From f7a04c69eced4d67cba92ff293c805fe19c999ab Mon Sep 17 00:00:00 2001 From: jgarnek Date: Sat, 24 Dec 2022 10:34:56 +0000 Subject: [PATCH] obliczanie dzialania na dR chyba dziala --- sage/.run.term-0.term | 7230 +++++++++++++++++++++++++++- sage/as_covers/as_cech_class.sage | 48 +- sage/as_covers/as_cover_class.sage | 1 - 3 files changed, 7256 insertions(+), 23 deletions(-) diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term index a5d06eb..71eae0b 100644 --- a/sage/.run.term-0.term +++ b/sage/.run.term-0.term @@ -12692,4 +12692,7232 @@ File :85, in coordinates(self, threshold, basis ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. [?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 \ No newline at end of file +[?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[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?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 commit -cm "praca nad as_cech coordinate; przed poprawa drugiej czecsci" +[master d77adde] praca nad as_cech coordinate; przed poprawa drugiej czesci + 5 files changed, 11731 insertions(+), 54 deletions(-) +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push +Username for 'https://git.wmi.amu.edu.pl': jgare  rnek +Password for 'https://jgarnek@git.wmi.amu.edu.pl': +Enumerating objects: 35, done. +Counting objects: 2% (1/35) Counting objects: 5% (2/35) Counting objects: 8% (3/35) Counting objects: 11% (4/35) Counting objects: 14% (5/35) Counting objects: 17% (6/35) Counting objects: 20% (7/35) Counting objects: 22% (8/35) Counting objects: 25% (9/35) Counting objects: 28% (10/35) Counting objects: 31% (11/35) Counting objects: 34% (12/35) Counting objects: 37% (13/35) Counting objects: 40% (14/35) Counting objects: 42% (15/35) Counting objects: 45% (16/35) Counting objects: 48% (17/35) Counting objects: 51% (18/35) Counting objects: 54% (19/35) Counting objects: 57% (20/35) Counting objects: 60% (21/35) Counting objects: 62% (22/35) Counting objects: 65% (23/35) Counting objects: 68% (24/35) Counting objects: 71% (25/35) Counting objects: 74% (26/35) Counting objects: 77% (27/35) Counting objects: 80% (28/35) Counting objects: 82% (29/35) Counting objects: 85% (30/35) Counting objects: 88% (31/35) Counting objects: 91% (32/35) Counting objects: 94% (33/35) Counting objects: 97% (34/35) Counting objects: 100% (35/35) Counting objects: 100% (35/35), 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: 21% (5/23) Writing objects: 26% (6/23) Writing objects: 30% (7/23) 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), 66.79 KiB | 250.00 KiB/s, done. +Total 23 (delta 19), reused 0 (delta 0) +remote: . Processing 1 references +remote: Processed 1 references in total +To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git + c098f37..d77adde master -> master +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sacd 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[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1]^2 - z[0]*(z[1]+x^4))/(x^2*z[0]*z[1]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l(); ff= as_function(AS, (-z0^2*z1- z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l(((-1)* AS.z[1]^2)/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l(-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +--------------------------------------------------------------------------- +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 :21, 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  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :83, in coordinates(self, threshold, basis) + +AttributeError: 'as_cech' object has no attribute 'form' +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +--------------------------------------------------------------------------- +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 :21, 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  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :69, in coordinates(self, threshold, basis) + +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 /ext/sage/9.7/src/sage/structure/parent.pyx:989, in sage.structure.parent.Parent.__mul__() + 987 pass + 988 if _mul_ is None: +--> 989 raise TypeError(_LazyString("For implementing multiplication, provide the method '_mul_' for %s resp. %s", (self, x), {})) + 990 if switch: + 991 return _mul_(self, switch_sides=True) + +TypeError: For implementing multiplication, provide the method '_mul_' for 10 resp. R Interpreter +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +--------------------------------------------------------------------------- +NameError 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 :21, 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  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :74, in coordinates(self, threshold, basis) + +NameError: name 'pr' 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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +--------------------------------------------------------------------------- +TypeError 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 :21, 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  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :72, in coordinates(self, threshold, basis) + +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[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +--------------------------------------------------------------------------- +UnboundLocalError 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 :21, 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  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :79, in coordinates(self, threshold, basis) + +UnboundLocalError: local variable 'S' referenced before assignment +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +--------------------------------------------------------------------------- +TypeError 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 :21, 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  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :10, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[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 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 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]] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[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 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 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]] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 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] +[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 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]] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 0 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 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 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 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]] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 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 0 1 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 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 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]] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 0 0 0 0 0] +[0 1 1 0 1 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 2 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 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 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]] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 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 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 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]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 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 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 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]] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 0 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 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] +[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 0 0] +[0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0]] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 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 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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 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 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]] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [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 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]] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 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] +[0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0]] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 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 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]] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 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 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]] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 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]] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 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]] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 0 0 1 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]] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 0 0 1 0 0 0 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 0 0 0] +[0 0 0 0 0 0 0 0 0 0]] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 0 0 1 0 0 0 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 0 1 0] +[0 0 0 0 0 0 0 0 0 0]] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +--------------------------------------------------------------------------- +TypeError 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 :21, 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  + +File :31, in group_action_matrices_dR(AS, threshold) + +File :11, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +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 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 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]] +2: 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 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 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]] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 1 [[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 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 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]] +2: 0 1 [[1 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] +[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 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]] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 2 [[1 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] +[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 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]] +2: 0 2 [[1 0 0 0 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 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 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 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]] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 3 [[1 0 0 0 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 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 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 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]] +2: 0 3 [[1 0 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 0 1 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 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 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]] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 4 [[1 0 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 0 1 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 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 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]] +2: 0 4 [[1 0 0 1 0 0 0 0 0 0] +[0 1 1 0 1 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 2 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 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 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]] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 5 [[1 0 0 1 0 0 0 0 0 0] +[0 1 1 0 1 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 2 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 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 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]] +2: 0 5 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 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 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 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]] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 6 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 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 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 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]] +2: 0 6 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 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 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 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]] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 7 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 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 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 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]] +2: 0 7 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 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0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 0 0 1 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]] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +1 7 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 0 0 1 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]] +2: 1 7 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 0 0 1 0 0 0 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 0 0 0] +[0 0 0 0 0 0 0 0 0 0]] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +1 8 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 0 0 1 0 0 0 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 0 0 0] +[0 0 0 0 0 0 0 0 0 0]] +2: 1 8 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 0 0 1 0 0 0 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 0 1 0] +[0 0 0 0 0 0 0 0 0 0]] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +1 9 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 0 0 1 0 0 0 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 0 1 0] +[0 0 0 0 0 0 0 0 0 0]] +2: 1 9 [[1 0 0 1 0 1 0 0 0 0] +[0 1 1 0 1 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 0 0 0] +[0 0 2 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 2 1 0] +[0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 1 0] +[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0] +[0 1 2 0 0 0 0 0 0 0] +[0 0 1 0 0 0 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 1 0 0 1 0 0 0 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 0 1 0] +[0 0 0 0 0 0 0 0 0 1]] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +--------------------------------------------------------------------------- +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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :11, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +--------------------------------------------------------------------------- +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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :11, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 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] +2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 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] +2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 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] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[1, 0, 1, 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] +2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 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] +2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[1, 0, 2, 0, 1, 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] +2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 1, 0, 2, 0, 1, 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] +[0] +[0] +[0] +[0] +[0] +2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +None +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +--------------------------------------------------------------------------- +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 :21, 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  + +File :34, in group_action_matrices_dR(AS, threshold) + +File :13, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 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] +2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 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] +2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 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] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[1, 0, 1, 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] +2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 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] +2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[1, 0, 2, 0, 1, 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] +2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 1, 0, 2, 0, 1, 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] +[0] +[0] +[0] +[0] +[0] +2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[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] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +[0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +None +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +--------------------------------------------------------------------------- +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 :21, 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  + +File :34, in group_action_matrices_dR(AS, threshold) + +File :13, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 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, 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] +2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 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, 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] +2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 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] +2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 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, 0, 0, 1, 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] +2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 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, 0, 0, 1, 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] +2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 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] +2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 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, 1, 0, 0, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 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, 0, 0, 1, 0, 1, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 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, 1] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 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] +2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 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] +2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +[1, 0, 1, 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] +2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 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] +2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +[1, 0, 2, 0, 1, 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] +2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +[0, 1, 0, 2, 0, 1, 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] +[0] +[0] +[0] +[0] +[0] +2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [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, 1, 1, 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] +2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +[0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] +0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None +None +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +[0] +--------------------------------------------------------------------------- +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 :21, 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  + +File :34, in group_action_matrices_dR(AS, threshold) + +File :13, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None +--------------------------------------------------------------------------- +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 :21, 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  + +File :31, in group_action_matrices_dR(AS, threshold) + +File :11, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None +--------------------------------------------------------------------------- +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 :21, 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  + +File :31, in group_action_matrices_dR(AS, threshold) + +File :11, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None +--------------------------------------------------------------------------- +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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :12, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +333: +mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None +--------------------------------------------------------------------------- +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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :12, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +--------------------------------------------------------------------------- +IndexError 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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :10, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :155, in holomorphic_combinations_fcts(S, pole_order) + +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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +A0: 0 +--------------------------------------------------------------------------- +IndexError 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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :10, in group_action_matrices(space, list_of_group_elements, basis) + +File :81, in coordinates(self, threshold, basis) + +File :155, in holomorphic_combinations_fcts(S, pole_order) + +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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +10 1 [[0, 1, 2], [0, 1, 2]] +A0: 0 +--------------------------------------------------------------------------- +IndexError 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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :10, in group_action_matrices(space, list_of_group_elements, basis) + +File :82, in coordinates(self, threshold, basis) + +File :155, in holomorphic_combinations_fcts(S, pole_order) + +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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +10 1 [[0, 1, 2], [0, 1, 2]] +A0: 0 +--------------------------------------------------------------------------- +IndexError 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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :10, in group_action_matrices(space, list_of_group_elements, basis) + +File :83, in coordinates(self, threshold, basis) + +File :155, in holomorphic_combinations_fcts(S, pole_order) + +IndexError: list index out of range +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lrint(len(AS1.at_most_poles(M, threshold=20)))[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: product +[?7h[?12l[?25h[?2004l[?7h +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7lor eta in AS.de_rham_basis():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for k in product(*pr): +....: [?7h[?12l[?25h[?25l[?7lprint(eta.omega0, eta.omega8.valuation())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?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[?7lnt(eta.omega0, eta.omega8.valuation())[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print(k) +....: [?7h[?12l[?25h[?25l[?7lsage: for k in product(*pr): +....:  print(k) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [22], in () +----> 1 for k in product(*pr): + 2 print(k) + +NameError: name 'pr' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for k in product(*pr): +....:  print(k)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lproduct + [?7h[?12l[?25h[?25l[?7lloa('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +10 1 [[0, 1, 2], [0, 1, 2]] +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +dodajemy +A0: 90 +A: 1 +B: 2 +333: +mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None +--------------------------------------------------------------------------- +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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :12, in group_action_matrices(space, list_of_group_elements, basis) + +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:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types) + 230 if universe is None: + 231 orig_x = x +--> 232 x = list(x) # make a copy even if x is a list, we're going to change it + 234 if len(x) == 0: + 235 from sage.categories.objects import Objects + +TypeError: 'NoneType' object is not iterable +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +--------------------------------------------------------------------------- +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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :10, in group_action_matrices(space, list_of_group_elements, basis) + +File :86, in coordinates(self, threshold, basis) + +TypeError: unsupported operand type(s) for -: 'sage.rings.fraction_field_element.FractionFieldElement' and 'as_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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +--------------------------------------------------------------------------- +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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :10, in group_action_matrices(space, list_of_group_elements, basis) + +File :88, in coordinates(self, threshold, basis) + +NameError: name 'coordinates' 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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0] +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (-z0*z1 + z1) * dx, 0 ) +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0] +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: [2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0] +nowe: ( (-z0*z1 + z1) * dx, 0 ) +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0] +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) [2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0] +--------------------------------------------------------------------------- +IndexError 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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :12, in group_action_matrices(space, list_of_group_elements, basis) + +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[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) (1, 0, 0, 0, 0, 0, 0, 0, 0, 0) +--------------------------------------------------------------------------- +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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :12, in group_action_matrices(space, list_of_group_elements, basis) + +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('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0) +--------------------------------------------------------------------------- +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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :12, in group_action_matrices(space, list_of_group_elements, basis) + +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('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +TypeError 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 :21, 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  + +File :32, in group_action_matrices_dR(AS, threshold) + +File :10, in group_action_matrices(space, list_of_group_elements, basis) + +File :94, in coordinates(self, threshold, basis) + +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: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 +: 'Vector space of dimension 10 over Finite Field of size 3' and 'Vector space of dimension 20 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[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +cc: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0) +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +cc: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20 +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +cc: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0] 20 +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0) +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +cc: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0] 20 +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0) +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +cc: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0] 20 +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0) +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20 +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0) +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0] 20 +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0) +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0] 20 +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0) +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +cc: [2, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20 +nowe: ( (-z0*z1 + z1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0] +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1) +nowe: ( (-z0*z1 + z1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0] +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1) +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z1 + 1) * dx, 0 ) +nowe: ( (z1 + 1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 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] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0) * dx, 0 ) +nowe: ( (z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0*z1 + z0) * dx, 0 ) +nowe: ( (z0*z1 + z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0^2) * dx, 0 ) +nowe: ( (z0^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (-x*z0^2 + x*z1 + x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z1 + x) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 1, 0, 0] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x*z0) * dx, 0 ) +nowe: ( (x*z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (0) * dx, (z1 + 1)/x ) +nowe: ( (0) * dx, (z1 + 1)/x ) +cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x ) +nowe: ( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x ) +cc: [2, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20 +nowe: ( (x^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0) +nowe: ( (x^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0) +( (-x^2*z0) * dx, (z0*z1 + z0)/x ) +nowe: ( (-x^2*z0) * dx, (z0*z1 + z0)/x ) +cc: [0, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20 +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0) +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) +nowe: ( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) +cc: [0, 0, 2, 1, 0, 0, 0, 0, 0, 0] 20 +nowe: ( (-z0^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 2, 0, 0, 0, 0] +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0) +nowe: ( (-z0^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 2, 0, 0, 0, 0] +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0) +( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) +nowe: ( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) +cc: [1, 0, 0, 0, 1, 0, 0, 0, 0, 0] 20 +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0) +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0) +( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) +nowe: ( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) +cc: [1, 0, 0, 0, 2, 1, 0, 0, 0, 0] 20 +nowe: ( (z0*z1 - z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0] +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0) +nowe: ( (z0*z1 - z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0] +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0) +( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) +nowe: ( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20 +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0) +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0) +( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) +nowe: ( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 0, 1, 0, 0] 20 +nowe: ( (x*z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +nowe: ( (x*z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) +nowe: ( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 1, 0, 1, 0] 20 +nowe: ( (0) * dx, z0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 2, 0, 0, 0] +(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0) +nowe: ( (0) * dx, z0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 2, 0, 0, 0] +(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0) +( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 ) +nowe: ( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20 +nowe: ( (z0^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) +nowe: ( (z0^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) +[ +RModule of dimension 6 over GF(3), +RModule of dimension 14 over GF(3) +] +--------------------------------------------------------------------------- +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 :21, 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  + +TypeError: 'text' is an invalid keyword argument for print() +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z1) * dx, 0 ) +nowe: ( (z1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0 + 1) * dx, 0 ) +nowe: ( (z0 + 1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0*z1 + z1) * dx, 0 ) +nowe: ( (z0*z1 + z1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0^2 - z0 + 1) * dx, 0 ) +nowe: ( (z0^2 - z0 + 1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x*z0 + x) * dx, 0 ) +nowe: ( (x*z0 + x) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 1, 0] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (0) * dx, z1/x ) +nowe: ( (0) * dx, z1/x ) +cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z1) * dx, z1^2/x ) +nowe: ( (x^2*z1) * dx, z1^2/x ) +cc: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0) +( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) +cc: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20 +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) +cc: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0] 20 +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0) +( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +cc: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0] 20 +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0) +( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +cc: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0] 20 +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0) +( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20 +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 1, 0, 2, 0] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0) +( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0] 20 +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 1, 0, 0] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0) +( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0] 20 +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0) +( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +cc: [2, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20 +nowe: ( (-z0*z1 + z1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0] +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1) +nowe: ( (-z0*z1 + z1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0] +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1) +( (1) * dx, 0 ) +nowe: ( (1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z1 + 1) * dx, 0 ) +nowe: ( (z1 + 1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 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] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) +nowe: ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0) * dx, 0 ) +nowe: ( (z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0*z1 + z0) * dx, 0 ) +nowe: ( (z0*z1 + z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (z0^2) * dx, 0 ) +nowe: ( (z0^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x) * dx, 0 ) +nowe: ( (x) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (-x*z0^2 + x*z1 + x) * dx, 0 ) +nowe: ( (-x*z0^2 + x*z1 + x) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 1, 0, 0] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x*z0) * dx, 0 ) +nowe: ( (x*z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2) * dx, 0 ) +nowe: ( (x^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (0) * dx, (z1 + 1)/x ) +nowe: ( (0) * dx, (z1 + 1)/x ) +cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x ) +nowe: ( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x ) +cc: [2, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20 +nowe: ( (x^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0) +nowe: ( (x^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0) +( (-x^2*z0) * dx, (z0*z1 + z0)/x ) +nowe: ( (-x^2*z0) * dx, (z0*z1 + z0)/x ) +cc: [0, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20 +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0) +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0) +( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) +nowe: ( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) +cc: [0, 0, 2, 1, 0, 0, 0, 0, 0, 0] 20 +nowe: ( (-z0^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 2, 0, 0, 0, 0] +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0) +nowe: ( (-z0^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 2, 0, 0, 0, 0] +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0) +( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) +nowe: ( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) +cc: [1, 0, 0, 0, 1, 0, 0, 0, 0, 0] 20 +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0) +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0) +( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) +nowe: ( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) +cc: [1, 0, 0, 0, 2, 1, 0, 0, 0, 0] 20 +nowe: ( (z0*z1 - z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0] +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0) +nowe: ( (z0*z1 - z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0] +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0) +( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) +nowe: ( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20 +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0) +nowe: ( (0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0) +( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) +nowe: ( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 0, 1, 0, 0] 20 +nowe: ( (x*z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +nowe: ( (x*z0) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) +nowe: ( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) +cc: [0, 0, 0, 0, 0, 0, 1, 0, 1, 0] 20 +nowe: ( (0) * dx, z0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 2, 0, 0, 0] +(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0) +nowe: ( (0) * dx, z0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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, 2, 0, 0, 0] +(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0) +( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 ) +nowe: ( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20 +nowe: ( (z0^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +111: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) +nowe: ( (z0^2) * dx, 0 ) +cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20 +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +222: [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] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) +[ +RModule of dimension 6 over GF(3), +RModule of dimension 14 over GF(3) +] +None +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 6 over GF(3), +RModule of dimension 14 over GF(3) +] +None +[?2004h[?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$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ g \ No newline at end of file diff --git a/sage/as_covers/as_cech_class.sage b/sage/as_covers/as_cech_class.sage index 04626c9..9eb2b90 100644 --- a/sage/as_covers/as_cech_class.sage +++ b/sage/as_covers/as_cech_class.sage @@ -44,6 +44,10 @@ class as_cech: def coordinates(self, threshold=10, basis = 0): '''Find coordinates of self in the de Rham cohomology basis. Threshold is an argument passed to AS.de_rham_basis().''' AS = self.curve + C = AS.quotient + m = C.exponent + r = C.polynomial.degree() + n = AS.height RxyzQ, Rxyz, x, y, z = AS.fct_field if basis == 0: basis = [AS.holomorphic_differentials_basis(), AS.cohomology_of_structure_sheaf_basis(), AS.de_rham_basis(threshold=threshold)] @@ -54,7 +58,6 @@ class as_cech: f_products = [] for f in coh_basis: f_products += [[omega.serre_duality_pairing(f) for omega in holo_diffs]] - print(f_products) product_of_fct_and_omegas = [] fct = self.f product_of_fct_and_omegas = [omega.serre_duality_pairing(fct) for omega in holo_diffs] @@ -63,27 +66,30 @@ class as_cech: coh_coordinates = V.coordinates(product_of_fct_and_omegas) #coeficients of self in the basis elts coming from cohomology of OX for i in range(AS.genus()): self -= coh_coordinates[i]*dR[i+AS.genus()] - #We remove now from f the summands which are obviously regular at infty - print(self, []) - f_num = numerator(self.f.function) - f_den = denominator(self.f.function) - v_f_den = as_function(AS, f_den).valuation() - for a in f_num.monomials(): - if as_function(AS, a).valuation() >= v_f_den: - self.f.function -= f_num.monomial_coefficient(a)*a/f_den - f_num = numerator(self.f.function) - f_den = denominator(self.f.function) - quo, rem = f_num.quo_rem(f_den) - if as_function(AS, rem/f_den).valuation() >= 0: - self.f = as_function(AS, quo) - hol_form = self.omega0 - self.f.diffn() #now this should be a holomorphic form - hol_form = as_form(AS, as_reduction(AS, hol_form.form)) - print('hol_form', hol_form) - return hol_form.coordinates() + coh_coordinates - print(self, [omega.serre_duality_pairing(self.f) for omega in holo_diffs]) - raise ValueError('I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.') + coh_coordinates = AS.genus()*[0] + list(coh_coordinates) + if self.f.function not in Rxyz: + #We remove now from f the summands which are obviously regular at infty + pr = [list(GF(p)) for _ in range(n)] + S = [] + from itertools import product + for i in range(0, threshold*r): + for j in range(0, m): + for k in product(*pr): + g = (AS.x)^i*prod((AS.z[i1])^(k[i1]) for i1 in range(n))*(AS.y)^j + S += [(g, g.expansion_at_infty())] + S += [(self.f, self.f.expansion_at_infty())] + fcts = holomorphic_combinations_fcts(S, 0) + for g in fcts: + if g.function not in Rxyz: + for a in F: + if (self.f.function - a*g.function in Rxyz): + self.f.function = self.f.function - a*g.function + return vector(coh_coordinates)+vector(self.coordinates(threshold=threshold, basis = basis)) + else: + self.omega0 -= self.f.diffn() + return vector(coh_coordinates) + vector(list(self.omega0.coordinates())+AS.genus()*[0]) + raise ValueError("Increase threshold.") - def group_action(self, g): AS = self.curve omega = self.omega0 diff --git a/sage/as_covers/as_cover_class.sage b/sage/as_covers/as_cover_class.sage index 89b2a09..316ab5a 100644 --- a/sage/as_covers/as_cover_class.sage +++ b/sage/as_covers/as_cover_class.sage @@ -335,7 +335,6 @@ class as_cover: def lift_to_de_rham(self, fct, threshold = 30): '''Given function fct, find form eta regular on affine part such that eta - d(fct) is regular in infty. (Works for one place at infty now)''' - print(fct) from itertools import product x_series = self.x_series y_series = self.y_series