18 + 3*x^16 + 4*x^14 + 4*x^6 + 3*x^4 + 4)/x^6)*y) ) +( [(2*x^16 + 3*x^12 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [3*x^21 + 4*x^17 + 4*x^13 + 3*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((4*x^154 + 4*x^150 + 4*x^144 + x^142 + 4*x^140 + 2*x^138 + 4*x^136 + 4*x^134 + 2*x^132 + 4*x^130 + x^128 + 2*x^126 + 3*x^124 + 2*x^122 + 3*x^120 + 3*x^116 + 4*x^114 + 3*x^112 + x^106 + 3*x^104 + 3*x^102 + 2*x^98 + 3*x^96 + 4*x^94 + x^92 + 4*x^88 + 4*x^84 + x^80 + x^78 + 4*x^74 + 3*x^72 + 2*x^70 + 2*x^68 + 3*x^66 + x^64 + 4*x^62 + 3*x^60 + 4*x^56 + 3*x^54 + 3*x^50 + 4*x^48 + 3*x^46 + 4*x^42 + 2*x^38 + 4*x^36 + 3*x^34 + 4*x^32 + 2*x^28 + 3*x^26 + 2*x^20 + 2*x^16 + 3*x^14 + 3*x^10 + 2*x^8 + 2*x^6 + 4*x^4)*y) dx + (x^159 + 4*x^151 + 4*x^147 + 3*x^145 + 4*x^143 + 3*x^141 + 2*x^139 + x^137 + 3*x^135 + 2*x^133 + 4*x^131 + 3*x^129 + 4*x^127 + 4*x^125 + 2*x^123 + x^121 + 4*x^119 + 3*x^117 + x^113 + 3*x^111 + 4*x^109 + 3*x^103 + 3*x^99 + 3*x^97 + 4*x^95 + 3*x^91 + 2*x^89 + 4*x^87 + 2*x^83 + 3*x^81 + 4*x^79 + 4*x^77 + 4*x^73 + 2*x^71 + 3*x^69 + 2*x^65 + 2*x^63 + x^61 + x^59 + 2*x^55 + 2*x^53 + x^51 + 3*x^49 + 2*x^45 + 2*x^43 + x^41 + 4*x^39 + 4*x^37 + 3*x^35 + 3*x^33 + x^31 + x^29 + x^27 + 2*x^25 + 2*x^21 + 2*x^19 + 4*x^17 + 2*x^15 + 3*x^9 + x^7 + 2*x^5 + x^3) dy) + dV(0), [2/x^3*y] + V(((3*x^138 + x^134 + 4*x^132 + 2*x^130 + x^126 + 3*x^124 + x^122 + 3*x^118 + 4*x^116 + 2*x^114 + 4*x^112 + 2*x^110 + 4*x^108 + 2*x^106 + 3*x^104 + 2*x^102 + 4*x^100 + x^98 + x^96 + 4*x^94 + 2*x^92 + 2*x^90 + 2*x^88 + 4*x^86 + x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 3*x^70 + 4*x^66 + x^64 + 4*x^62 + x^58 + 4*x^56 + 4*x^54 + x^52 + 2*x^50 + 3*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + x^34 + 4*x^32 + 3*x^30 + 3*x^26 + 2*x^22 + 3*x^20 + 3*x^18 + x^16 + x^14 + 4*x^12 + 2*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2 + 4)/x^7)*y) ) +( [(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x)*y] d[x] + [4*x^20 + 4*x^16 + 4*x^12 + 4*x^8 + 4*x^4 + 1] d[y] + V(((2*x^149 + x^139 + 2*x^135 + x^131 + 2*x^127 + 4*x^125 + x^123 + x^121 + 3*x^119 + x^117 + 2*x^111 + 2*x^109 + 4*x^107 + 4*x^105 + 3*x^103 + 2*x^101 + 3*x^99 + 4*x^97 + 2*x^95 + 3*x^93 + 2*x^89 + 3*x^83 + x^81 + x^79 + 2*x^77 + 3*x^73 + 3*x^71 + 2*x^69 + x^67 + 2*x^63 + 3*x^61 + 4*x^59 + 2*x^57 + 3*x^55 + 4*x^53 + 4*x^51 + x^47 + 2*x^45 + 2*x^43 + 3*x^37 + x^35 + 4*x^33 + 2*x^31 + 2*x^29 + 3*x^27 + x^25 + 4*x^23 + 2*x^21 + 4*x^19 + 2*x^17 + 3*x^15 + 3*x^13 + 3*x^11 + x^9 + 2*x^3 + 3*x)*y) dx + (3*x^154 + 2*x^150 + x^144 + x^140 + 3*x^136 + x^134 + x^132 + 4*x^130 + 3*x^128 + 2*x^126 + x^122 + 4*x^120 + 3*x^118 + 3*x^114 + x^112 + 3*x^110 + 4*x^108 + 4*x^106 + 4*x^102 + 3*x^96 + 3*x^94 + x^90 + 3*x^86 + 2*x^84 + 3*x^82 + x^80 + x^78 + 3*x^76 + 4*x^74 + 3*x^66 + x^64 + 3*x^62 + 4*x^60 + 2*x^58 + 2*x^54 + x^52 + 4*x^50 + x^48 + 2*x^46 + 4*x^44 + 3*x^42 + 3*x^40 + 2*x^38 + 3*x^36 + x^32 + 3*x^24 + 4*x^22 + 2*x^18 + x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 4*x^4 + x^2 + 2) dy) + dV(0), [2/x^4*y] + V(((4*x^132 + 3*x^128 + 2*x^126 + x^124 + 3*x^120 + 4*x^118 + 3*x^116 + x^112 + 2*x^110 + 3*x^106 + 4*x^104 + 2*x^102 + x^98 + 2*x^94 + x^92 + 4*x^90 + 2*x^88 + 3*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + 3*x^76 + 2*x^74 + 2*x^72 + x^70 + 2*x^68 + 4*x^66 + 4*x^62 + 4*x^60 + x^58 + x^56 + 3*x^54 + 2*x^52 + 3*x^48 + 3*x^44 + 3*x^42 + 4*x^40 + x^38 + 2*x^36 + 2*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + x^4 + 2)/x^6)*y) ) +( [(x^10 + 2*x^6 + 2*x^2)*y] d[x] + [4*x^15 + 4*x^11 + x^5 + 2*x^3 + 3*x] d[y] + V(((2*x^124 + x^114 + x^112 + 2*x^110 + x^108 + 3*x^104 + x^102 + 3*x^100 + 4*x^96 + x^94 + x^92 + 4*x^90 + 4*x^86 + 3*x^82 + 3*x^80 + 4*x^78 + 3*x^74 + 2*x^72 + 3*x^70 + 4*x^68 + 2*x^66 + 2*x^64 + 4*x^60 + 3*x^58 + x^54 + 4*x^52 + 2*x^48 + 4*x^42 + x^40 + 3*x^36 + 3*x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 2*x^20 + 4*x^18 + 3*x^16 + 3*x^14 + 2*x^12 + 4*x^10 + 3*x^8 + 3*x^6 + 2*x^2)*y) dx + (3*x^129 + 2*x^125 + x^119 + 4*x^117 + x^115 + 4*x^111 + 4*x^109 + 2*x^107 + 3*x^105 + 2*x^101 + x^99 + 2*x^97 + 2*x^95 + 4*x^91 + x^87 + x^85 + 4*x^83 + x^81 + x^79 + 4*x^77 + 3*x^75 + 3*x^73 + 4*x^71 + 2*x^67 + 4*x^65 + x^63 + 2*x^61 + 3*x^59 + 4*x^57 + x^55 + 3*x^53 + 4*x^49 + x^45 + x^39 + 4*x^37 + 2*x^35 + 3*x^33 + x^31 + 2*x^29 + x^25 + 3*x^23 + 4*x^21 + x^19 + x^15 + 2*x^13 + x^11 + 4*x^9 + 3*x^7 + 2*x^3 + 3*x) dy) + dV(0), [2/x^5*y] + V(((4*x^106 + 3*x^102 + 2*x^100 + x^98 + 3*x^94 + 4*x^92 + 3*x^90 + x^86 + 2*x^84 + 3*x^80 + 4*x^78 + 2*x^76 + x^72 + 2*x^68 + 2*x^66 + 4*x^64 + 4*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^52 + 3*x^50 + x^48 + 3*x^46 + x^44 + 2*x^42 + 4*x^40 + 4*x^38 + 3*x^36 + x^34 + x^32 + 3*x^30 + x^24 + 3*x^22 + 2*x^20 + 2*x^18 + x^16 + x^12 + 3*x^8 + x^6 + 4)/x^5)*y) ) +( [(4*x^13 + x^5)*y] d[x] + [x^18 + 4*x^14 + 4*x^10 + 4*x^8 + x^6 + 4*x^4] d[y] + V(((3*x^139 + 4*x^135 + x^131 + x^129 + 3*x^127 + x^125 + 2*x^123 + 4*x^121 + 2*x^119 + 2*x^117 + x^115 + x^113 + x^109 + 2*x^107 + 3*x^103 + 2*x^101 + x^97 + x^95 + x^93 + 3*x^91 + x^89 + 4*x^87 + 4*x^85 + 3*x^83 + x^81 + 4*x^77 + x^75 + 4*x^73 + x^71 + 4*x^69 + x^65 + 4*x^61 + x^59 + 3*x^57 + x^55 + 4*x^49 + 2*x^47 + x^45 + 2*x^43 + 4*x^41 + 2*x^39 + 3*x^35 + 3*x^33 + 2*x^29 + 2*x^27 + x^25 + 4*x^23 + x^21 + 2*x^17 + 2*x^15 + 4*x^13 + x^11 + 2*x^7 + x^5 + 4*x^3 + 2*x)*y) dx + (2*x^144 + 4*x^140 + 3*x^136 + 2*x^134 + 3*x^132 + 2*x^130 + x^128 + x^124 + 3*x^122 + 3*x^120 + 4*x^118 + 2*x^116 + x^112 + 2*x^110 + 3*x^108 + 4*x^106 + 3*x^104 + 4*x^102 + 4*x^100 + x^98 + x^94 + 2*x^92 + 4*x^90 + 3*x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 2*x^74 + x^70 + 3*x^68 + x^66 + x^64 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 3*x^52 + 4*x^50 + 3*x^46 + 4*x^44 + 2*x^42 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 2*x^32 + x^30 + 3*x^24 + x^22 + 3*x^20 + 4*x^18 + 2*x^16 + 2*x^12 + 2*x^10 + 3*x^6 + x^4 + 3*x^2 + 3) dy) + dV(0), [2/x^6*y] + V(((x^120 + 2*x^116 + 3*x^114 + 4*x^112 + 2*x^108 + x^106 + 2*x^104 + 2*x^100 + 3*x^98 + x^96 + x^94 + 3*x^92 + 3*x^90 + x^88 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^76 + x^74 + x^70 + 3*x^68 + 2*x^66 + 4*x^64 + 3*x^62 + 2*x^60 + 4*x^52 + x^50 + x^48 + 2*x^46 + 2*x^44 + x^40 + 3*x^38 + 4*x^34 + 2*x^32 + 3*x^30 + x^28 + 2*x^26 + x^24 + 2*x^22 + 4*x^20 + 3*x^16 + x^14 + 4*x^12 + 2*x^10 + 3*x^8 + 3*x^6 + 2*x^4 + 2)/x^4)*y) ) +( [(3*x^12 + 4*x^8 + 3*x^4)*y] d[x] + [2*x^17 + 4*x^13 + x^9 + 3*x^7 + 3*x^5 + 2*x^3] d[y] + V(((x^134 + 2*x^130 + 2*x^126 + 4*x^124 + 3*x^122 + 2*x^120 + 4*x^118 + x^116 + 4*x^114 + 3*x^110 + x^108 + 2*x^104 + x^102 + x^100 + 3*x^98 + 3*x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 4*x^88 + 4*x^86 + x^84 + 2*x^82 + 2*x^80 + 3*x^76 + 3*x^74 + 2*x^72 + 2*x^70 + 4*x^68 + 3*x^64 + 2*x^62 + 3*x^58 + 3*x^54 + 4*x^52 + 3*x^50 + 2*x^48 + 4*x^42 + 3*x^40 + 2*x^38 + 3*x^36 + 2*x^34 + 2*x^30 + 3*x^28 + 2*x^26 + x^24 + 2*x^22 + 3*x^18 + 4*x^16 + 4*x^14 + 2*x^12 + 3*x^10 + x^8 + x^2)*y) dx + (4*x^139 + 4*x^135 + 2*x^129 + 4*x^127 + 4*x^123 + x^121 + 4*x^119 + 4*x^117 + 2*x^115 + x^113 + x^107 + x^103 + 2*x^101 + x^99 + 4*x^97 + 3*x^93 + 3*x^91 + 3*x^89 + 2*x^85 + 4*x^83 + x^81 + x^75 + 2*x^73 + 3*x^69 + 3*x^67 + 2*x^65 + 3*x^63 + 4*x^61 + 2*x^59 + 2*x^57 + 2*x^55 + x^53 + 4*x^49 + 2*x^47 + 2*x^45 + 3*x^39 + 2*x^37 + x^35 + 3*x^33 + 4*x^31 + 4*x^27 + x^25 + x^23 + 3*x^21 + 2*x^19 + x^17 + 4*x^15 + 3*x^13 + 2*x^9 + 3*x^7 + 4*x^5 + x^3 + 4*x) dy) + dV(0), [2/x^7*y] + V(((2*x^118 + 4*x^114 + x^112 + 3*x^110 + 4*x^106 + 2*x^104 + 4*x^102 + x^96 + 4*x^94 + x^88 + 4*x^86 + 4*x^82 + x^80 + 3*x^78 + 3*x^76 + 4*x^70 + 2*x^62 + 4*x^60 + 4*x^58 + 2*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + x^46 + 4*x^42 + 4*x^38 + 4*x^36 + x^34 + 2*x^30 + 4*x^28 + 4*x^26 + 4*x^22 + 4*x^20 + 2*x^18 + 4*x^12 + 2*x^10 + 4*x^8 + 2*x^4 + 3*x^2 + 2)/x^7)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, (1/(x*y)) dx)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C1.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), + ((x/y) dx, 0, (x/y) dx), + ((x^2/y) dx, 0, (x^2/y) dx), + ((x^3/y) dx, 0, (x^3/y) dx), + ((x^4/y) dx, 0, (x^4/y) dx), + ((x^5/y) dx, 0, (x^5/y) dx), + ((x^6/y) dx, 0, (x^6/y) dx), + (((-2*x^13 - 2*x^9 - 2*x^3 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx), + (((x^12 - x^8 - x^4 + x^2 + 1)/y) dx, 2/x^2*y, (2/(x^2*y)) dx), + (((-x^11 - 2*x^3 - x)/y) dx, 2/x^3*y, (2/(x*y)) dx), + (((2*x^10 + x^6 + 2*x^2 + 2)/y) dx, 2/x^4*y, ((-2)/(x^4*y)) dx), + (((2*x^5 + x)/y) dx, 2/x^5*y, ((-2*x^2 + 1)/(x^5*y)) dx), + (((-2*x^8 - 2*x^4)/y) dx, 2/x^6*y, ((2*x^4 + x^2 - 1)/(x^6*y)) dx), + (((x^7 - x^3)/y) dx, 2/x^7*y, ((x^6 - x^4 - x^2 + 2)/(x^7*y)) dx)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h \ No newline at end of file diff --git a/sage/drafty/draft.sage b/sage/drafty/draft.sage index 06d0e4f..f4033be 100644 --- a/sage/drafty/draft.sage +++ b/sage/drafty/draft.sage @@ -1,14 +1,14 @@ p = 5 m = 2 F = GF(p) -Rx. = PolynomialRing(F) +Rxx. = PolynomialRing(F) #f = (x^3 - x)^3 + x^3 - x f = x^3 + x f1 = f(x = x^5 - x) C = superelliptic(f, m) -C1 = superelliptic(f1, m) +C1 = superelliptic(f1, m, prec = 500) B = C.crystalline_cohomology_basis(prec = 100, info = 1) -B1 = C1.crystalline_cohomology_basis(prec = 500, info = 1) +B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1) def crystalline_matrix(C, prec = 50): B = C.crystalline_cohomology_basis(prec = prec) @@ -20,6 +20,12 @@ def crystalline_matrix(C, prec = 50): M[i, :] = vector(autom(b).coordinates(basis = B)) return M +for b in B: + print(b.regular_form()) + +for b in B1: + print(b.regular_form()) + #M = crystalline_matrix(C, prec = 150) #print(M) #print(M^3) \ No newline at end of file diff --git a/sage/superelliptic/superelliptic_class.sage b/sage/superelliptic/superelliptic_class.sage index 60ce5cb..dc61f23 100644 --- a/sage/superelliptic/superelliptic_class.sage +++ b/sage/superelliptic/superelliptic_class.sage @@ -1,7 +1,7 @@ class superelliptic: """Class of a superelliptic curve. Given a polynomial f(x) with coefficient field F, it constructs the curve y^m = f(x)""" - def __init__(self, f, m): + def __init__(self, f, m, prec = 100): Rx = f.parent() x = Rx.gen() F = Rx.base() @@ -20,6 +20,31 @@ class superelliptic: self.y = superelliptic_function(self, Rxy(y)) self.dx = superelliptic_form(self, Rxy(1)) self.one = superelliptic_function(self, Rxy(1)) + # We compute now expansions at infinity of x and y. + Rt. = LaurentSeriesRing(F, default_prec=prec) + RptW. = PolynomialRing(Rt) + RptWQ = FractionField(RptW) + Rxy. = PolynomialRing(F) + RxyQ = FractionField(Rxy) + delta, a, b = xgcd(m, r) + a = -a + M = m/delta + R = r/delta + while a<0: + a += R + b += M + g = (x^r*f(x = 1/x)) + gW = RptWQ(g(x = t^M * W^b)) - W^(delta) + self.x_series = [] + self.y_series = [] + self.dx_series = [] + for place in range(delta): + ww = naive_hensel(gW, F, start = root_of_unity(F, delta)^place, prec = prec) + xx = Rt(1/(t^M*ww^b)) + yy = 1/(t^R*ww^a) + self.x_series += [xx] + self.y_series += [yy] + self.dx_series += [xx.derivative()] def __repr__(self): f = self.polynomial diff --git a/sage/superelliptic/superelliptic_form_class.sage b/sage/superelliptic/superelliptic_form_class.sage index 6c0763d..257dac1 100644 --- a/sage/superelliptic/superelliptic_form_class.sage +++ b/sage/superelliptic/superelliptic_form_class.sage @@ -137,10 +137,10 @@ class superelliptic_form: g = self.form C = self.curve g = superelliptic_function(C, g) - g = g.expansion_at_infty(place = place, prec=prec) - x_series = C.x.expansion_at_infty(place = place, prec=prec) - dx_series = x_series.derivative() - return g*dx_series + F = C.base_ring + Rt. = LaurentSeriesRing(F, default_prec=prec) + g = Rt(g.expansion_at_infty(place = place, prec=prec)) + return g*C.dx_series[place] def expansion(self, pt, prec = 50): '''Expansion in the completed ring of the point pt. If pt is an integer, it means the corresponding place at infinity.''' diff --git a/sage/superelliptic/superelliptic_function_class.sage b/sage/superelliptic/superelliptic_function_class.sage index 63b0f6d..9ffc1c3 100644 --- a/sage/superelliptic/superelliptic_function_class.sage +++ b/sage/superelliptic/superelliptic_function_class.sage @@ -108,31 +108,11 @@ class superelliptic_function: def expansion_at_infty(self, place = 0, prec=20): C = self.curve - f = C.polynomial - m = C.exponent - F = C.base_ring - Rx. = PolynomialRing(F) - f = Rx(f) - Rt. = LaurentSeriesRing(F, default_prec=prec) - RptW. = PolynomialRing(Rt) - RptWQ = FractionField(RptW) - Rxy. = PolynomialRing(F) - RxyQ = FractionField(Rxy) fct = self.function - fct = RxyQ(fct) - r = f.degree() - delta, a, b = xgcd(m, r) - a = -a - M = m/delta - R = r/delta - while a<0: - a += R - b += M - g = (x^r*f(x = 1/x)) - gW = RptWQ(g(x = t^M * W^b)) - W^(delta) - ww = naive_hensel(gW, F, start = root_of_unity(F, delta)^place, prec = prec) - xx = Rt(1/(t^M*ww^b)) - yy = 1/(t^R*ww^a) + F = C.base_ring + Rt. = LaurentSeriesRing(F, default_prec=prec) + xx = C.x_series[place] + yy = C.y_series[place] return Rt(fct(x = Rt(xx), y = Rt(yy))) def expansion(self, pt, prec = 50): diff --git a/sage/superelliptic_drw/de_rham_witt_lift.sage b/sage/superelliptic_drw/de_rham_witt_lift.sage index 921aed3..a698188 100644 --- a/sage/superelliptic_drw/de_rham_witt_lift.sage +++ b/sage/superelliptic_drw/de_rham_witt_lift.sage @@ -34,10 +34,10 @@ def de_rham_witt_lift(cech_class, prec = 50): def crystalline_cohomology_basis(self, prec = 50, info = 0): result = [] + prec1 = prec for i, a in enumerate(self.de_rham_basis()): if info: print("Computing " + str(i) +". basis element") - prec1 = prec while True: try: result += [de_rham_witt_lift(a, prec = prec1)] diff --git a/sage/superelliptic_drw/regular_form.sage b/sage/superelliptic_drw/regular_form.sage index 069bdea..a92ec4b 100644 --- a/sage/superelliptic_drw/regular_form.sage +++ b/sage/superelliptic_drw/regular_form.sage @@ -74,12 +74,14 @@ class superelliptic_regular_drw_form: def regular_drw_form(omega): C = omega.curve + p = C.characteristic omega_aux = omega.r() omega_aux = omega_aux.regular_form() aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() aux.omega, fct = decomposition_omega0_hpdh(aux.omega) aux.h2 += fct^p - aux.h2 = decomposition_g0_p2th_power(aux.h2)[0] + aux.h2, A = decomposition_g0_pth_power(aux.h2) + aux.omega += (A.diffn()).inv_cartier() result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) return result diff --git a/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage b/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage index 96e11bc..3f084d4 100644 --- a/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage +++ b/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage @@ -1,4 +1,8 @@ def decomposition_g0_pth_power(fct): + C = fct.curve + Fxy, Rxy, xy, y = C.fct_field + if fct.function in Rxy: + return (fct, 0*C.x) '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).''' omega = fct.diffn().regular_form() g0 = omega.int() @@ -7,6 +11,8 @@ def decomposition_g0_pth_power(fct): def decomposition_g0_p2th_power(fct): '''Decompose fct as g0 + A^(p^2), if possible. Output: (g0, A).''' + C = fct.curve + p = C.characteristic g0, A = decomposition_g0_pth_power(fct) A0, A1 = decomposition_g0_pth_power(A) return (g0 + A0^p, A1) @@ -14,6 +20,9 @@ def decomposition_g0_p2th_power(fct): def decomposition_omega0_hpdh(omega): '''Decompose omega = (regular on U0) + h^(p-1) dh, so that Cartier(omega) = (regular on U0) + dh. Result: (regular on U0, h)''' + C = omega.curve + if omega.is_regular_on_U0(): + return (omega, 0*C.x) omega1 = omega.cartier().cartier() omega1 = omega1.inv_cartier().inv_cartier() fct = (omega.cartier() - omega1.cartier()).int() @@ -27,6 +36,9 @@ def decomposition_omega8_hpdh(omega, prec = 50): Fxy, Rxy, x, y = C.fct_field F = C.base_ring p = C.characteristic + C = omega.curve + if omega.is_regular_on_Uinfty(): + return (omega, 0*C.x) Rt. = LaurentSeriesRing(F) omega_analytic = Rt(laurent_analytic_part(omega.expansion_at_infty(prec = prec))) Cv = C.uniformizer() @@ -44,6 +56,8 @@ def decomposition_g8_pth_power(fct, prec = 50): F = C.base_ring Rt. = LaurentSeriesRing(F) Fxy, Rxy, x, y = C.fct_field + if fct.expansion_at_infty().valuation() >= 0: + return (fct, 0*C.x) A = laurent_analytic_part(fct.expansion_at_infty(prec = prec)) Cv = C.uniformizer() v = Cv.function diff --git a/sage/superelliptic_drw/superelliptic_drw_cech.sage b/sage/superelliptic_drw/superelliptic_drw_cech.sage index 7dd569d..541e382 100644 --- a/sage/superelliptic_drw/superelliptic_drw_cech.sage +++ b/sage/superelliptic_drw/superelliptic_drw_cech.sage @@ -56,13 +56,19 @@ class superelliptic_drw_cech: C = self.curve return superelliptic_cech(C, omega0.h1*C.dx, f.t) - def div_by_p(self): + def div_by_p(self, info = 0): '''Given a regular cocycle of the form (V(omega) + dV(h), [f] + V(t), ...), where [f] = 0 in H^1(X, OX), find de Rham cocycle (xi0, f, xi8) such that (V(omega) + dV(h), [f] + V(t), ...) = p*(xi0, f, xi8).''' + # + if info: print("Computing " + str(self) + " divided by p.") + # C = self.curve aux = self Fxy, Rxy, x, y = C.fct_field aux_f_t_0 = decomposition_g0_g8(aux.f.t, prec=50)[0] + # + if info: print("Computed decomposition_g0_g8 of self.f.t.") + # aux.f.t = 0*C.x aux.omega0 -= aux_f_t_0.teichmuller().diffn() aux.omega8 = aux.omega0 - aux.f.diffn() @@ -72,9 +78,17 @@ class superelliptic_drw_cech: omega = aux.omega0.omega aux.omega0.omega, fct = decomposition_omega0_hpdh(aux.omega0.omega) aux.omega0.h2 += fct^p + # + if info: print("Computed decomposition_omega0_hpdh of self.omega0.omega.") + # # Now we have to ensure that aux.omega0.h2.function in Rxy... - # In other words, we decompose h2 = (regular on U0) + A^(p^2). - aux.omega0.h2 = decomposition_g0_p2th_power(aux.omega0.h2)[0] + # In other words, we decompose h2 = (regular on U0) + A^p. + # Then we replace h2 by (regular on U0) and omega by omega + inverse Cartier(dA) + aux.omega0.h2, A = decomposition_g0_pth_power(aux.omega0.h2) + aux.omega0.omega += (A.diffn()).inv_cartier() + # + if info: print("Computed decomposition_g0_p2th_power(aux.omega0.h2).") + # # Now we can reduce: (... + dV(h2), V(f), ...) --> (..., V(f - h2), ...) aux.f -= aux.omega0.h2.verschiebung() aux.omega0.h2 = 0*C.x @@ -87,18 +101,21 @@ class superelliptic_drw_cech: aux_divided_by_p = superelliptic_cech(C, aux.omega0.omega.cartier(), aux.f.f.pth_root()) return aux_divided_by_p - def coordinates(self, basis = 0, prec = 50): + def coordinates(self, basis = 0, prec = 50, info = 0): + if info: print("Computing coordinates of " + str(self)) C = self.curve g = C.genus() coord_mod_p = self.r().coordinates() + if info: print("Computed coordinates mod p.") coord_lifted = [lift(a) for a in coord_mod_p] if basis == 0: basis = C.crystalline_cohomology_basis() aux = self for i, a in enumerate(basis): aux -= coord_lifted[i]*a - aux_divided_by_p = aux.div_by_p() + aux_divided_by_p = aux.div_by_p(info = info) coord_aux_divided_by_p = aux_divided_by_p.coordinates() + if info: print("Computed coordinates mod p of (self - lift)/p.") coord_aux_divided_by_p = [ZZ(a) for a in coord_aux_divided_by_p] coordinates = [ (coord_lifted[i] + p*coord_aux_divided_by_p[i])%p^2 for i in range(2*g)] return coordinates diff --git a/sage/tests.sage b/sage/tests.sage index 791d236..cf0054a 100644 --- a/sage/tests.sage +++ b/sage/tests.sage @@ -1,6 +1,6 @@ -load('init.sage') -#print("Expansion at infty test:") -#load('superelliptic/tests/expansion_at_infty.sage') +#load('init.sage') +print("Expansion at infty test:") +load('superelliptic/tests/expansion_at_infty.sage') #print("superelliptic form coordinates test:") #load('superelliptic/tests/form_coordinates_test.sage') #print("p-th root test:")