From 599aa94db7672a9114697e54e36a6c1e1a0c5353 Mon Sep 17 00:00:00 2001 From: jgarnek Date: Fri, 22 Sep 2023 06:45:48 +0000 Subject: [PATCH] frobenius kernel --- sage/.run.term-0.term | 20437 +++++++++++++++++++- sage/as_covers/as_cover_class.sage | 7 +- sage/as_covers/as_form_class.sage | 2 +- sage/as_covers/as_function_class.sage | 28 +- sage/as_covers/group_action_matrices.sage | 13 +- sage/drafty/draft.sage | 47 +- sage/init.sage | 3 +- sage/superelliptic/frobenius_kernel.sage | 25 + 8 files changed, 20509 insertions(+), 53 deletions(-) create mode 100644 sage/superelliptic/frobenius_kernel.sage diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term index 694a2f8..d146b98 100644 --- a/sage/.run.term-0.term +++ b/sage/.run.term-0.term @@ -34868,4 +34868,20439 @@ File src/cysignals/signals.pyx:310, in cysignals.signals.pytho [0] d[x] + [0] d[y] + V((a*x^27 + x^21 + (2*a + 2)*x^19 + a*x^18 + (2*a + 2)*x^9 + 2*a*x^3 + (2*a + 1)*x + 2*a + 2) dy) + dV(0) [0] d[x] + [0] d[y] + V((0) dy) + dV(0) [0] d[x] + [0] d[y] + V((2*a*x^21 + 2*x^15 + (a + 1)*x^13 + 2*a*x^12) dy) + dV(0) -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h \ No newline at end of file +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() +[?7h[?12l[?25h[?2004l +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ccd ..cd .. +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git addd -u +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""u"s"u"n"i"e"t"e" "z"b"e"n""d"n"e" "k"o"m"u"n"i"k"a"t"y" +[master 5e738d4] usuniete zbedne komunikaty + 2 files changed, 604 insertions(+), 8 deletions(-) +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push +Username for 'https://git.wmi.amu.edu.pl': jgarnek +Password for 'https://jgarnek@git.wmi.amu.edu.pl': +Enumerating objects: 11, done. +Counting objects: 9% (1/11) Counting objects: 18% (2/11) Counting objects: 27% (3/11) Counting objects: 36% (4/11) Counting objects: 45% (5/11) Counting objects: 54% (6/11) Counting objects: 63% (7/11) Counting objects: 72% (8/11) Counting objects: 81% (9/11) Counting objects: 90% (10/11) Counting objects: 100% (11/11) Counting objects: 100% (11/11), done. +Delta compression using up to 4 threads +Compressing objects: 16% (1/6) Compressing objects: 33% (2/6) Compressing objects: 50% (3/6) Compressing objects: 66% (4/6) Compressing objects: 83% (5/6) Compressing objects: 100% (6/6) Compressing objects: 100% (6/6), done. +Writing objects: 16% (1/6) Writing objects: 33% (2/6) Writing objects: 50% (3/6) Writing objects: 66% (4/6) Writing objects: 83% (5/6) Writing objects: 100% (6/6) Writing objects: 100% (6/6), 4.88 KiB | 72.00 KiB/s, done. +Total 6 (delta 5), reused 0 (delta 0) +remote: . Processing 1 references +remote: Processed 1 references in total +To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git + 1f66cae..5e738d4 master -> master +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372: +******************************************************************************** +Denominators of fraction field elements are sometimes dropped without warning. +This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. +******************************************************************************** +[( (1) * dx, 0 ), ( ((a + 1)*z0 + z1) * dx, 0 ), ( (x) * dx, 0 ), ( (0) * dx, z1/x ), ( (a*x*z0 + x*z1) * dx, z0*z1/x ), ( (a*z0 + z1) * dx, z0*z1/x^2 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0 = omega.int()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: group + group_action_matrices group_action_matrices_log  + group_action_matrices_dR group_action_matrices_old  + group_action_matrices_holo groups  + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_action_matrices + group_action_matrices  + + + [?7h[?12l[?25h[?25l[?7l_dR + group_action_matrices  + group_action_matrices_dR [?7h[?12l[?25h[?25l[?7l( + + + +[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices_dR(C) +[?7h[?12l[?25h[?2004l[?7h[ +[ 1 a + 1 0 0 0 a] [1 1 0 0 0 1] +[ 0 1 0 0 0 0] [0 1 0 0 0 0] +[ 0 0 1 0 a 0] [0 0 1 0 1 0] +[ 0 0 0 1 1 0] [0 0 0 1 a 0] +[ 0 0 0 0 1 0] [0 0 0 0 1 0] +[ 0 0 0 0 0 1], [0 0 0 0 0 1] +] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: magma + magma magma_free  + magma_console magmathis  + + + [?7h[?12l[?25h[?25l[?7l + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAgroup_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l,group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lBgroup_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l=group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: magma_this(A, B) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [4], line 1 +----> 1 magma_this(A, B) + +NameError: name 'magma_this' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagma_this(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: magma_this(A, B) + magma magma_free  + magma_console magmathis  + + + [?7h[?12l[?25h[?25l[?7l + magma  + + [?7h[?12l[?25h[?25l[?7l_free + magma  magma_free [?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: magma_free(A, B) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [5], line 1 +----> 1 magma_free(A, B) + +File /ext/sage/9.8/src/sage/misc/lazy_import.pyx:404, in sage.misc.lazy_import.LazyImport.__call__() + 402 True + 403 """ +--> 404 return self.get_object()(*args, **kwds) + 405 + 406 def __repr__(self): + +File /ext/sage/9.8/src/sage/interfaces/magma_free.py:85, in MagmaFree.__call__(self, code, strip, columns) + 84 def __call__(self, code, strip=True, columns=0): +---> 85 return magma_free_eval(code, strip=strip, columns=columns) + +File /ext/sage/9.8/src/sage/interfaces/magma_free.py:45, in magma_free_eval(code, strip, columns) + 43 refererPath = "/calc/" + 44 refererUrl = "http://%s%s" % ( server, refererPath) +---> 45 code = "SetColumns(%s);\n"%columns + code + 46 params = urlencode({'input':code}) + 47 headers = {"Content-type": "application/x-www-form-urlencoded", + 48 "Accept": "Accept: text/html, application/xml, application/xhtml+xml", "Referer": refererUrl} + +TypeError: can only concatenate str (not "sage.matrix.matrix_gf2e_dense.Matrix_gf2e_dense") to str +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagma_free(A, B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagma_free(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 0 a^2] +[ 0 1 1] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 a^2 0] +[ 0 1 0] +[ 0 0 1], +[ 1 1 a^2] +[ 0 1 0] +[ 0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), ( (x^2) * dx, 0 ), ( (a*x^3) * dx, z1/x ), ( (x^3) * dx, z0/x ), ( (a*x^3*z0 + x^3*z1 + (a + 1)*x^3) * dx, z0*z1/x ), ( (a*x^2) * dx, z1/x^2 ), ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 a] +[ 0 1 0] +[ 0 0 1], +[ 1 0 0] +[ 0 1 1] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 a^2 a] +[ 0 1 0] +[ 0 0 1], +[ 1 1 a] +[ 0 1 0] +[ 0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.nth_root(p)[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: (a+1)/a +[?7h[?12l[?25h[?2004l[?7ha +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( ((a + 1)*z0 + z1) * dx, 0 ), ( (x) * dx, 0 ), ( (0) * dx, z1/x ), ( (a*x*z0 + x*z1) * dx, z0*z1/x ), ( (a*z0 + z1) * dx, z0*z1/x^2 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: A, B +[?7h[?12l[?25h[?2004l[?7h( +[ 1 a + 1 0 0 0 a] [1 1 0 0 0 1] +[ 0 1 0 0 0 0] [0 1 0 0 0 0] +[ 0 0 1 0 a 0] [0 0 1 0 1 0] +[ 0 0 0 1 1 0] [0 0 0 1 a 0] +[ 0 0 0 0 1 0] [0 0 0 0 1 0] +[ 0 0 0 0 0 1], [0 0 0 0 0 1] +) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef sumka2(N):[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: dR = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldR = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l&[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: dR[1] + a*dR[5] +[?7h[?12l[?25h[?2004l[?7h( ((a + 1)*z1) * dx, a*z0*z1/x^2 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldR[1] + a*dR[5][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(dR[1] + a*dR[5])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: (dR[1] + a*dR[5]).group_action([1, 0]) +[?7h[?12l[?25h[?2004l[?7h( ((a + 1)*z1) * dx, (a*z0*z1 + a*z1)/x^2 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(dR[1] + a*dR[5]).group_action([1, 0])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldR[1] + a*dR[5][?7h[?12l[?25h[?25l[?7lsage: (dR[1] + a*dR[5]).group_action([1, 0]) == dR[1] + a*dR[5] +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(dR[1] + a*dR[5]).group_action([1, 0]) == dR[1] + a*dR[5][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (dR[1] + a*dR[5]).group_action([1, 0]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(0, 1, 0, 0, 0, a) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x^2*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^4*z0 + z1) * dx, z0*z1/x^2 ), ( (x^3*z0) * dx, z0*z1/x^3 ), ( (x^2*z0) * dx, z0*z1/x^4 )] +[1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 1 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 1 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 1 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 1 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 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1] [1 1 0 0 0 0 0 0 0 0 0 1 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 1 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 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x^2*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^4*z0 + z1) * dx, z0*z1/x^2 ), ( (x^3*z0) * dx, z0*z1/x^3 ), ( (x^2*z0) * dx, z0*z1/x^4 )] +[1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 1 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 1 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 1 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 1 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 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 0 0 0 0 0 0 0 0 0 1 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 1 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 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x^2*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^4*z0 + z1) * dx, z0*z1/x^2 ), ( (x^3*z0) * dx, z0*z1/x^3 ), ( (x^2*z0) * dx, z0*z1/x^4 )] +[1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 1 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 1 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 1 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 1 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 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 0 0 0 0 0 0 0 0 0 1 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 1 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 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (x^5*z0) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^4*z0) * dx, z0*z1/x^2 ), ( (x^3) * dx, z1/x^3 ), ( (x^3*z0) * dx, z0*z1/x^3 )] +[1 1 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 1 1 0 0 0 0 0 0 0 0] +[0 0 0 1 0 0 0 0 0 0 0 0] +[0 0 0 0 1 1 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 1 1 0 0 0 0] +[0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 1 1 0 0] +[0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 1 1] +[0 0 0 0 0 0 0 0 0 0 0 1] + [1 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 1 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 1 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 1 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 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372: +******************************************************************************** +Denominators of fraction field elements are sometimes dropped without warning. +This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. +******************************************************************************** +[( (1) * dx, 0 ), ( ((a + 1)*z0 + z1) * dx, 0 ), ( (x) * dx, 0 ), ( (0) * dx, z1/x ), ( (a*x*z0 + x*z1) * dx, z0*z1/x ), ( (a*z0 + z1) * dx, z0*z1/x^2 )] +[ 1 a + 1 0 0 0 a] +[ 0 1 0 0 0 0] +[ 0 0 1 0 a 0] +[ 0 0 0 1 1 0] +[ 0 0 0 0 1 0] +[ 0 0 0 0 0 1] + [1 1 0 0 0 1] +[0 1 0 0 0 0] +[0 0 1 0 1 0] +[0 0 0 1 a 0] +[0 0 0 0 1 0] +[0 0 0 0 0 1] +[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 0 a^2] +[ 0 1 1] +[ 0 0 1], +[ 1 0 1] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 a^2 0] +[ 0 1 0] +[ 0 0 1], +[ 1 1 a^2] +[ 0 1 0] +[ 0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( ((a + 1)*z0 + z1) * dx, 0 ), ( (x) * dx, 0 ), ( (0) * dx, z1/x ), ( (a*x*z0 + x*z1) * dx, z0*z1/x ), ( (a*z0 + z1) * dx, z0*z1/x^2 )] +[ 1 a + 1 0 0 0 a] +[ 0 1 0 0 0 0] +[ 0 0 1 0 a 0] +[ 0 0 0 1 1 0] +[ 0 0 0 0 1 0] +[ 0 0 0 0 0 1] + [1 1 0 0 0 1] +[0 1 0 0 0 0] +[0 0 1 0 1 0] +[0 0 0 1 a 0] +[0 0 0 0 1 0] +[0 0 0 0 0 1] +[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 0 a^2] +[ 0 1 1] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 a^2 a] +[ 0 1 0] +[ 0 0 1], +[ 1 1 1] +[ 0 1 0] +[ 0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), ( (x^2) * dx, 0 ), ( (a*x^3) * dx, z1/x ), ( (x^3) * dx, z0/x ), ( (a*x^3*z0 + x^3*z1 + (a + 1)*x^3) * dx, z0*z1/x ), ( (a*x^2) * dx, z1/x^2 ), ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] +[ 1 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 1 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 1] +[ 0 0 0 0 1 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 1 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 1 0 0 0] +[ 0 0 0 0 0 0 0 0 0 1 1 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 0 0 0 0 0 0 0 0 0 0] +[0 1 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 1 1 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 a 0] +[0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 1 1 0 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 0 0 1 a 0] +[0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 a^2 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 a^2] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 a^2] +[ 0 1 a] +[ 0 0 1], +[ 1 0 1] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 a] +[ 0 1 0] +[ 0 0 1], +[ 1 0 0] +[ 0 1 1] +[ 0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, m)[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations: +z0^2 - z0 = x^5 +z1^2 - z1 = a*x^5 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.mult_by_p()[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7lfC.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7l C.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7l=C.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7l C.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^3 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.f.coordinates()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7laluation[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.valuation() +[?7h[?12l[?25h[?2004l[?7h-8 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.valuation()[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^4 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^4[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lluation()[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7lsage: ff.valuation()\ +[?7h[?12l[?25h[?2004l[?7h-4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.valuation()\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.mult_by_p()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?7h[z1/x, z0/x, z0*z1/x, z1/x^2, z0*z1/x^2, z0*z1/x^3] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), ( (x^2) * dx, 0 ), ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^4) * dx, 0 ), ( (a*x^5) * dx, z1/x ), ( (x^5) * dx, z0/x ), ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ), ( (a*x^4) * dx, z1/x^2 ), ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ), ( (0) * dx, z1/x^3 ), ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ), ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ), ( (x*z0) * dx, z0*z1/x^5 )] +[ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 a 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 a 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 1 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 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 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 1 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 a 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 1 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 a 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 1 a 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 1 a] +[ 0 1 0] +[ 0 0 1], +[ 1 a^2 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 a^2] +[ 0 1 1] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 a] +[ 0 0 1], +[ 1 0 0] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 0 a^2] +[ 0 1 1] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 a^2 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.mult_bp()[?7h[?12l[?25h[?25l[?7le_rhamasis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (z0) * dx, + (x) * dx, + ((a + 1)*x*z0 + x*z1) * dx, + (x^2) * dx, + ((a + 1)*x^2*z0 + x^2*z1) * dx, + (x^3) * dx, + (x^4) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.valuation()\[?7h[?12l[?25h[?25l[?7lor b in C1.de_rham_basis():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis(): +....: [?7h[?12l[?25h[?25l[?7lprint(mult_by_p(b.omega0).regular_form())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(mult_by_p(b.omega0).regular_form())[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(C.holomorphic_differentials_basis()[4].duality_pairing(b)) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis(): +....:  print(C.holomorphic_differentials_basis()[4].duality_pairing(b)) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [16], line 2 + 1 for b in C.cohomology_of_structure_sheaf_basis(): +----> 2 print(C.holomorphic_differentials_basis()[Integer(4)].duality_pairing(b)) + +AttributeError: 'as_form' object has no attribute 'duality_pairing' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis(): +....:  print(C.holomorphic_differentials_basis()[4].duality_pairing(b))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[4][?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l....:  +....:  print()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[] +()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(b.duality_pairing(om)) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis(): +....:  om = C.holomorphic_differentials_basis()[4] +....:  print(b.duality_pairing(om)) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [17], line 3 + 1 for b in C.cohomology_of_structure_sheaf_basis(): + 2 om = C.holomorphic_differentials_basis()[Integer(4)] +----> 3 print(b.duality_pairing(om)) + +AttributeError: 'as_function' object has no attribute 'duality_pairing' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(). d +....: iffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + 2*C 1 +....: .x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^47 + 3* C +....: 1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + 2*C1.x^ 1 +....: 7 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^10 8 +....:  + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74   +....: + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x ^ +....: 34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one)*C1.y. d +....: iffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om = C.holomorphic_differentials_basis()[4] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + [?7h[?12l[?25h[?25l[?7lom = C.holomorphic_differentials_basis()[4][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier() == om8.cartir() + A.diffn()[?7h[?12l[?25h[?25l[?7l + om.cartier om.expansion om.group_action om.trace  + om.coordinates om.expansion_at_infty om.residue om.valuation  + om.curve om.form om.serre_duality_pairing [?7h[?12l[?25h[?25l[?7lcartier + om.cartier  + + + [?7h[?12l[?25h[?25l[?7loordinates + om.cartier  + om.coordinates [?7h[?12l[?25h[?25l[?7lurve + + om.coordinates  + om.curve [?7h[?12l[?25h[?25l[?7l + + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.holomorphic_differentials_basis()[4][?7h[?12l[?25h[?25l[?7lfor b in C.chomology_of_structure_heaf_basis(): +....:  om = C.holomorphic_differentials_basis()[4] +....:  print(b.duality_pairing(om))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsduality_pairing(om)[?7h[?12l[?25h[?25l[?7leduality_pairing(om)[?7h[?12l[?25h[?25l[?7lrduality_pairing(om)[?7h[?12l[?25h[?25l[?7lrduality_pairing(om)[?7h[?12l[?25h[?25l[?7leduality_pairing(om)[?7h[?12l[?25h[?25l[?7l_duality_pairing(om)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis(): +....:  om = C.holomorphic_differentials_basis()[4] +....:  print(b.serre_duality_pairing(om)) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [19], line 3 + 1 for b in C.cohomology_of_structure_sheaf_basis(): + 2 om = C.holomorphic_differentials_basis()[Integer(4)] +----> 3 print(b.serre_duality_pairing(om)) + +AttributeError: 'as_function' object has no attribute 'serre_duality_pairing' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis(): +....:  om = C.holomorphic_differentials_basis()[4] +....:  print(b.serre_duality_pairing(om))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7lb))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sere_duality_pairing(b)[?7h[?12l[?25h[?25l[?7lo.sere_duality_pairing(b)[?7h[?12l[?25h[?25l[?7lm.sere_duality_pairing(b)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(om.serre_duality_pairing(b)) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis(): +....:  om = C.holomorphic_differentials_basis()[4] +....:  print(om.serre_duality_pairing(b)) +....:  +[?7h[?12l[?25h[?2004l0 +0 +0 +a + 1 +a +0 +0 +0 +0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()[3] +[?7h[?12l[?25h[?2004l[?7hz1/x^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[3][?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[3][?7h[?12l[?25h[?25l[?7l()[3][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()[4] +[?7h[?12l[?25h[?2004l[?7hz0*z1/x^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.holomorphic_differentials_basis()[4][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om +[?7h[?12l[?25h[?2004l[?7h((a + 1)*x*z0 + x*z1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z1) * dx, 0 ), ( (x^2*z1 + x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (0) * dx, z1/x ), ( (x^5) * dx, z0/x ), ( (x^5*z1 + x^4 + x^3*z0) * dx, z0*z1/x ), ( (x^2) * dx, z1/x^2 ), ( (x^4) * dx, z0/x^2 ), ( (x^4*z1 + x^2*z0) * dx, z0*z1/x^2 ), ( (x^3*z1 + x^2*z1) * dx, z0*z1/x^3 ), ( (x^2*z1 + z0) * dx, z0*z1/x^4 )] +[1 0 1 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 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 1 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 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 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 1 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 1 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[4][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhlrphic_differential_bsis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (z0) * dx, + (x) * dx, + (x*z1) * dx, + (x^2*z1 + x*z0) * dx, + (x^2) * dx, + (x^3) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lz)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.z[1] + C.z[0]) +[?7h[?12l[?25h[?2004l[?7hx*z1 + z0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.z[1] + C.z[0])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.z[1] + C.z[0]).valuation() +[?7h[?12l[?25h[?2004l[?7h-9 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.z[1] + C.z[0]).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.z[1]).valuation() +[?7h[?12l[?25h[?2004l[?7h-14 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: C.exponent_of_different + C.exponent_of_different  + C.exponent_of_different_prim + + + [?7h[?12l[?25h[?25l[?7l + C.exponent_of_different  + + [?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.exponent_of_different() +[?7h[?12l[?25h[?2004l[?7h22 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lC.exponent_of_different()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l_()[?7h[?12l[?25h[?25l[?7lp()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lm()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.exponent_of_different_prim() +[?7h[?12l[?25h[?2004l[?7h19 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (x^3*z1 + z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z1) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z1) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^4) * dx, 0 ), ( (0) * dx, z1/x ), ( (x^7) * dx, z0/x ), ( (x^7*z1 + x*z0) * dx, z0*z1/x ), ( (x^6) * dx, z0/x^2 ), ( (x^6*z1 + z0) * dx, z0*z1/x^2 ), ( (x^5) * dx, z0/x^3 ), ( (x^5*z1) * dx, z0*z1/x^3 ), ( (x^4*z1) * dx, z0*z1/x^4 ), ( (x^3*z1) * dx, z0*z1/x^5 )] +[1 0 1 0 0 0 0 0 0 0 0 0 0 1 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 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 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 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 1 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 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 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 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 1] + [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholmorphicials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (x^3*z1 + z0) * dx, + (x) * dx, + (x*z1) * dx, + (x^2) * dx, + (x^2*z1) * dx, + (x^3) * dx, + (x^4) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^9 +z1^2 - z1 = x^3 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(M-m)+ 3/2*(M-m)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: M = 9 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7l = 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: m = 3 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(M-m)+ 3/2*(M-m)[?7h[?12l[?25h[?25l[?7lsage: (M-m)+ 3/2*(M-m) +[?7h[?12l[?25h[?2004l[?7h15 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ldx.mult_by_p()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.exponent_of_different() +[?7h[?12l[?25h[?2004l[?7h24 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.exponent_of_different()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l_t()[?7h[?12l[?25h[?25l[?7lpt()[?7h[?12l[?25h[?25l[?7lrt()[?7h[?12l[?25h[?25l[?7lit()[?7h[?12l[?25h[?25l[?7lmt()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt_prim()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.exponent_of_different_prim() +[?7h[?12l[?25h[?2004l[?7h21 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 3[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: m+2*M +[?7h[?12l[?25h[?2004l[?7h21 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm+2*M[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: m+2*M + 3 +[?7h[?12l[?25h[?2004l[?7h24 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld.mult_by_p()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.valuation() +[?7h[?12l[?25h[?2004l[?7h16 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(M-m)+ 3/2*(M-m)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lM)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (m+2*M - 3)/2 +[?7h[?12l[?25h[?2004l[?7h9 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus() +[?7h[?12l[?25h[?2004l[?7h9 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (z0) * dx, + (x) * dx, + (x^2*z0 + x*z1) * dx, + (x*z0) * dx, + (x^2) * dx, + (x^3) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh1.diffn().regular_form().int()[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: h1.diffn().regular_form().int()[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: h1.diffn().regular_form().int()[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: h1.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7lsage: h1.diffn().regular_form().int() + + + + + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: h1.diffn().regular_form().int()[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: h1.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7lsage: h1.diffn().regular_form().int() + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +  + + + + + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = 9[?7h[?12l[?25h[?25l[?7lsage: M +[?7h[?12l[?25h[?2004l[?7h9 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lm+2*M + 3[?7h[?12l[?25h[?25l[?7lsage: m +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^5 +z1^2 - z1 = x^7 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ldx.valuaton()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lsage: C.dx.valuation() +[?7h[?12l[?25h[?2004l[?7h14 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + [?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: 5+14 - 5 +[?7h[?12l[?25h[?2004l[?7h14 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + [?7h[?12l[?25h[?25l[?7lC.dx.valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le_rham_basis()[0][?7h[?12l[?25h[?25l[?7l_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( ((a + 1)*z0 + z1) * dx, 0 ), + ( (x) * dx, 0 ), + ( (0) * dx, z1/x ), + ( (a*x*z0 + x*z1) * dx, z0*z1/x ), + ( (a*z0 + z1) * dx, z0*z1/x^2 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[4][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis()[4][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?7h[z1/x, z0*z1/x, z0*z1/x^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega0.r()[?7h[?12l[?25h[?25l[?7lsage: x +[?7h[?12l[?25h[?2004l[?7hx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x.divides(x^2) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTraceback (most recent call last): + + File /ext/sage/9.8/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/IPython/core/interactiveshell.py:3433 in run_code + exec(code_obj, self.user_global_ns, self.user_ns) + + Cell In [57], line 1 + load('init.sage') + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.8/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :32 + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.8/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :24 + print(result == ) + ^ +SyntaxError: invalid syntax + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File /ext/sage/9.8/src/sage/structure/element.pyx:1970, in sage.structure.element.Element._mod_() + 1969 try: +-> 1970 python_op = (self)._mod_ + 1971 except AttributeError: + +File /ext/sage/9.8/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + +File /ext/sage/9.8/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + +File /ext/sage/9.8/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + +AttributeError: 'InfinityRing_class_with_category' object has no attribute '__custom_name' + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Cell In [58], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :13 + +File :45, in __init__(self, C, list_of_fcts, branch_points, prec) + +File :185, in artin_schreier_transform(power_series, prec) + +File /ext/sage/9.8/src/sage/structure/element.pyx:1939, in sage.structure.element.Element.__mod__() + 1937 return (left)._mod_(right) + 1938 if BOTH_ARE_ELEMENT(cl): +-> 1939 return coercion_model.bin_op(left, right, mod) + 1940 + 1941 try: + +File /ext/sage/9.8/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.8/src/sage/structure/element.pyx:1937, in sage.structure.element.Element.__mod__() + 1935 cdef int cl = classify_elements(left, right) + 1936 if HAVE_SAME_PARENT(cl): +-> 1937 return (left)._mod_(right) + 1938 if BOTH_ARE_ELEMENT(cl): + 1939 return coercion_model.bin_op(left, right, mod) + +File /ext/sage/9.8/src/sage/structure/element.pyx:1972, in sage.structure.element.Element._mod_() + 1970 python_op = (self)._mod_ + 1971 except AttributeError: +-> 1972 raise bin_op_exception('%', self, other) + 1973 else: + 1974 return python_op(other) + +TypeError: unsupported operand parent(s) for %: 'The Infinity Ring' and 'The Infinity Ring' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTrue +True +True +True +True +--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Cell In [59], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :20 + +File :344, in cohomology_of_structure_sheaf_basis(self, threshold) + +File :344, in (.0) + +File :131, in serre_duality_pairing(self, fct) + +File /ext/sage/9.8/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) + 583 return expression.sum(*args, **kwds) + 584 elif max(len(args),len(kwds)) <= 1: +--> 585 return sum(expression, *args, **kwds) + 586 else: + 587 from sage.symbolic.ring import SR + +File :131, in (.0) + +File :124, in residue(self, place) + +File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:618, in sage.rings.laurent_series_ring_element.LaurentSeries.residue() + 616 Integer Ring + 617 """ +--> 618 return self[-1] + 619 + 620 def exponents(self): + +File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() + 542 return type(self)(self._parent, f, self.__n) + 543 +--> 544 return self.__u[i - self.__n] + 545 + 546 def __iter__(self): + +File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() + 451 return self.base_ring().zero() + 452 else: +--> 453 raise IndexError("coefficient not known") + 454 return self.__f[n] + 455 + +IndexError: coefficient not known +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTrue +True +True +True +True +True +True +True +I haven't found all forms, only 16 of 18 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [60], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :20 + +File :318, in cohomology_of_structure_sheaf_basis(self, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTrue +True +True +True +True +True +True +True +True +True +True +True +True +^C--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_zz_pex.pyx:281, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__() + 280 try: +--> 281 if a.parent() is not K: + 282 a = K.coerce(a) + +AttributeError: 'tuple' object has no attribute 'parent' + +During handling of the above exception, another exception occurred: + +KeyboardInterrupt Traceback (most recent call last) +Cell In [61], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :13 + +File :45, in __init__(self, C, list_of_fcts, branch_points, prec) + +File :196, in artin_schreier_transform(power_series, prec) + +File :12, in new_reverse(power_series, prec) + +File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() + 1829 if x: + 1830 raise ValueError("must not specify %s keyword and positional argument" % name) +-> 1831 a = self(kwds[name]) + 1832 del kwds[name] + 1833 try: + +File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__() + 1850 x = x[0] + 1851 +-> 1852 return self.__u(*x)*(x[0]**self.__n) + 1853 + 1854 def __pari__(self): + +File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__() + 363 x[0] = a + 364 x = tuple(x) +--> 365 return self.__f(x) + 366 + 367 def _unsafe_mutate(self, i, value): + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_zz_pex.pyx:284, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__() + 282 a = K.coerce(a) + 283 except (TypeError, AttributeError, NotImplementedError): +--> 284 return Polynomial.__call__(self, a) + 285 + 286 _a = self._parent._modulus.ZZ_pE(list(a.polynomial())) + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:904, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() + 902 return result + 903 pol._compiled = CompiledPolynomialFunction(pol.list()) +--> 904 return pol._compiled.eval(a) + 905 + 906 def compose_trunc(self, Polynomial other, long n): + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval() + 123 cdef object temp + 124 try: +--> 125 pd_eval(self._dag, x, self._coeffs) #see further down + 126 temp = self._dag.value #for an explanation + 127 pd_clean(self._dag) #of these 3 lines + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() + 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: + 352 if pd.value is None: +--> 353 pd.eval(vars, coeffs) + 354 pd.hits += 1 + 355 + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() + 505 + 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: +--> 507 pd_eval(self.left, vars, coeffs) + 508 pd_eval(self.right, vars, coeffs) + 509 self.value = self.left.value * self.right.value + coeffs[self.index] + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() + 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: + 352 if pd.value is None: +--> 353 pd.eval(vars, coeffs) + 354 pd.hits += 1 + 355 + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() + 505 + 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: +--> 507 pd_eval(self.left, vars, coeffs) + 508 pd_eval(self.right, vars, coeffs) + 509 self.value = self.left.value * self.right.value + coeffs[self.index] + + [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (55 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (54 times)] + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() + 505 + 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2: +--> 507 pd_eval(self.left, vars, coeffs) + 508 pd_eval(self.right, vars, coeffs) + 509 self.value = self.left.value * self.right.value + coeffs[self.index] + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval() + 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2: + 352 if pd.value is None: +--> 353 pd.eval(vars, coeffs) + 354 pd.hits += 1 + 355 + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval() + 507 pd_eval(self.left, vars, coeffs) + 508 pd_eval(self.right, vars, coeffs) +--> 509 self.value = self.left.value * self.right.value + coeffs[self.index] + 510 pd_clean(self.left) + 511 pd_clean(self.right) + +File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__() + 1511 cdef int cl = classify_elements(left, right) + 1512 if HAVE_SAME_PARENT(cl): +-> 1513 return (left)._mul_(right) + 1514 if BOTH_ARE_ELEMENT(cl): + 1515 return coercion_model.bin_op(left, right, mul) + +File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_() + 911 cdef LaurentSeries right = right_r + 912 return type(self)(self._parent, +--> 913 self.__u * right.__u, + 914 self.__n + right.__n) + 915 + +File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__() + 1511 cdef int cl = classify_elements(left, right) + 1512 if HAVE_SAME_PARENT(cl): +-> 1513 return (left)._mul_(right) + 1514 if BOTH_ARE_ELEMENT(cl): + 1515 return coercion_model.bin_op(left, right, mul) + +File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_() + 538 """ + 539 prec = self._mul_prec(right_r) +--> 540 return PowerSeries_poly(self._parent, + 541 self.__f * (right_r).__f, + 542 prec=prec, + +File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() + 42 ValueError: series has negative valuation + 43 """ +---> 44 R = parent._poly_ring() + 45 if isinstance(f, Element): + 46 if (f)._parent is R: + +File /ext/sage/9.8/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) + 958 pass + 959 return False +--> 961 def _poly_ring(self): + 962  """ + 963  Return the underlying polynomial ring used to represent elements of + 964  this power series ring. + (...) + 970  Univariate Polynomial Ring in t over Integer Ring + 971  """ + 972 return self.__poly_ring + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTrue +True +True +True +True +True +True +True +True +True +True +True +True +True +True +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTrue +True +True +True +True +True +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372: +******************************************************************************** +Denominators of fraction field elements are sometimes dropped without warning. +This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. +******************************************************************************** +[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (a*x^5) * dx, z1/x ), + ( (x^5) * dx, z0/x ), + ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ), + ( (a*x^4) * dx, z1/x^2 ), + ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ), + ( (0) * dx, z1/x^3 ), + ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ), + ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ), + ( (x*z0) * dx, z0*z1/x^5 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: A, B +[?7h[?12l[?25h[?2004l[?7h( +[ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 a 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 a 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 1 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1], + +[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 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 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 1 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 a 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 1 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 a 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 1 a 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (x^2*z0 + z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^5) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^5*z0 + x*z1) * dx, z0*z1/x ), + ( (x^4) * dx, z1/x^2 ), + ( (x^4*z0 + z1) * dx, z0*z1/x^2 ), + ( (x^3*z0) * dx, z0*z1/x^3 ), + ( (x^2*z0) * dx, z0*z1/x^4 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(m, M) + type1(m, M) + type2(m, M) + type3(m, M)[?7h[?12l[?25h[?25l[?7lC.x*C.z[1]).valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm(C.x)^(-1)[?7h[?12l[?25h[?25l[?7l(C.x)^(-1)[?7h[?12l[?25h[?25l[?7lo(C.x)^(-1)[?7h[?12l[?25h[?25l[?7lm(C.x)^(-1)[?7h[?12l[?25h[?25l[?7l (C.x)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l= (C.x)^(-1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: om= (C.x)^(-1)*C.z[1]*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom= (C.x)^(-1)*C.z[1]*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier) == om8.cartier() + A.diffn()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7luation[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.valuation() +[?7h[?12l[?25h[?2004l[?7h2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C); A, B +[?7h[?12l[?25h[?2004l[?7h( +[1 0 1 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] +[0 1 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 1 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 1 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 1 0 0 0 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 1 0 0 0 0 0 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 1 0 0 0 0 0 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 1 0 1 0 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 1 1 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 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 0 0 0 0 1] +) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^7 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 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 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2*z0 + x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^5) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), + ( (x^4) * dx, z1/x^2 ), + ( (x^2) * dx, z0/x^2 ), + ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), + ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), + ( (x^2*z0 + z1) * dx, z0*z1/x^4 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leC.de_rham_basis()[?7h[?12l[?25h[?25l[?7ltC.de_rham_basis()[?7h[?12l[?25h[?25l[?7laC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: eta[-2] + eta[4] +[?7h[?12l[?25h[?2004l[?7h( (x^3*z0 + x*z1) * dx, z0*z1/x^3 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta[-2] + eta[4][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta[4].group_action([0, 1]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta[4].group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l-2] + eta[4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta[-2] + eta[4][?7h[?12l[?25h[?25l[?7lteta[-2] + eta[4][?7h[?12l[?25h[?25l[?7laeta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l2eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l4eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l=eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta24 = eta[-2] + eta[4] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta24 = eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l[4].group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[4.group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l.group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l.group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l2.group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l4.group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta24.group_action([0, 1]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lagmathis(A, B)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lthis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^5 +z1^2 - z1 = x^7 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 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 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2*z0 + x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^5) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), + ( (x^4) * dx, z1/x^2 ), + ( (x^2) * dx, z0/x^2 ), + ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), + ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), + ( (x^2*z0 + z1) * dx, z0*z1/x^4 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta24.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l= C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: eta = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7limport itertools[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lsage: is + is is_commutative is_fundamental_discriminant is_pAdicField is_prime is_real_place isinstance  + is_M32 is_even is_integrally_closed is_pAdicRing is_prime_power is_square isogeny_codomain_from_kernel + is_ProductProjectiveSpaces is_field is_iterator is_package_installed is_pseudoprime is_squarefree isqrt  + is_ProjectiveSpace is_final is_odd is_power_of_two is_pseudoprime_power is_triangular_number issubclass  + [?7h[?12l[?25h[?25l[?7l + is  + + + + [?7h[?12l[?25h[?25l[?7lis_M32 + is  + is_M32 [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1]) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l24.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l = eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l= eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7lsage: eta24 = eta[-2] + eta[4] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7leta24 = eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: eta24 +[?7h[?12l[?25h[?2004l[?7h( (x^3*z0 + x*z1) * dx, z0*z1/x^3 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lisM[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7lM32(eta[-1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta24) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta24)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-3]) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-3])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l6])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-6]) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-6])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l0])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[0]) +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l4])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[4]) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lthis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def gene(x): +....:  y1 = x - x.group_action([0, 1]) +....:  y2 = x - x.group_action([1, 0]) +....:  print(y1, y2)[?7h[?12l[?25h[?25l[?7l....:  print(y1, y2) +....: [?7h[?12l[?25h[?25l[?7lsage: def gene(x): +....:  y1 = x - x.group_action([0, 1]) +....:  y2 = x - x.group_action([1, 0]) +....:  print(y1, y2) +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgenus(5, 7)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: gene(eta[-1]) +[?7h[?12l[?25h[?2004l( (1) * dx, z0/x^4 ) ( (x^2) * dx, z1/x^4 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(eta[-1])[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gene(eta24) +[?7h[?12l[?25h[?2004l( (x) * dx, z0/x^3 ) ( (x^3) * dx, z1/x^3 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus() +[?7h[?12l[?25h[?2004l[?7h8 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(eta24)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[-1])[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: gene(eta[-3]) +[?7h[?12l[?25h[?2004l( (x^2) * dx, z0/x^2 ) ( (x^4) * dx, z1/x^2 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[ 1 a + 1 0 0 0 a] +[ 0 1 0 0 0 0] +[ 0 0 1 0 a 0] +[ 0 0 0 1 1 0] +[ 0 0 0 0 1 0] +[ 0 0 0 0 0 1] + [1 1 0 0 0 1] +[0 1 0 0 0 0] +[0 0 1 0 1 0] +[0 0 0 1 a 0] +[0 0 0 0 1 0] +[0 0 0 0 0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( ((a + 1)*z0 + z1) * dx, 0 ), + ( (x) * dx, 0 ), + ( (0) * dx, z1/x ), + ( (a*x*z0 + x*z1) * dx, z0*z1/x ), + ( (a*z0 + z1) * dx, z0*z1/x^2 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[4])[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lisM[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_M32(eta[4])[?7h[?12l[?25h[?25l[?7lM32(eta[4])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l-])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1]) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-2]) +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta24[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta24[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: eta = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lis_M32(eta[-2])[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-2]) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1]) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 0 a^2] +[ 0 1 a^2] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a^2] +[ 0 0 1] +} +{ +[ 1 a^2 a^2] +[ 0 1 0] +[ 0 0 1], +[ 1 1 a^2] +[ 0 1 0] +[ 0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lvaluation(305)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: v1 = vector((1, 0)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1 = vector((1, 0))[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: v2 = vector((2, 0)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv2 = vector((2, 0))[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: v1. + v1.Mod v1.base_ring v1.coefficient v1.coordinate_ring v1.degree v1.derivative   + v1.additive_order v1.cartesian_product v1.coefficients v1.cross_product v1.denominator v1.dict   + v1.apply_map v1.category v1.column v1.cross_product_matrix v1.dense_coefficient_list v1.diff > + v1.base_extend v1.change_ring v1.conjugate v1.curl v1.dense_vector v1.div   + [?7h[?12l[?25h[?25l[?7lMod + v1.Mod  + + + + [?7h[?12l[?25h[?25l[?7lbase_ring + v1.Mod  v1.base_ring [?7h[?12l[?25h[?25l[?7lcoefficient + v1.base_ring  v1.coefficient [?7h[?12l[?25h[?25l[?7lordnate_ring + v1.coefficient  v1.coordinate_ring [?7h[?12l[?25h[?25l[?7ldegee + v1.coordinate_ring  v1.degree [?7h[?12l[?25h[?25l[?7lrivative + v1.degree  v1.derivative [?7h[?12l[?25h[?25l[?7lot_product + base_ringcoefficientordnate_ringdegee rivativeot_product + cartesian_productoefficients ross_productdenominator ict ump +<category olumn ross_product_matrixdenecoefficien_listiff umps + chang_rigonjugate url dense_vectoriv element[?7h[?12l[?25h[?25l[?7lge +coefficientordnate_ringdegee rivativeot_productge  +oefficients ross_productdenominator ict umphaming_weight +olumn ross_product_matrixdenecoefficien_listiff umpshermitian_inner_product +onjugate url dense_vectoriv elementinner_product[?7h[?12l[?25h[?25l[?7l +  +  +  +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsum(floor(305/5^n) for n in range(1, 10))[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: span(v1, v2) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [48], line 1 +----> 1 span(v1, v2) + +File /ext/sage/9.8/src/sage/modules/free_module.py:734, in span(gens, base_ring, check, already_echelonized) + 731 raise TypeError("generators must be given as an iterable structure") + 733 if R not in PrincipalIdealDomains(): +--> 734 raise TypeError("The base_ring (= %s) must be a principal ideal " + 735 "domain." % R) + 736 if not gens: + 737 return FreeModule(R, 0) + +TypeError: The base_ring (= (2, 0)) must be a principal ideal domain. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: V = QQ^2 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV = QQ^2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: V.linear_ + V.linear_combination  + V.linear_combination_of_basis + V.linear_dependence  + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcombination + V.linear_combination  + + + [?7h[?12l[?25h[?25l[?7l_of_basis + V.linear_combination  + V.linear_combination_of_basis[?7h[?12l[?25h[?25l[?7ldependence + + V.linear_combination_of_basis + V.linear_dependence [?7h[?12l[?25h[?25l[?7l( + + + +[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: V.linear_dependence([v1, v2]) +[?7h[?12l[?25h[?2004l[?7h[ +(2, -1) +] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv2 = vector((2, 0))[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: v3 = vector((2, 0)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 0))[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v2])[?7h[?12l[?25h[?25l[?7lsage: V.linear_dependence([v1, v2]) +[?7h[?12l[?25h[?2004l[?7h[ +(2, -1) +] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l3])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: V.linear_dependence([v1, v3]) +[?7h[?12l[?25h[?2004l[?7h[ +(2, -1) +] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v3])[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 0))[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v2])[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 0))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: v3 = vector((2, 1)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 1))[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v3])[?7h[?12l[?25h[?25l[?7lsage: V.linear_dependence([v1, v3]) +[?7h[?12l[?25h[?2004l[?7h[ + +] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def is_M32(x): +....:  n = len(x.coordinates()) +....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  if y1.coordinates() == vector(n*[0]): +....:  return False +....:  if y1.group_action([0, 1]).coordinates() != y1.coordinates() or y1.group_action([1, 0]).coordinates() != y1.coordinates(): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  if y2.coordinates() == vector(n*[0]): +....:  return False +....:  if y2.group_action([0, 1]).coordinates() != y2.coordinates() or y2.group_action([1, 0]).coordinates() != y2.coordinates(): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence(y1.coordinates(), y2.coordinates())) > 0: +....:  return False +....:  return True[?7h[?12l[?25h[?25l[?7l....:  return True +....: [?7h[?12l[?25h[?25l[?7lsage: def is_M32(x): +....:  n = len(x.coordinates()) +....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  if y1.coordinates() == vector(n*[0]): +....:  return False +....:  if y1.group_action([0, 1]).coordinates() != y1.coordinates() or y1.group_action([1, 0]).coordinates() != y1.coordinates(): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  if y2.coordinates() == vector(n*[0]): +....:  return False +....:  if y2.group_action([0, 1]).coordinates() != y2.coordinates() or y2.group_action([1, 0]).coordinates() != y2.coordinates(): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence(y1.coordinates(), y2.coordinates())) > 0: +....:  return False +....:  return True +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l32(eta[-1])[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1]) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [57], line 1 +----> 1 is_M32(eta[-Integer(1)]) + +Cell In [56], line 15, in is_M32(x) + 13 return False + 14 V = F**n +---> 15 if len(V.linear_dependence(y1.coordinates(), y2.coordinates())) > Integer(0): + 16 return False + 17 return True + +File /ext/sage/9.8/src/sage/modules/free_module.py:5026, in FreeModule_generic_field.linear_dependence(self, vectors, zeros, check) + 5024 for v in vectors: + 5025 if v not in self: +-> 5026 raise ValueError('vector %s is not an element of %s' % (v, self)) + 5027 if zeros == 'left': + 5028 basis = 'echelon' + +ValueError: vector 1 is not an element of Vector space of dimension 6 over Finite Field in a of size 2^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def is_M32(x): +....:  n = len(x.coordinates()) +....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  if y1.coordinates() == vector(n*[0]): +....:  return False +....:  if y1.group_action([0, 1]).coordinates() != y1.coordinates() or y1.group_action([1, 0]).coordinates() != y1.coordinates(): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  if y2.coordinates() == vector(n*[0]): +....:  return False +....:  if y2.group_action([0, 1]).coordinates() != y2.coordinates() or y2.group_action([1, 0]).coordinates() != y2.coordinates(): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence([y1.coordinates(), y2.coordinates()])) > 0: +....:  return False +....:  return True[?7h[?12l[?25h[?25l[?7l....:  return True +....: [?7h[?12l[?25h[?25l[?7lsage: def is_M32(x): +....:  n = len(x.coordinates()) +....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  if y1.coordinates() == vector(n*[0]): +....:  return False +....:  if y1.group_action([0, 1]).coordinates() != y1.coordinates() or y1.group_action([1, 0]).coordinates() != y1.coordinates(): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  if y2.coordinates() == vector(n*[0]): +....:  return False +....:  if y2.group_action([0, 1]).coordinates() != y2.coordinates() or y2.group_action([1, 0]).coordinates() != y2.coordinates(): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence([y1.coordinates(), y2.coordinates()])) > 0: +....:  return False +....:  return True +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def is_M32(x): +....:  n = len(x.coordinates()) +....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  if y1.coordinates() == vector(n*[0]): +....:  return False +....:  if y1.group_action([0, 1]).coordinates() != y1.coordinates() or y1.group_action([1, 0]).coordinates() != y1.coordinates(): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  if y2.coordinates() == vector(n*[0]): +....:  return False +....:  if y2.group_action([0, 1]).coordinates() != y2.coordinates() or y2.group_action([1, 0]).coordinates() != y2.coordinates(): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence([y1.coordinates(), y2.coordinates()])) > 0: +....:  return False +....:  return True[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1]) +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1]) +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-2]) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 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 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +False +False +False +False +True +False +False +False +False +False +True +False +False +True +False +True +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ lolosage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372: +******************************************************************************** +Denominators of fraction field elements are sometimes dropped without warning. +This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. +******************************************************************************** +[ 1 a + 1 0 0 0 a] +[ 0 1 0 0 0 0] +[ 0 0 1 0 a 0] +[ 0 0 0 1 1 0] +[ 0 0 0 0 1 0] +[ 0 0 0 0 0 1] + [1 1 0 0 0 1] +[0 1 0 0 0 0] +[0 0 1 0 1 0] +[0 0 0 1 a 0] +[0 0 0 0 1 0] +[0 0 0 0 0 1] +False +False +False +False +True +False +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[ 1 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 1 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 1] +[ 0 0 0 0 1 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 1 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 1 0 0 0] +[ 0 0 0 0 0 0 0 0 0 1 1 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 0 0 0 0 0 0 0 0 0 0] +[0 1 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 1 1 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 a 0] +[0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 1 1 0 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 0 0 1 a 0] +[0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 1] +False +False +False +False +False +False +False +False +^C--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2080, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__call__() + 2079 # Attempt evaluation via singular. +-> 2080 coerced_x = [parent.coerce(e) for e in x] + 2081 except TypeError: + +File /ext/sage/9.8/src/sage/structure/parent.pyx:1212, in sage.structure.parent.Parent.coerce() + 1211 _record_exception() +-> 1212 raise TypeError(_LazyString("no canonical coercion from %s to %s", (parent(x), self), {})) + 1213 else: + +TypeError: no canonical coercion from Laurent Series Ring in t over Finite Field in a of size 2^2 to Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field in a of size 2^2 + +During handling of the above exception, another exception occurred: + +KeyboardInterrupt Traceback (most recent call last) +Cell In [2], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :48 + +File :29, in is_M32(x) + +File :54, in coordinates(self, threshold, basis) + +File :392, in de_rham_basis(self, threshold) + +File :371, in lift_to_de_rham(self, fct, threshold) + +File :136, in holomorphic_differentials_basis(self, threshold) + +File :61, in expansion(self, pt) + +File /ext/sage/9.8/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() + 941 5 + 942 """ +--> 943 return self.subs(in_dict,**kwds) + 944 + 945 cpdef _act_on_(self, x, bint self_on_left): + +File /ext/sage/9.8/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs() + 832 else: + 833 variables.append(gen) +--> 834 return self(*variables) + 835 + 836 def numerical_approx(self, prec=None, digits=None, algorithm=None): + +File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__() + 447 (-2*x1*x2 + x1 + 1)/(x1 + x2) + 448 """ +--> 449 return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds) + 450 + 451 def _is_atomic(self): + +File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2085, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__call__() + 2083 y = parent.base_ring().zero() + 2084 for (m,c) in self.dict().iteritems(): +-> 2085 y += c*mul([ x[i]**m[i] for i in m.nonzero_positions()]) + 2086 return y + 2087 + +File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:953, in sage.rings.laurent_series_ring_element.LaurentSeries.__pow__() + 951 if right.denominator() == 1: + 952 right = right.numerator() +--> 953 return type(self)(self._parent, self.__u**right, self.__n*right) + 954 + 955 if self.is_zero(): + +File /ext/sage/9.8/src/sage/rings/power_series_ring_element.pyx:1152, in sage.rings.power_series_ring_element.PowerSeries.__pow__() + 1150 if right.denominator() == 1: + 1151 right = right.numerator() +-> 1152 return super().__pow__(right, dummy) + 1153 + 1154 if self.is_zero(): + +File /ext/sage/9.8/src/sage/structure/element.pyx:2058, in sage.structure.element.Element.__pow__() + 2056 return (left)._pow_(right) + 2057 if BOTH_ARE_ELEMENT(cl): +-> 2058 return coercion_model.bin_op(left, right, pow) + 2059 + 2060 cdef long value + +File /ext/sage/9.8/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op() + 1194 return (action)._act_(x, y) + 1195 else: +-> 1196 return (action)._act_(y, x) + 1197 + 1198 # Now coerce to a common parent and do the operation there + +File /ext/sage/9.8/src/sage/structure/coerce_actions.pyx:892, in sage.structure.coerce_actions.IntegerPowAction._act_() + 890 integer_check_long(n, &value, &err) + 891 if not err: +--> 892 return e._pow_long(value) + 893 return e._pow_int(n) + 894 + +File /ext/sage/9.8/src/sage/structure/element.pyx:2135, in sage.structure.element.Element._pow_long() + 2133 Generic path for powering with a C long. + 2134 """ +-> 2135 return self._pow_int(n) + 2136 + 2137 + +File /ext/sage/9.8/src/sage/structure/element.pyx:2712, in sage.structure.element.RingElement._pow_int() + 2710 OverflowError: exponent overflow (670592745) + 2711 """ +-> 2712 return arith_generic_power(self, n) + 2713 + 2714 def powers(self, n): + +File /ext/sage/9.8/src/sage/arith/power.pyx:83, in sage.arith.power.generic_power() + 81 raise NotImplementedError("non-integral exponents not supported") + 82 if not err: +---> 83 return generic_power_long(a, value) + 84 + 85 if n < 0: + +File /ext/sage/9.8/src/sage/arith/power.pyx:102, in sage.arith.power.generic_power_long() + 100 u = -u + 101 a = invert(a) +--> 102 return generic_power_pos(a, u) + 103 + 104 + +File /ext/sage/9.8/src/sage/arith/power.pyx:123, in sage.arith.power.generic_power_pos() + 121 apow *= apow + 122 if n & 1: +--> 123 res = apow * res + 124 n >>= 1 + 125 + +File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__() + 1511 cdef int cl = classify_elements(left, right) + 1512 if HAVE_SAME_PARENT(cl): +-> 1513 return (left)._mul_(right) + 1514 if BOTH_ARE_ELEMENT(cl): + 1515 return coercion_model.bin_op(left, right, mul) + +File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_() + 538 """ + 539 prec = self._mul_prec(right_r) +--> 540 return PowerSeries_poly(self._parent, + 541 self.__f * (right_r).__f, + 542 prec=prec, + +File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() + 42 ValueError: series has negative valuation + 43 """ +---> 44 R = parent._poly_ring() + 45 if isinstance(f, Element): + 46 if (f)._parent is R: + +File /ext/sage/9.8/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) + 958 pass + 959 return False +--> 961 def _poly_ring(self): + 962  """ + 963  Return the underlying polynomial ring used to represent elements of + 964  this power series ring. + (...) + 970  Univariate Polynomial Ring in t over Integer Ring + 971  """ + 972 return self.__poly_ring + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (a*x^3) * dx, z1/x ), + ( (x^3) * dx, z0/x ), + ( (a*x^3*z0 + x^3*z1 + (a + 1)*x^3) * dx, z0*z1/x ), + ( (a*x^2) * dx, z1/x^2 ), + ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^2 ), + ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor m in range(1, 20):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li2):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l4][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l8][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]:[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 8, 10, 11]: +....: [?7h[?12l[?25h[?25l[?7lprint(y1, y2)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(b))[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7l....:  print(is_ + is_M32 is_commutative is_final is_iterator is_pAdicRing  + is_ProductProjectiveSpaces is_even is_fundamental_discriminant is_odd is_package_installed > + is_ProjectiveSpace is_field is_integrally_closed is_pAdicField is_power_of_two  + [?7h[?12l[?25h[?25l[?7lM32 + is_M32  + + + [?7h[?12l[?25h[?25l[?7l( + + + +[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.r().regular_form()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomolgy_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lfor i in [4, 8, 10, 11]: +....: ....: print(is_M32(C.de_rham_basis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [4, 8, 10, 11]: +....: ....: print(is_M32(B[i])) +....:  +[?7h[?12l[?25h[?2004lFalse +True +True +False +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[0].omga0.r().regular_form()[?7h[?12l[?25h[?25l[?7l1egular_fom()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[11].group_action([1, 0]) - B[11] +[?7h[?12l[?25h[?2004l[?7h( (x) * dx, z1/x^3 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11].group_action([1, 0]) - B[11][?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (a*x^3) * dx, z1/x ), + ( (x^3) * dx, z0/x ), + ( (a*x^3*z0 + x^3*z1 + (a + 1)*x^3) * dx, z0*z1/x ), + ( (a*x^2) * dx, z1/x^2 ), + ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^2 ), + ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[11].group_action([1, 0]) - B[11][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l]) - B[1][?7h[?12l[?25h[?25l[?7l]) - B[1][?7h[?12l[?25h[?25l[?7l]) - B[1][?7h[?12l[?25h[?25l[?7l]) - B[1][?7h[?12l[?25h[?25l[?7l0]) - B[1][?7h[?12l[?25h[?25l[?7l,]) - B[1][?7h[?12l[?25h[?25l[?7l ]) - B[1][?7h[?12l[?25h[?25l[?7l1]) - B[1][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[11].group_action([0, 1]) - B[11] +[?7h[?12l[?25h[?2004l[?7h( (0) * dx, z0/x^3 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.z[0] +[?7h[?12l[?25h[?2004l[?7hz0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[0][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x^3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]/C.x^3).valuation() +[?7h[?12l[?25h[?2004l[?7h2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11].group_action([0, 1]) - B[11][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[11] +[?7h[?12l[?25h[?2004l[?7h( (x*z0) * dx, z0*z1/x^3 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[8] +[?7h[?12l[?25h[?2004l[?7h( (a*x^3*z0 + x^3*z1 + (a + 1)*x^3) * dx, z0*z1/x ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[8][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[8][?7h[?12l[?25h[?25l[?7l11][?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x^3).valuation()[?7h[?12l[?25h[?25l[?7lC.z[0][?7h[?12l[?25h[?25l[?7lB[11].group_action([0, 1]) - B[11][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l8][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l].group_action([0, 1]) - B[8][?7h[?12l[?25h[?25l[?7l].group_action([0, 1]) - B[8][?7h[?12l[?25h[?25l[?7l8].group_action([0, 1]) - B[8][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[8].group_action([0, 1]) - B[8] +[?7h[?12l[?25h[?2004l[?7h( (x^3) * dx, z0/x ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[8].group_action([0, 1]) - B[8][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]) - B[8][?7h[?12l[?25h[?25l[?7l]) - B[8][?7h[?12l[?25h[?25l[?7l]) - B[8][?7h[?12l[?25h[?25l[?7l]) - B[8][?7h[?12l[?25h[?25l[?7l1]) - B[8][?7h[?12l[?25h[?25l[?7l,]) - B[8][?7h[?12l[?25h[?25l[?7l ]) - B[8][?7h[?12l[?25h[?25l[?7l0]) - B[8][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[8].group_action([1, 0]) - B[8] +[?7h[?12l[?25h[?2004l[?7h( (a*x^3) * dx, z1/x ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lthis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) +[?7h[?12l[?25h[?2004l[?7h>> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],[ 1 * dx, 0 , z1 * dx, 0 , z0 * dx + ^ +User error: Identifier 'dx' has not been declared or assigned +>> /x^2 , x*z0 * dx, z0*z1/x^3 ]>;M := RModule(RSpace(GF(4),12), A);L := Inde + ^ +User error: Identifier 'A' has not been declared or assigned +>> 4),12), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Ge + ^ +User error: Identifier 'M' has not been declared or assigned +>> 4),12), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Ge + ^ +User error: Identifier 'L' has not been declared or assigned +>> 4),12), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Ge + ^ +User error: Identifier 'L' has not been declared or assigned +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(C); A, B[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(C); A, B[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l A, B[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C); magmathis(A, B) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 a] +[ 0 1 0] +[ 0 0 1], +[ 1 0 1] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 0 a^2] +[ 0 1 a] +[ 0 0 1], +[ 1 0 0] +[ 0 1 1] +[ 0 0 1] +} +{ +[ 1 a^2 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 1] +[ 0 1 0] +[ 0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[8].group_action([1, 0]) - B[8][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l11][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[11] +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11][?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[11][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[11] +[?7h[?12l[?25h[?2004l[?7h( (x*z0) * dx, z0*z1/x^3 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[3] +[?7h[?12l[?25h[?2004l[?7h( (x) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[3][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[3][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l A, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lA = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l2 = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: A1, A2 = group_action_matrices_dR(C); A1, A2 +[?7h[?12l[?25h[?2004l[?7h( +[ 1 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 1 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 1] +[ 0 0 0 0 1 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 1 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 1 0 0 0] +[ 0 0 0 0 0 0 0 0 0 1 1 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1], + +[1 1 0 0 0 0 0 0 0 0 0 0] +[0 1 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 1 1 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 a 0] +[0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 1 1 0 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 0 0 1 a 0] +[0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 1] +) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(eta[-3])[?7h[?12l[?25h[?25l[?7lroup_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[3][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[3] +[?7h[?12l[?25h[?2004l[?7h( (x) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[3][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]group_action[?7h[?12l[?25h[?25l[?7l[].group_action[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[4].group_action([1, 0]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, a + 1, 1, 0, 0, 0, 0, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[4].group_action([1, 0]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].group_action([1, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l1].group_action([1, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l1].group_action([1, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[11].group_action([1, 0]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11].group_action([1, 0]).coordinates()[?7h[?12l[?25h[?25l[?7l4].group_action([1, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 0]).cordinates()[?7h[?12l[?25h[?25l[?7l 0]).cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0]).cordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l,]).cordinates()[?7h[?12l[?25h[?25l[?7l ]).cordinates()[?7h[?12l[?25h[?25l[?7l1]).cordinates()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[4].group_action([0, 1]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[4].group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l1].group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l1].group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[11].group_action([0, 1]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v3])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11].group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4].group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[4] +[?7h[?12l[?25h[?2004l[?7h( ((a + 1)*x*z0 + x*z1) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372: +******************************************************************************** +Denominators of fraction field elements are sometimes dropped without warning. +This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. +******************************************************************************** +[ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 a 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 a 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 1 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 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 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 1 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 a 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 1 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 a 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 1 a 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +False +^C--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2080, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__call__() + 2079 # Attempt evaluation via singular. +-> 2080 coerced_x = [parent.coerce(e) for e in x] + 2081 except TypeError: + +File /ext/sage/9.8/src/sage/structure/parent.pyx:1212, in sage.structure.parent.Parent.coerce() + 1211 _record_exception() +-> 1212 raise TypeError(_LazyString("no canonical coercion from %s to %s", (parent(x), self), {})) + 1213 else: + +TypeError: no canonical coercion from Laurent Series Ring in t over Finite Field in a of size 2^2 to Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field in a of size 2^2 + +During handling of the above exception, another exception occurred: + +KeyboardInterrupt Traceback (most recent call last) +Cell In [1], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :48 + +File :27, in is_M32(x) + +File :54, in coordinates(self, threshold, basis) + +File :392, in de_rham_basis(self, threshold) + +File :376, in lift_to_de_rham(self, fct, threshold) + +File :39, in expansion_at_infty(self, place) + +File /ext/sage/9.8/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() + 941 5 + 942 """ +--> 943 return self.subs(in_dict,**kwds) + 944 + 945 cpdef _act_on_(self, x, bint self_on_left): + +File /ext/sage/9.8/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs() + 832 else: + 833 variables.append(gen) +--> 834 return self(*variables) + 835 + 836 def numerical_approx(self, prec=None, digits=None, algorithm=None): + +File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__() + 447 (-2*x1*x2 + x1 + 1)/(x1 + x2) + 448 """ +--> 449 return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds) + 450 + 451 def _is_atomic(self): + +File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2085, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__call__() + 2083 y = parent.base_ring().zero() + 2084 for (m,c) in self.dict().iteritems(): +-> 2085 y += c*mul([ x[i]**m[i] for i in m.nonzero_positions()]) + 2086 return y + 2087 + +File /ext/sage/9.8/src/sage/misc/misc_c.pyx:144, in sage.misc.misc_c.prod() + 142 return z + 143 +--> 144 prod = balanced_list_prod(x, 0, n, recursion_cutoff) + 145 + 146 if z is not None: + +File /ext/sage/9.8/src/sage/misc/misc_c.pyx:180, in sage.misc.misc_c.balanced_list_prod() + 178 prod = PySequence_Fast_GET_ITEM(L, offset) + 179 for k from offset < k < offset + count: +--> 180 prod *= PySequence_Fast_GET_ITEM(L, k) + 181 return prod + 182 else: + +File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__() + 1511 cdef int cl = classify_elements(left, right) + 1512 if HAVE_SAME_PARENT(cl): +-> 1513 return (left)._mul_(right) + 1514 if BOTH_ARE_ELEMENT(cl): + 1515 return coercion_model.bin_op(left, right, mul) + +File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_() + 911 cdef LaurentSeries right = right_r + 912 return type(self)(self._parent, +--> 913 self.__u * right.__u, + 914 self.__n + right.__n) + 915 + +File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__() + 1511 cdef int cl = classify_elements(left, right) + 1512 if HAVE_SAME_PARENT(cl): +-> 1513 return (left)._mul_(right) + 1514 if BOTH_ARE_ELEMENT(cl): + 1515 return coercion_model.bin_op(left, right, mul) + +File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_() + 538 """ + 539 prec = self._mul_prec(right_r) +--> 540 return PowerSeries_poly(self._parent, + 541 self.__f * (right_r).__f, + 542 prec=prec, + +File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__() + 42 ValueError: series has negative valuation + 43 """ +---> 44 R = parent._poly_ring() + 45 if isinstance(f, Element): + 46 if (f)._parent is R: + +File /ext/sage/9.8/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self) + 958 pass + 959 return False +--> 961 def _poly_ring(self): + 962  """ + 963  Return the underlying polynomial ring used to represent elements of + 964  this power series ring. + (...) + 970  Univariate Polynomial Ring in t over Integer Ring + 971  """ + 972 return self.__poly_ring + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[0][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (a*x^5) * dx, z1/x ), + ( (x^5) * dx, z0/x ), + ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ), + ( (a*x^4) * dx, z1/x^2 ), + ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ), + ( (0) * dx, z1/x^3 ), + ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ), + ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ), + ( (x*z0) * dx, z0*z1/x^5 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[4][?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 a 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 a 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 1 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 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 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 1 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 a 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 1 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 a 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 1 a 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (a*x^5) * dx, z1/x ), + ( (x^5) * dx, z0/x ), + ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ), + ( (a*x^4) * dx, z1/x^2 ), + ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ), + ( (0) * dx, z1/x^3 ), + ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ), + ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ), + ( (x*z0) * dx, z0*z1/x^5 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [4, 8, 10, 11]:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li in [4, 8, 10, 11]:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l4]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l6]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l3]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l5]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l6]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l7]:[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 6, 11, 13, 15, 16, 17]: +....: [?7h[?12l[?25h[?25l[?7lprint(y1, y2)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(is_M32(B[i], B)) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [4, 6, 11, 13, 15, 16, 17]: +....:  print(is_M32(B[i], B)) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [7], line 2 + 1 for i in [Integer(4), Integer(6), Integer(11), Integer(13), Integer(15), Integer(16), Integer(17)]: +----> 2 print(is_M32(B[i], B)) + +File :27, in is_M32(x, B) + +File :60, in coordinates(self, threshold, basis) + +TypeError: 'as_cech' object is not iterable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[4][?7h[?12l[?25h[?25l[?7l0.omega0.r().regular_form()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].coordinates(basis = B) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [8], line 1 +----> 1 B[Integer(0)].coordinates(basis = B) + +File :60, in coordinates(self, threshold, basis) + +TypeError: 'as_cech' object is not iterable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (a*x^5) * dx, z1/x ), + ( (x^5) * dx, z0/x ), + ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ), + ( (a*x^4) * dx, z1/x^2 ), + ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ), + ( (0) * dx, z1/x^3 ), + ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ), + ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ), + ( (x*z0) * dx, z0*z1/x^5 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[0] +[?7h[?12l[?25h[?2004l[?7h( (1) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0][?7h[?12l[?25h[?25l[?7l[].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].coordinates() +[?7h[?12l[?25h[?2004l[?7h(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[0].coordinates(basis = B) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [12], line 1 +----> 1 B[Integer(0)].coordinates(basis = B) + +File :60, in coordinates(self, threshold, basis) + +TypeError: 'as_cech' object is not iterable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (a*x^5) * dx, z1/x ), + ( (x^5) * dx, z0/x ), + ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ), + ( (a*x^4) * dx, z1/x^2 ), + ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ), + ( (0) * dx, z1/x^3 ), + ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ), + ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ), + ( (x*z0) * dx, z0*z1/x^5 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 6, 11, 13, 15, 16, 17]: +....:  print(is_M32(B[i], B))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lB))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(is_M32(B[i], BB)) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [4, 6, 11, 13, 15, 16, 17]: +....:  print(is_M32(B[i], BB)) +....:  +[?7h[?12l[?25h[?2004lFalse +False +True +True +True +False +False +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations: +z0^2 - z0 = x^7 +z1^2 - z1 = a*x^7 + +[?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[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l11].group_ction([0,1]).coordinates()[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7lsage: A1, A2 = group_action_matrices_dR(C); A1, A2 +[?7h[?12l[?25h[?2004l[?7h( +[ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 a 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 a 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 1 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1], + +[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 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 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 1 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 a 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 1 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 a 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 1 a 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l11].group_ction([0,1]).coordinates()[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[17], B[4] +[?7h[?12l[?25h[?2004l[?7h(( (x*z0) * dx, z0*z1/x^5 ), ( ((a + 1)*x*z0 + x*z1) * dx, 0 )) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[17], B[4][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[16], B[5] +[?7h[?12l[?25h[?2004l[?7h(( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ), ( (x^2) * dx, 0 )) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[16], B[5][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l6][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[16], B[6] +[?7h[?12l[?25h[?2004l[?7h(( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ), + ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 )) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations: +z0^2 - z0 = x^7 +z1^2 - z1 = a*x^7 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [4, 6, 11, 13, 15, 16, 17]:[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: f0 +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [24], line 1 +----> 1 f0 + +NameError: name 'f0' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf0[?7h[?12l[?25h[?25l[?7lf.valuation()\[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?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[?7lf0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f1 +[?7h[?12l[?25h[?2004l[?7hx^7 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x^3).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = C.holmorphic_differentials_basis()[4][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l C.holomorphic_differentials_basis()[4][?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC f0.difn()[?7h[?12l[?25h[?25l[?7l. f0.difn()[?7h[?12l[?25h[?25l[?7lz f0.difn()[?7h[?12l[?25h[?25l[?7l[ f0.difn()[?7h[?12l[?25h[?25l[?7l[] f0.difn()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0] f0.difn()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]* f0.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf0.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = C.z[1]*f1.diffn() +C.z[0]*f0.diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [26], line 1 +----> 1 om = C.z[Integer(1)]*f1.diffn() +C.z[Integer(0)]*f0.diffn() + +NameError: name 'f0' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.z[1]*f1.diffn() +C.z[0]*f0.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l2.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = C.z[1]*f1.diffn() +C.z[0]*f2.diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [27], line 1 +----> 1 om = C.z[Integer(1)]*f1.diffn() +C.z[Integer(0)]*f2.diffn() + +TypeError: unsupported operand type(s) for +: 'NoneType' and 'NoneType' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.diffn().int()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.diffn() +[?7h[?12l[?25h[?2004l[?7h(x^6) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1.diffn()[?7h[?12l[?25h[?25l[?7lom = C.z[1]*f1.diffn() +C.z[0]*f2.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l(.difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l().difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC_super.x^7)diffn() +C.z[0]*f2.diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7la).difn()[?7h[?12l[?25h[?25l[?7l*).difn()[?7h[?12l[?25h[?25l[?7lC_super.x^7).diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = C.z[1]*(C.x^7).diffn() +C.z[0]*(a*C.x^7).diffn() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.z[1]*(C.x^7).diffn() +C.z[0]*(a*C.x^7).diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation)[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.valuation() +[?7h[?12l[?25h[?2004l[?7h-22 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations: +z0^2 - z0 = x^7 +z1^2 - z1 = a*x^7 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: 7*2 + 1 +[?7h[?12l[?25h[?2004l[?7h15 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 1 0 0] +[0 1 0 0] +[0 0 1 1] +[0 0 0 1] + [1 0 0 0] +[0 1 0 0] +[0 0 1 0] +[0 0 0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, z1/x ), + ( (x*z0) * dx, z0*z1/x )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 1 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 1 0 0 0 0] +[0 0 0 0 1 1 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 1] + [1 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0] +[0 0 1 0 0 0 0 0] +[0 0 0 1 0 0 0 0] +[0 0 0 0 1 0 0 0] +[0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^3) * dx, z1/x ), + ( (x^3*z0) * dx, z0*z1/x ), + ( (x^2) * dx, z1/x^2 ), + ( (x^2*z0) * dx, z0*z1/x^2 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + [1 1 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 1 0 0 0 1 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 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] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (x*z0 + z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^3*z0 + x*z1) * dx, z0*z1/x ), + ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), + ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[16], B[6][?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-2])[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_M32(eta[-2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1], BB) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [43], line 1 +----> 1 is_M32(eta[-Integer(1)], BB) + +TypeError: 'function' object is not subscriptable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[-1], B)[?7h[?12l[?25h[?25l[?7l[-1], B)[?7h[?12l[?25h[?25l[?7l[-1], B)[?7h[?12l[?25h[?25l[?7lB[-1], B)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-1], BB) +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7lis], B)[?7h[?12l[?25h[?25l[?7li], B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus() +[?7h[?12l[?25h[?2004l[?7h5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7lsage: A1, A2 = group_action_matrices_dR(C); A1, A2 +[?7h[?12l[?25h[?2004l[?7h( +[1 0 1 0 0 0 0 0 0 0] [1 1 0 0 0 0 0 0 1 0] +[0 1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0] +[0 1 0 1 0 0 0 0 0 1] [0 0 0 1 0 0 0 1 0 0] +[0 0 0 0 1 0 0 0 1 0] [0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 1 0 0] [0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 0 1 0] [0 0 0 0 0 0 1 1 0 0] +[0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 1] +) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A, B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1A, A2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, A2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, A2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, A2) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sagre +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + [1 1 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 1 0 0 0 1 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 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] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^5 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (x*z0 + z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^3*z0 + x*z1) * dx, z0*z1/x ), + ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), + ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = C.de_rhm_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lOX= C.cooology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-1], BB)[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l32(B[-1], BB)[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-1], BB) +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l2], B)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-2], BB) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-2], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l3], B)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-3], BB) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-3], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l1], B)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[1], BB) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7lsage: A1, A2 = group_action_matrices_dR(C); A1, A2 +[?7h[?12l[?25h[?2004l[?7h( +[1 0 1 0 0 0 0 0 0 0] [1 1 0 0 0 0 0 0 1 0] +[0 1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0] +[0 1 0 1 0 0 0 0 0 1] [0 0 0 1 0 0 0 1 0 0] +[0 0 0 0 1 0 0 0 1 0] [0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 1 0 0] [0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 0 1 0] [0 0 0 0 0 0 1 1 0 0] +[0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 1] +) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lnus()[?7h[?12l[?25h[?25l[?7lsage: C.genus() +[?7h[?12l[?25h[?2004l[?7h5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l[16], B[6][?7h[?12l[?25h[?25l[?7l7].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[7] +[?7h[?12l[?25h[?2004l[?7h( (x^3*z0 + x*z1) * dx, z0*z1/x ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[7][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, A2) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + [1 1 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 1 0 0 0 1 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 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] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (x*z0 + z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^3*z0 + x*z1) * dx, z0*z1/x ), + ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), + ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^5 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^3).valuation()[?7h[?12l[?25h[?25l[?7l^3).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]/C.x).valuation() +[?7h[?12l[?25h[?2004l[?7h-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x).valuation()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]/C.x).diffn() +[?7h[?12l[?25h[?2004l[?7h((x^3 + z0)/x^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[7][?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[7][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[-4] +[?7h[?12l[?25h[?2004l[?7h( (0) * dx, z0/x ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-4][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B[-4].omega8 +[?7h[?12l[?25h[?2004l[?7h((x^3 + z0)/x^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^5 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (x*z0 + z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^3*z0 + x*z1) * dx, z0*z1/x ), + ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), + ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-4].omega8[?7h[?12l[?25h[?25l[?7l = Cde_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[-4]omega8[?7h[?12l[?25h[?25l[?7l-4].omega8[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[-2].group_action([0, 1]) - B[-2] +[?7h[?12l[?25h[?2004l[?7h( (1) * dx, z0/x^2 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-2].group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-2].group_action([0, 1]) - B[-2])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (B[-2].group_action([0, 1]) - B[-2]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(1, 0, 0, 0, 0, 0, 0, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef ch(m, M):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ldef [?7h[?12l[?25h[?25l[?7ltotal(m, M):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l +....: [?7h[?12l[?25h[?25l[?7lreturn lhs == rhs[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lreturn[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lmax(result, 0)[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lm))[?7h[?12l[?25h[?25l[?7l+))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7lM))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7l-))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: def te(m, M): +....:  return m - 1 - floor((m+2*M - 1)/4) +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7ltry:[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: te(3, 5) +[?7h[?12l[?25h[?2004l[?7h-1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lte(3, 5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l7)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: te(3, 7) +[?7h[?12l[?25h[?2004l[?7h-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lte(3, 7)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 7)[?7h[?12l[?25h[?25l[?7l1, 7)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: te(1, 5) +[?7h[?12l[?25h[?2004l[?7h-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + [?7h[?12l[?25h[?25l[?7lte(1, 5)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: te(13, 17) +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lte(13, 17)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(13, 17)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: te(11, 13) +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + [?7h[?12l[?25h[?25l[?7lte(11, 13)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l9)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: te(9, 11) +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + [?7h[?12l[?25h[?25l[?7lte(9, 11)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l7)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l9)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: te(7,9) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor m in range(1, 20):[?7h[?12l[?25h[?25l[?7lf.valuatio()\[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/x^8 +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [23], line 1 +----> 1 fff = C.z[Integer(0)]*C.z[Integer(1)]/x**Integer(8) + +File :52, in __truediv__(self, other) + +File /ext/sage/9.8/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.8/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.8/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/x^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^8[?7h[?12l[?25h[?25l[?7l./x^8[?7h[?12l[?25h[?25l[?7lCx^8[?7h[?12l[?25h[?25l[?7l.x^8[?7h[?12l[?25h[?25l[?7lx^8[?7h[?12l[?25h[?25l[?7lx^8[?7h[?12l[?25h[?25l[?7lx^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^8 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lte[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [25], line 1 +----> 1 fff.coordinates() + +AttributeError: 'as_function' object has no attribute 'coordinates' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfff.coordinates([?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^8 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^9 +z1^2 - z1 = x^11 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7luation[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.valuation() +[?7h[?12l[?25h[?2004l[?7h-8 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, m)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^9 +z1^2 - z1 = x^11 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-2].group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7lOmega = C.holomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]cordinates()[?7h[?12l[?25h[?25l[?7l[].cordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: BOX[1].coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.valuation()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^4 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^4[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7luation()[?7h[?12l[?25h[?25l[?7lsage: fff.valuation() +[?7h[?12l[?25h[?2004l[?7h-24 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.valuation()[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^1 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^1[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lluation()[?7h[?12l[?25h[?25l[?7lsage: fff.valuation() +[?7h[?12l[?25h[?2004l[?7h-36 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.valuation()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff +[?7h[?12l[?25h[?2004l[?7hz0*z1/x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^1[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0]*C.z[1]/C.x^1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^8 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff +[?7h[?12l[?25h[?2004l[?7hz0*z1/x^8 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]^*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l2*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]^/C.x^8[?7h[?12l[?25h[?25l[?7l2/C.x^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]^2*C.z[1]^2/C.x^8 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]^2*C.z[1]^2/C.x^8[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?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[?7lC[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^9 +z1^2 - z1 = x^11 + +[?2004h[?25l[?7lsage: C[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + [1 1 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 1 0 0 0 1 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 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 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (x*z0 + z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^3*z0 + x*z1) * dx, z0*z1/x ), + ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), + ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX[1].coordinates()[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[1], BB)[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_M32(B[1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lOX[1].coordinates()[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l = C.chomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l= C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[1], BB)[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_M32(B[1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-1], B)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-1], BB) +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l2], B)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-2], BB) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-2], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l3], B)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-3], BB) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(eta[-3])[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: gene(eta[-3]) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [12], line 1 +----> 1 gene(eta[-Integer(3)]) + +TypeError: 'function' object is not subscriptable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(eta[-3])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[-3])[?7h[?12l[?25h[?25l[?7l[-3])[?7h[?12l[?25h[?25l[?7l[-3])[?7h[?12l[?25h[?25l[?7l[-3])[?7h[?12l[?25h[?25l[?7l([-3])[?7h[?12l[?25h[?25l[?7lB[-3])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gene(B[-3]) +[?7h[?12l[?25h[?2004l( (x) * dx, z0/x ) ( (x^3) * dx, z1/x ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(B[-3])[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: gene(B[-2]) +[?7h[?12l[?25h[?2004l( (1) * dx, z0/x^2 ) ( (x^2) * dx, z1/x^2 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] +[1 1 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 1 0 0 0 1 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 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 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + + +[1 1 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 1 0 0 0 1 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 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 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = C.de_rhm_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[-2]group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l].group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7lsage: B[-2].group_action([0, 1]) - B[-2] +[?7h[?12l[?25h[?2004l[?7h( (1) * dx, z0/x^2 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-2].group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7l[]_[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-2].group_action([0, 1]) - B[-2])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l().coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().coordinates()[?7h[?12l[?25h[?25l[?7lsage: (B[-2].group_action([0, 1]) - B[-2]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(1, 0, 0, 0, 0, 0, 0, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-2].group_action([0, 1]) - B[-2]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l3).cordinates()[?7h[?12l[?25h[?25l[?7l]).cordinates()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].group_action([0, 1]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l3].group_action([0, 1]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (B[-3].group_action([0, 1]) - B[-3]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 1, 0, 0, 1, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-3].group_action([0, 1]) - B[-3]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l1]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l,]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l ]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l0]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (B[-3].group_action([1, 0]) - B[-3]).coordinates() +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 1, 0, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A1.kernel() +[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 0 over Finite Field of size 2 +Basis matrix: +[] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lind[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lix[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: I = identity_matrix(10) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1.kernel()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = A1 * C1.y[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lsage: A1 - I +[?7h[?12l[?25h[?2004l[?7h[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 1 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-3].group_action([1, 0]) - B[-3]).coordinates()[?7h[?12l[?25h[?25l[?7lA  A1 - C1.y).diffn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV(A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l1(A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l (A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l=(A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l (A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: V1 = (A1 - I).kernel() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV1 = (A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - I).kernel()[?7h[?12l[?25h[?25l[?7l2 - I).kernel()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = (A2 - I).kernel()[?7h[?12l[?25h[?25l[?7l2 = (A2 - I).kernel()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: V2 = (A2 - I).kernel() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV2 = (A2 - I).kernel()[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: V1. + V1.CartesianProduct V1.algebra  + V1.Element V1.ambient  + V1.Hom V1.ambient_module > + V1.addition_table V1.ambient_vector_space  + [?7h[?12l[?25h[?25l[?7lCartesianProduct + V1.CartesianProduct  + + + + [?7h[?12l[?25h[?25l[?7lalgebra + V1.CartesianProduct  V1.algebra [?7h[?12l[?25h[?25l[?7ln_lement + algebra n_lement + ambinnhilator +<ambient_modulennhilatr_basis + mbent_vector_spacere_linearly_dependnt[?7h[?12l[?25h[?25l[?7lbas +n_lementbas  +nnhilatorbase_extend +nnhilatr_basisbase_field  +re_linearly_dependntbase_ring [?7h[?12l[?25h[?25l[?7lis +bas is +base_extendis_matrix +base_field crdinality +base_ring crtesan_product[?7h[?12l[?25h[?25l[?7lctegories +isctegories +is_matrixctegory  +crdinalityhange_rng +crtesan_productodimension [?7h[?12l[?25h[?25l[?7loerce +ctegoriesoerce  +ctegory oerce_embedding +hange_rngoercmap_from +odimension mplment [?7h[?12l[?25h[?25l[?7lnstruction +oerce nstruction +oerce_embeddingnvert_ap_from +oercmap_fromodinatemodule +mplment ordinate_ring[?7h[?12l[?25h[?25l[?7lordinae_vector +nstructionordinae_vector +nvert_ap_fromordinates  +odinatemoduledegee  +ordinate_ringdenomor [?7h[?12l[?25h[?25l[?7ldense_module +ordinae_vectordense_module  +ordinates dimension  +degee irect_sum +denomor iscrminant[?7h[?12l[?25h[?25l[?7lump +dense_module ump  +dimension ups  +irect_sumechlon_coordinate_vector +iscrminantechelon_coordinates[?7h[?12l[?25h[?25l[?7lechelon_form +ump echelon_form +ups echelon_to_user_matrix +echlon_coordinate_vectorized_basis  +echelon_coordinatesized_basis_matrix[?7h[?12l[?25h[?25l[?7llementclass +echelon_formlementclass +echelon_to_user_matrixndomrphism_ring  +ized_basis first  +ized_basis_matrixfre_module [?7h[?12l[?25h[?25l[?7lfre_resoution +lementclassfre_resoution +ndomrphism_ring from_vector  +first gen  +fre_module gens [?7h[?12l[?25h[?25l[?7lgensdict +fre_resoutiongensdict  +from_vector gensdi_ecursive +gen t_action +gens raded_free_resolution[?7h[?12l[?25h[?25l[?7lrammatrix +gensdict rammatrix +gensdi_ecursivehas_coerce_map_from +t_actionhasuser_basis +raded_free_resolutionhom [?7h[?12l[?25h[?25l[?7lindex_in +rammatrixindex_in  +has_coerce_map_fromindex_in_saturatin +hasuser_basisinject_variables +hom inner_product_matrix[?7h[?12l[?25h[?25l[?7ltrsection +index_in trsection +index_in_saturatinvariat_module  +inject_variabless_ambient  +inner_product_matrixs_dense [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: V1.intersection(V2) +[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 5 over Finite Field of size 2 +Basis matrix: +[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 1 0 0] +[0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV1.intersection(V2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = (A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: W1 = (A1 - I).image() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW1 = (A1 - I).image()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: W2 = (A2 - I).image() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW2 = (A2 - I).image()[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lW[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: W1.intersection(W2) +[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 1 over Finite Field of size 2 +Basis matrix: +[0 0 0 0 0 0 0 1 0 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 1))[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1 - I[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l305.valuation(5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1 - I[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1, 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: A3 = matrix([[1, 1], [0, 0]]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 = matrix([[1, 1], [0, 0]])[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: A3 +[?7h[?12l[?25h[?2004l[?7h[1 1] +[0 0] +[?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[?7lA3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A3.image() +[?7h[?12l[?25h[?2004l[?7hFree module of degree 2 and rank 1 over Integer Ring +Echelon basis matrix: +[1 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW1.intersection(W2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = (A1 - I).image()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(A1 - I).image()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltimage()[?7h[?12l[?25h[?25l[?7lrimage()[?7h[?12l[?25h[?25l[?7laimage()[?7h[?12l[?25h[?25l[?7lnimage()[?7h[?12l[?25h[?25l[?7lsimage()[?7h[?12l[?25h[?25l[?7lpimage()[?7h[?12l[?25h[?25l[?7loimage()[?7h[?12l[?25h[?25l[?7lsimage()[?7h[?12l[?25h[?25l[?7leimage()[?7h[?12l[?25h[?25l[?7l(image()[?7h[?12l[?25h[?25l[?7l()image()[?7h[?12l[?25h[?25l[?7l().image()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: W1 = (A1 - I).transpose().image() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW1 = (A1 - I).transpose().image()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l- I).transpose().image()[?7h[?12l[?25h[?25l[?7l- I).transpose().image()[?7h[?12l[?25h[?25l[?7l2- I).transpose().image()[?7h[?12l[?25h[?25l[?7l - I).transpose().image()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: W2 = (A2 - I).transpose().image() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW2 = (A2 - I).transpose().image()[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7l.intersection(W2)[?7h[?12l[?25h[?25l[?7lintersection(W2)[?7h[?12l[?25h[?25l[?7lsage: W1.intersection(W2) +[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 1 over Finite Field of size 2 +Basis matrix: +[1 0 0 0 0 0 0 0 0 0] +[?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(B[-3].group_action([1, 0]) - B[-3]).coordinates()[?7h[?12l[?25h[?25l[?7lA  A1 - C1.y).diffn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (A1 - I).transpose().image() +[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 4 over Finite Field of size 2 +Basis matrix: +[1 0 0 0 0 0 0 0 0 0] +[0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 1 0 1 0 0 0] +[0 0 0 0 0 1 0 0 0 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 1))[?7h[?12l[?25h[?25l[?7l110[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lF10*[0])[?7h[?12l[?25h[?25l[?7lD10*[0])[?7h[?12l[?25h[?25l[?7l10*[0])[?7h[?12l[?25h[?25l[?7l10*[0])[?7h[?12l[?25h[?25l[?7lG10*[0])[?7h[?12l[?25h[?25l[?7lF10*[0])[?7h[?12l[?25h[?25l[?7l(10*[0])[?7h[?12l[?25h[?25l[?7l210*[0])[?7h[?12l[?25h[?25l[?7l()10*[0])[?7h[?12l[?25h[?25l[?7l(),10*[0])[?7h[?12l[?25h[?25l[?7l 10*[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: v1 = vector(GF(2), 10*[0]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1 = vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7l2(2, 0))[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lvector((2, 0))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1 = vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l()10*[0][?7h[?12l[?25h[?25l[?7l(10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0*[0][?7h[?12l[?25h[?25l[?7l20*[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: v1 = 20*[0] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1 = 20*[0][?7h[?12l[?25h[?25l[?7l2vector((2, 0))[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbase_ring(parent(x))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1 = 20*[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: v = 20*[0] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = 20*[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l+][?7h[?12l[?25h[?25l[?7l4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: v[10+4] = 1 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[10+4] = 1[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+4] = 1[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: v[10+6] = 1 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[10+6] = 1[?7h[?12l[?25h[?25l[?7lsage: v +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3.image()[?7h[?12l[?25h[?25l[?7l1 - I[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbase_ring(parent(x))[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: block_matrix([A1, A2]) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [44], line 1 +----> 1 block_matrix([A1, A2]) + +File /ext/sage/9.8/src/sage/matrix/special.py:2005, in block_matrix(*args, **kwds) + 2003 if nrows is None: + 2004 if ncols is None: +-> 2005 raise ValueError("must specify either nrows or ncols") + 2006 else: + 2007 nrows = n // ncols + +ValueError: must specify either nrows or ncols +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lblock_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[A1, A2]])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: block_matrix([[A1, A2]]) +[?7h[?12l[?25h[?2004l[?7h[1 0 1 0 0 0 0 0 0 0|1 1 0 0 0 0 0 0 1 0] +[0 1 0 0 0 0 0 0 0 0|0 1 0 0 0 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0|0 0 1 0 0 0 0 0 0 0] +[0 1 0 1 0 0 0 0 0 1|0 0 0 1 0 0 0 1 0 0] +[0 0 0 0 1 0 0 0 1 0|0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 1 0 1 0 0|0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 1 0 1 0|0 0 0 0 0 0 1 1 0 0] +[0 0 0 0 0 0 0 1 0 0|0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0|0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 1|0 0 0 0 0 0 0 0 0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lblock_matrix([[A1, A2]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAblock_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l3block_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l block_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l=block_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l block_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3 = block_matrix([[A1, A2]]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 = block_matrix([[A1, A2]])[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: A3 * vector(10*[0]) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [47], line 1 +----> 1 A3 * vector(Integer(10)*[Integer(0)]) + +File /ext/sage/9.8/src/sage/structure/element.pyx:3920, in sage.structure.element.Matrix.__mul__() + 3918 + 3919 if BOTH_ARE_ELEMENT(cl): +-> 3920 return coercion_model.bin_op(left, right, mul) + 3921 + 3922 cdef long value + +File /ext/sage/9.8/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1246 # We should really include the underlying error. + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + 1250 cpdef canonical_coercion(self, x, y): + +TypeError: unsupported operand parent(s) for *: 'Full MatrixSpace of 10 by 20 dense matrices over Finite Field of size 2' and 'Ambient free module of rank 10 over the principal ideal domain Integer Ring' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 * vector(10*[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lG10*[0])[?7h[?12l[?25h[?25l[?7lF10*[0])[?7h[?12l[?25h[?25l[?7l(10*[0])[?7h[?12l[?25h[?25l[?7l210*[0])[?7h[?12l[?25h[?25l[?7l()10*[0])[?7h[?12l[?25h[?25l[?7l(),10*[0])[?7h[?12l[?25h[?25l[?7l 10*[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3 * vector(GF(2), 10*[0]) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [48], line 1 +----> 1 A3 * vector(GF(Integer(2)), Integer(10)*[Integer(0)]) + +File /ext/sage/9.8/src/sage/structure/element.pyx:3920, in sage.structure.element.Matrix.__mul__() + 3918 + 3919 if BOTH_ARE_ELEMENT(cl): +-> 3920 return coercion_model.bin_op(left, right, mul) + 3921 + 3922 cdef long value + +File /ext/sage/9.8/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1246 # We should really include the underlying error. + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + 1250 cpdef canonical_coercion(self, x, y): + +TypeError: unsupported operand parent(s) for *: 'Full MatrixSpace of 10 by 20 dense matrices over Finite Field of size 2' and 'Vector space of dimension 10 over Finite Field of size 2' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 * vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7l10*[0])[?7h[?12l[?25h[?25l[?7l=block_matrix([[A1, A2]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[], A2])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[A2])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3 = block_matrix([[A1], [A2]]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 = block_matrix([[A1], [A2]])[?7h[?12l[?25h[?25l[?7l*vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7lsage: A3 * vector(GF(2), 10*[0]) +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lsage: v +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l = 20*[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lve[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: v = vector(GF(2), v) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 * vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.image()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lght(v)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3.solve_right(v) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [53], line 1 +----> 1 A3.solve_right(v) + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right() + 903 + 904 if not self.is_square(): +--> 905 X = self._solve_right_general(C, check=check) + 906 else: + 907 try: + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general() + 1026 # Have to check that we actually solved the equation. + 1027 if self*X != B: +-> 1028 raise ValueError("matrix equation has no solutions") + 1029 return X + 1030 + +ValueError: matrix equation has no solutions +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lthis(A1, A2)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, A2) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = vector(GF(2), v)[?7h[?12l[?25h[?25l[?7lsage: v +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lmagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lA3.solve_right(v[?7h[?12l[?25h[?25l[?7lv = vecto(GF(2), v)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 * vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7l=block_matrix([[A1], [A2]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l1]])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], [A1])[?7h[?12l[?25h[?25l[?7l2], [A1])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3 = block_matrix([[A2], [A1]]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lA3 = block_matrix([[A2], [A1]])[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.solve_righ(v)[?7h[?12l[?25h[?25l[?7lsolve_right(v)[?7h[?12l[?25h[?25l[?7lsage: A3.solve_right(v) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [57], line 1 +----> 1 A3.solve_right(v) + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right() + 903 + 904 if not self.is_square(): +--> 905 X = self._solve_right_general(C, check=check) + 906 else: + 907 try: + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general() + 1026 # Have to check that we actually solved the equation. + 1027 if self*X != B: +-> 1028 raise ValueError("matrix equation has no solutions") + 1029 return X + 1030 + +ValueError: matrix equation has no solutions +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3.solve_right(v)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: A3 +[?7h[?12l[?25h[?2004l[?7h20 x 10 dense matrix over Finite Field of size 2 (use the '.str()' method to see the entries) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3[?7h[?12l[?25h[?25l[?7l.solve_right(v)[?7h[?12l[?25h[?25l[?7l = block_marix([[A2], [A1]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l ], [A1])[?7h[?12l[?25h[?25l[?7l-], [A1])[?7h[?12l[?25h[?25l[?7l ], [A1])[?7h[?12l[?25h[?25l[?7lI], [A1])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l_]])[?7h[?12l[?25h[?25l[?7lI]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7l-]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7lI]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3 = block_matrix([[A2 - I], [A1 - I]]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 = block_matrix([[A2 - I], [A1 - I]])[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.solve_righ(v)[?7h[?12l[?25h[?25l[?7lsolve_right(v)[?7h[?12l[?25h[?25l[?7lsage: A3.solve_right(v) +[?7h[?12l[?25h[?2004l[?7h(0, 1, 0, 0, 0, 0, 0, 0, 1, 1) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef te(m, M):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + + +[1 1 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 1 0 0 0 1 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 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 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] +Vector space of degree 10 and dimension 1 over Finite Field of size 2 +Basis matrix: +[0 0 0 0 0 0 0 1 0 0] +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [61], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :65 + +NameError: name 'solve_right' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 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 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^2) * dx, z0/x^2 ), ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), ( (x^2*z0 + z1) * dx, z0*z1/x^4 )] +Vector space of degree 16 and dimension 2 over Finite Field of size 2 +Basis matrix: +[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) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e1 = W.basis()[1] +....: A3 = block_matrix([[A1 - I], [A2 - I]]) +....: e = n*[0] + list(e1) +....: e = vector(GF(2), e) +....: print(A3.solve_right(e))[?7h[?12l[?25h[?25l[?7lsage: e1 = W.basis()[1] +....: A3 = block_matrix([[A1 - I], [A2 - I]]) +....: e = n*[0] + list(e1) +....: e = vector(GF(2), e) +....: print(A3.solve_right(e)) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [63], line 5 + 3 e = n*[Integer(0)] + list(e1) + 4 e = vector(GF(Integer(2)), e) +----> 5 print(A3.solve_right(e)) + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right() + 903 + 904 if not self.is_square(): +--> 905 X = self._solve_right_general(C, check=check) + 906 else: + 907 try: + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general() + 1026 # Have to check that we actually solved the equation. + 1027 if self*X != B: +-> 1028 raise ValueError("matrix equation has no solutions") + 1029 return X + 1030 + +ValueError: matrix equation has no solutions +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lthis(A1, A2)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, A2) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e1 = W.basis()[0] +....: A3 = block_matrix([[A1 - I], [A2 - I]]) +....: e = n*[0] + list(e1) +....: e = vector(GF(2), e) +....: print(A3.solve_right(e))[?7h[?12l[?25h[?25l[?7lsage: e1 = W.basis()[0] +....: A3 = block_matrix([[A1 - I], [A2 - I]]) +....: e = n*[0] + list(e1) +....: e = vector(GF(2), e) +....: print(A3.solve_right(e)) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [65], line 5 + 3 e = n*[Integer(0)] + list(e1) + 4 e = vector(GF(Integer(2)), e) +----> 5 print(A3.solve_right(e)) + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right() + 903 + 904 if not self.is_square(): +--> 905 X = self._solve_right_general(C, check=check) + 906 else: + 907 try: + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general() + 1026 # Have to check that we actually solved the equation. + 1027 if self*X != B: +-> 1028 raise ValueError("matrix equation has no solutions") + 1029 return X + 1030 + +ValueError: matrix equation has no solutions +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + + +[1 1 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 1 0 0 0 1 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 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 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] +Vector space of degree 10 and dimension 1 over Finite Field of size 2 +Basis matrix: +[0 0 0 0 0 0 0 1 0 0] +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [66], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :65 + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right() + 903 + 904 if not self.is_square(): +--> 905 X = self._solve_right_general(C, check=check) + 906 else: + 907 try: + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general() + 1026 # Have to check that we actually solved the equation. + 1027 if self*X != B: +-> 1028 raise ValueError("matrix equation has no solutions") + 1029 return X + 1030 + +ValueError: matrix equation has no solutions +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le = vector(GF(2), e)[?7h[?12l[?25h[?25l[?7l1 = W.basis()[0][?7h[?12l[?25h[?25l[?7lsage: e1 +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV1.intersection(V2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lintersection(V2)[?7h[?12l[?25h[?25l[?7lsage: V1.intersection(V2) +[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 1 over Finite Field of size 2 +Basis matrix: +[0 0 0 0 0 0 0 1 0 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (x*z0 + z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^3*z0 + x*z1) * dx, z0*z1/x ), + ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), + ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + + +[1 1 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 1 0 0 0 1 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 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 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] +Vector space of degree 10 and dimension 1 over Finite Field of size 2 +Basis matrix: +[1 0 0 0 0 0 0 0 0 0] +(0, 1, 0, 0, 0, 0, 0, 0, 0, 1) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: V1 = (A1 - I).transpose().image() +....: V2 = (A2 - I).transpose().image() +....: W1 = (A1 - I).transpose().kernel() +....: W2 = (A2 - I).transpose().kernel() +....: W = V1.intersection(V2) +....: W = W.intersection(W1) +....: W = W.intersection(W2) +....: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(GF(2), e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(GF(2), e) +....:  e3 = A3.solve_right(e) +....:  print(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l....:  print(e1, e2, e3) +....: [?7h[?12l[?25h[?25l[?7lsage: V1 = (A1 - I).transpose().image() +....: V2 = (A2 - I).transpose().image() +....: W1 = (A1 - I).transpose().kernel() +....: W2 = (A2 - I).transpose().kernel() +....: W = V1.intersection(V2) +....: W = W.intersection(W1) +....: W = W.intersection(W2) +....: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(GF(2), e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(GF(2), e) +....:  e3 = A3.solve_right(e) +....:  print(e1, e2, e3) +....:  +[?7h[?12l[?25h[?2004l(1, 0, 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) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 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 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^2) * dx, z0/x^2 ), ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), ( (x^2*z0 + z1) * dx, z0*z1/x^4 )] +(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def from_coor(coor, B): +....:  result = coor[0]*B[0] +....:  for i in range(1, len(coor)): +....:  result += coor[i]*B[i] +....:  return result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l....:  return resut +....: [?7h[?12l[?25h[?25l[?7lsage: def from_coor(coor, B): +....:  result = coor[0]*B[0] +....:  for i in range(1, len(coor)): +....:  result += coor[i]*B[i] +....:  return resut +....:  +[?7h[?12l[?25h[?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[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 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 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0, 0, 0, 1, 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, 1) (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^4 ) ( (x*z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-2].group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2*z0 + x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^5) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), + ( (x^4) * dx, z1/x^2 ), + ( (x^2) * dx, z0/x^2 ), + ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), + ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), + ( (x^2*z0 + z1) * dx, z0*z1/x^4 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 1 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 1 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 1 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 1 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 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 0 0 0 0 0 0 0 0 0 1 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 1 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 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^4 ) ( (z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^7 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (x^2*z0 + z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^5) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^5*z0 + x*z1) * dx, z0*z1/x ), + ( (x^4) * dx, z1/x^2 ), + ( (x^4*z0 + z1) * dx, z0*z1/x^2 ), + ( (x^3*z0) * dx, z0*z1/x^3 ), + ( (x^2*z0) * dx, z0*z1/x^4 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 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 1 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 0 0 0 0 0 0 0 0 0 0 0 1 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 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 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 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 1 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^5 ) ( (z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loC.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7lmC.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7l C.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7l=C.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7l C.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = (C.z[0]*C.z[1]/C.x^5).diffn() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.z[0]*C.z[1]/C.x^5).diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om +[?7h[?12l[?25h[?2004l[?7h((x^9*z0 + x^3*z1 + z0*z1)/x^6) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l = (C.z[0]*C.z[1]/C.x^5).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l6).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lsage: om = (C.z[0]*C.z[1]/C.x^6) * C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.z[0]*C.z[1]/C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7luation[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.valuation() +[?7h[?12l[?25h[?2004l[?7h16 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (C.z[0]*C.z[1]/C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7l= (C.z[0]*C.z[1]/C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l3) * C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l[C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7lC.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7lC.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7lC.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7lC.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = (C.z[1]/C.x^3) * C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7lsage: om.valuation() +[?7h[?12l[?25h[?2004l[?7h10 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.valuation()[?7h[?12l[?25h[?25l[?7l = (C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (x^3*z0 + z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^2*z0) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (x^7) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^7*z0 + x*z1) * dx, z0*z1/x ), + ( (x^6) * dx, z1/x^2 ), + ( (x^6*z0 + z1) * dx, z0*z1/x^2 ), + ( (x^5) * dx, z1/x^3 ), + ( (x^5*z0) * dx, z0*z1/x^3 ), + ( (x^4*z0) * dx, z0*z1/x^4 ), + ( (x^3*z0) * dx, z0*z1/x^5 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ s + age ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ g + it push ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git push ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ g + it push ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ g + it push]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 1 0 0 0 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 1 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 1 1 0 0 0 0 0 0 0 0 0 0 1 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 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1] +[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 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 1 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 1 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 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 1 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 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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 1 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 1 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 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 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^5 ) ( (x*z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, A2) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 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 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 1 0 0 0 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 1 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 1 1 0 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 1 1 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 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 1 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 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 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 1 0 1 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 1 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 1] + + +[1 1 0 0 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 0 1 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 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 1 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 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 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 1 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 1 1 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 1 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] +[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 1 1 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 1 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^6 ) ( (x*z0) * dx, 0 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, (x*z0*z1 + z0*z1)/x^6 ) ( (x^2*z0) * dx, z0*z1/x^6 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [4], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :392, in de_rham_basis(self, threshold) + +File :380, in lift_to_de_rham(self, fct, threshold) + +ValueError: Increase threshold! +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372: +******************************************************************************** +Denominators of fraction field elements are sometimes dropped without warning. +This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. +******************************************************************************** +[ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 a 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 a 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 1 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 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 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 1 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 a 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 1 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 a 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 1 a 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 a^2 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 a^2] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 1 a] +[ 0 1 0] +[ 0 0 1], +[ 1 a^2 a^2] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 0 a] +[ 0 1 a] +[ 0 0 1], +[ 1 0 0] +[ 0 1 1] +[ 0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, ((a + 1)*z0*z1)/x^5 ) ( (x*z0) * dx, z0*z1/x^5 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, ((a + 1)*z0*z1)/x^4 ) ( (x^2*z0) * dx, z0*z1/x^4 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372: +******************************************************************************** +Denominators of fraction field elements are sometimes dropped without warning. +This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. +******************************************************************************** +[ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 a 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 a 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 1 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 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 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 1 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 a 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 1 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 a 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 1 a 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 a^2 a] +[ 0 1 0] +[ 0 0 1], +[ 1 1 a] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 a^2 1] +[ 0 1 0] +[ 0 0 1], +[ 1 a 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 a^2] +[ 0 1 1] +[ 0 0 1], +[ 1 0 1] +[ 0 1 1] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 1] +[ 0 0 1], +[ 1 0 1] +[ 0 1 a^2] +[ 0 0 1] +} +{ +[ 1 0 a^2] +[ 0 1 a] +[ 0 0 1], +[ 1 0 1] +[ 0 1 1] +[ 0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, ((a + 1)*z0*z1)/x^5 ) ( (x*z0) * dx, z0*z1/x^5 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, ((a + 1)*z0*z1)/x^4 ) ( (x^2*z0) * dx, z0*z1/x^4 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 1 0 0] +[0 1 0 0] +[0 0 1 1] +[0 0 0 1] + + +[1 0 0 0] +[0 1 0 0] +[0 0 1 0] +[0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, z1/x ), + ( (x*z0) * dx, z0*z1/x )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 1 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 1 0 0 0 0] +[0 0 0 0 1 1 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 1] + + +[1 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0] +[0 0 1 0 0 0 0 0] +[0 0 0 1 0 0 0 0] +[0 0 0 0 1 0 0 0] +[0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^3) * dx, z1/x ), + ( (x^3*z0) * dx, z0*z1/x ), + ( (x^2) * dx, z1/x^2 ), + ( (x^2*z0) * dx, z0*z1/x^2 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + + +[1 1 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 1 0 0 0 1 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 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 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^3 ) ( (z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 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 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^4 ) ( (x*z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e1 in W.basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li in [4, 6, 11, 13, 15, 16, 17]:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2*z0 + x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^5) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), + ( (x^4) * dx, z1/x^2 ), + ( (x^2) * dx, z0/x^2 ), + ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), + ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), + ( (x^2*z0 + z1) * dx, z0*z1/x^4 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e1 in W.basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li in [4, 6, 11, 13, 15, 16, 17]:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [4, 6, 11, 13, 15, 16, 17]:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l4]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l0]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l3]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l4]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l5]:[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 10, 13, 14, 15]: +....: [?7h[?12l[?25h[?25l[?7lprint(e1, e2, e3)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print() +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [4, 10, 13, 14, 15]: +....:  print() +....:  +[?7h[?12l[?25h[?2004l + + + + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [4, 10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 10, 13, 14, 15]: +....: [?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lis_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7l(M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [4, 10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 10, 13, 14, 15]: +....: [?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lis_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7l(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l....:  print(is_M32(B[i], BB)) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [4, 10, 13, 14, 15]: +....:  print(is_M32(B[i], BB)) +....:  +[?7h[?12l[?25h[?2004lTrue +True +True +False +True +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  print(e1, e2, e3) +....:  print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B))[?7h[?12l[?25h[?25l[?7l....:  print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B)) +....: [?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  print(e1, e2, e3) +....:  print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B)) +....:  +[?7h[?12l[?25h[?2004l(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0, 0, 0, 1, 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, 1) (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^4 ) ( (x*z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lspan(v1, v2)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  print(e1, e2, e3) +....:  print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B))[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l[] +()[?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7li in [4, 10, 13, 14, 15]: +print(is_M32(B[], BB)) +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7l[] +()[?7h[?12l[?25h[?25l[?7l[] +()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7l10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7l10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lis)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lB))[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7li))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [10, 13, 14, 15]: +....:  print(gene(B[i])) +....:  +[?7h[?12l[?25h[?2004l( (x^3) * dx, z0/x ) ( (x^5) * dx, z1/x ) +None +( (x^2) * dx, z0/x^2 ) ( (x^4) * dx, z1/x^2 ) +None +( (0) * dx, z0/x^3 ) ( (x^3 + x^2) * dx, z1/x^3 ) +None +( (1) * dx, z0/x^4 ) ( (x^2) * dx, z1/x^4 ) +None +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7lfC.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7lfC.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l=C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]/C.x^3 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lluation()[?7h[?12l[?25h[?25l[?7lsage: fff.valuation() +[?7h[?12l[?25h[?2004l[?7h2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 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 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^4 ) ( (x*z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^2*z0 + x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^5) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), + ( (x^4) * dx, z1/x^2 ), + ( (x^2) * dx, z0/x^2 ), + ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), + ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), + ( (x^2*z0 + z1) * dx, z0*z1/x^4 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 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 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 1 0 0 0 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 1 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 1 1 0 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 1 1 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 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 1 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 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 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 1 0 1 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 1 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 1] + + +[1 1 0 0 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 0 1 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 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 1 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 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 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 1 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 1 1 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 1 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] +[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 1 1 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 1 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^6 ) ( (x*z0) * dx, 0 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, (x*z0*z1 + z0*z1)/x^6 ) ( (x^2*z0) * dx, z0*z1/x^6 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 1 0 0 0 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 1 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 1 1 0 0 0 0 0 0 0 0 0 0 1 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 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1] +[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 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 1 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 1 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 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 1 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 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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 1 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 1 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 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 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^5 ) ( (x*z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [5], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :392, in de_rham_basis(self, threshold) + +File :380, in lift_to_de_rham(self, fct, threshold) + +ValueError: Increase threshold! +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 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 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 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 1 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 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 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 1 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 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 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 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 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 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 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 1 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 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 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 1 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 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 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 1 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 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 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 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 1] + + +[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 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 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 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 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 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 1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 0] +[1 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 ) +( (x^3) * dx, 0 ) ( (x^3*z1) * dx, (x*z0*z1 + z0*z1)/x^7 ) ( (x^3*z0) * dx, z0*z1/x^7 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7lsage: B\ +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3*z0 + x^2*z1) * dx, 0 ), + ( (x^2*z0) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^4*z0 + x^3*z1) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (x^5) * dx, 0 ), + ( (x^6) * dx, 0 ), + ( (x^9) * dx, z1/x ), + ( (x^7) * dx, z0/x ), + ( (x^9*z0 + x^8 + x^7*z1) * dx, z0*z1/x ), + ( (x^8) * dx, z1/x^2 ), + ( (x^6) * dx, z0/x^2 ), + ( (x^8*z0 + x^6*z1) * dx, z0*z1/x^2 ), + ( (x^7) * dx, z1/x^3 ), + ( (0) * dx, z0/x^3 ), + ( (x^7*z0 + x^5*z1) * dx, z0*z1/x^3 ), + ( (x^4) * dx, z0/x^4 ), + ( (x^6*z0 + x^4*z1) * dx, z0*z1/x^4 ), + ( (x^5*z0 + x^4*z0) * dx, z0*z1/x^5 ), + ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^6 ), + ( (x^3*z0) * dx, z0*z1/x^7 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.valuation()[?7h[?12l[?25h[?25l[?7lfor i in [10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lin [10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l7]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l0]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l6]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l9]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l4]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l5]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l6]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l7]:[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]: +....: [?7h[?12l[?25h[?25l[?7lprint(gene(B[i]))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lis_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7l(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l....:  print(is_M32(B[i], BB)) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]: +....:  print(is_M32(B[i], BB)) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [8], line 2 + 1 for i in [Integer(7), Integer(10), Integer(16), Integer(19), Integer(22), Integer(24), Integer(25), Integer(26), Integer(27)]: +----> 2 print(is_M32(B[i], BB)) + +NameError: name 'BB' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB\[?7h[?12l[?25h[?25l[?7lOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]: +....:  print(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l....:  print(is_M32(B[i], BB)) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]: +....:  print(is_M32(B[i], BB)) +....:  +[?7h[?12l[?25h[?2004lTrue +True +True +True +True +True +False +True +False +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^9 +z1^2 - z1 = x^11 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  #print(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(e1, e2, e3) +....: [?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  print(e1, e2, e3) +....:  +[?7h[?12l[?25h[?2004l(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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1) (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: Z = [] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  #print(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l....:  Z += [e1, e2, e3] +....: [?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  Z += [e1, e2, e3] +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ = [][?7h[?12l[?25h[?25l[?7lsage: Z +[?7h[?12l[?25h[?2004l[?7h[(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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), + (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus() +[?7h[?12l[?25h[?2004l[?7h14 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llZ[0][?7h[?12l[?25h[?25l[?7leZ[0][?7h[?12l[?25h[?25l[?7lnZ[0][?7h[?12l[?25h[?25l[?7llen(Z[0][?7h[?12l[?25h[?25l[?7l()Z[0][?7h[?12l[?25h[?25l[?7l(Z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: len(Z[0]) +[?7h[?12l[?25h[?2004l[?7h28 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV2 = (A2 - I).transpose().image()[?7h[?12l[?25h[?25l[?7l = QQ^[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: V=F^28 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV=F^28[?7h[?12l[?25h[?25l[?7l.linear_dependence([v1, v3])[?7h[?12l[?25h[?25l[?7lsage: V.linear_dependence([v1, v3]) + V.CartesianProduct V.algebra V.annihilator V.base_extend V.basis_matrix   + V.Element V.ambient_module V.annihilator_basis V.base_field V.cardinality   + V.Hom V.ambient_vector_space V.are_linearly_dependent V.base_ring V.cartesian_product > + V.addition_table V.an_element V.base V.basis V.categories   + [?7h[?12l[?25h[?25l[?7lCartesianProduct + V.CartesianProduct  + + + + [?7h[?12l[?25h[?25l[?7lalgebra + V.CartesianProduct  V.algebra [?7h[?12l[?25h[?25l[?7lnnihilator + V.algebra  V.annihilator [?7h[?12l[?25h[?25l[?7lbase_extend + V.annihilator  V.base_extend [?7h[?12l[?25h[?25l[?7lis_matrix + V.base_extend  V.basis_matrix [?7h[?12l[?25h[?25l[?7lctegory + algebra nnihilatorbase_extendis_matrixctegory  + ambi_modulennhilatr_basisbase_field crdinalityhange_rng +<ambient_vector_spacere_linearly_dependntbase_ring crtesan_productodimension  + n_elemen bas isctegoriesoerce [?7h[?12l[?25h[?25l[?7loerce_embedding +nnihilatorbase_extendis_matrixctegory oerce_embedding +nnhilatr_basisbase_field crdinalityhange_rngoercmap_from +re_linearly_dependntbase_ring crtesan_productodimension mplment  +bas isctegoriesoerce nstruction[?7h[?12l[?25h[?25l[?7lnvert_ap_from +base_extendis_matrixctegory oerce_embeddingnvert_ap_from +base_field crdinalityhange_rngoercmap_fromodinatemodule +base_ring crtesan_productodimension mplment ordinate_ring +isctegoriesoerce nstructionordinae_vector[?7h[?12l[?25h[?25l[?7lordinates +is_matrixctegory oerce_embeddingnvert_ap_fromordinates  +crdinalityhange_rngoercmap_fromodinatemoduledegee  +crtesan_productodimension mplment ordinate_ringdenomor  +ctegoriesoerce nstructionordinae_vectordense_module [?7h[?12l[?25h[?25l[?7lnvert_map_from + V.convert_map_from  V.coordinates [?7h[?12l[?25h[?25l[?7l + + + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l + V.saturation V.span V.submodule_with_basis V.sum V.summation_from_element_class_add + V.save V.span_of_basis V.subspace V.sum_of_monomials  + V.scale V.sparse_module V.subspace_with_basis V.sum_of_terms  + V.some_elements V.submodule V.subspaces V.summation [?7h[?12l[?25h[?25l[?7laturation + V.saturation  + + + + [?7h[?12l[?25h[?25l[?7lpan + V.saturation  V.span [?7h[?12l[?25h[?25l[?7lubmodule_with_basis + V.span  V.submodule_with_basis [?7h[?12l[?25h[?25l[?7lspace + V.submodule_with_basis  + V.subspace [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: V.subspace(Z) +[?7h[?12l[?25h[?2004l[?7hVector space of degree 28 and dimension 12 over Finite Field of size 2 +Basis matrix: +[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 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 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 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 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 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 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 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 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 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 1 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 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.subspace(Z)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lWV.subspace(Z)[?7h[?12l[?25h[?25l[?7l V.subspace(Z)[?7h[?12l[?25h[?25l[?7l V.subspace(Z)[?7h[?12l[?25h[?25l[?7l=V.subspace(Z)[?7h[?12l[?25h[?25l[?7lV.subspace(Z)[?7h[?12l[?25h[?25l[?7lV.subspace(Z)[?7h[?12l[?25h[?25l[?7lV.subspace(Z)[?7h[?12l[?25h[?25l[?7lV.subspace(Z)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lWV.subspace(Z)[?7h[?12l[?25h[?25l[?7l V.subspace(Z)[?7h[?12l[?25h[?25l[?7l=V.subspace(Z)[?7h[?12l[?25h[?25l[?7l V.subspace(Z)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: W = V.subspace(Z) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW[?7h[?12l[?25h[?25l[?7lsage: Z[0] in W +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]: +....: ....: print(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7li])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7lj])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l=])[?7h[?12l[?25h[?25l[?7l=])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7li])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7lf])[?7h[?12l[?25h[?25l[?7lo])[?7h[?12l[?25h[?25l[?7lfor])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7lj])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7li])[?7h[?12l[?25h[?25l[?7lin])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7lr])[?7h[?12l[?25h[?25l[?7la])[?7h[?12l[?25h[?25l[?7ln])[?7h[?12l[?25h[?25l[?7lg])[?7h[?12l[?25h[?25l[?7lrange])[?7h[?12l[?25h[?25l[?7l(])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7l8])[?7h[?12l[?25h[?25l[?7l)])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpvector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7lrvector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7livector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7lnvector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7ltvector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7lprint(vector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7livector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7l,vector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7l vector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....: ....: print(i, vector([j == i for j in range(28)]) in W) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]: +....: ....: print(i, vector([j == i for j in range(28)]) in W) +....:  +[?7h[?12l[?25h[?2004l7 True +10 False +16 False +19 False +22 False +24 False +25 False +26 False +27 True +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l|[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^9 +z1^2 - z1 = x^11 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [7, 10, 16, 19, 22, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7lff.valuation()[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^4[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^7 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()\[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^11*z0 + x^9*z1 + z0*z1)/x^8) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^6 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^6[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn() +[?7h[?12l[?25h[?2004l[?7h(x^4*z0 + x^2*z1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(Z[0])[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0] +[0 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 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 1 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 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 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 1 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 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 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 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1] +[0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 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 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 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 1 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 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 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 1 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 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 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 1 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 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 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 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 1] + + +[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 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 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 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 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 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 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 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 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 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 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 1 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 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 1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 ) +( (x^3) * dx, 0 ) ( (x^3*z1) * dx, (x*z0*z1 + z0*z1)/x^7 ) ( (x^3*z0) * dx, z0*z1/x^7 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3*z0 + x^2*z1) * dx, 0 ), + ( (x^2*z0) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^4*z0 + x^3*z1) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (x^5) * dx, 0 ), + ( (x^6) * dx, 0 ), + ( (x^9) * dx, z1/x ), + ( (x^7) * dx, z0/x ), + ( (x^9*z0 + x^8 + x^7*z1) * dx, z0*z1/x ), + ( (x^8 + 1) * dx, z1/x^2 ), + ( (0) * dx, z0/x^2 ), + ( (x^8*z0 + x^6*z1) * dx, z0*z1/x^2 ), + ( (x^7) * dx, z1/x^3 ), + ( (0) * dx, z0/x^3 ), + ( (x^7*z0 + x^5*z1) * dx, z0*z1/x^3 ), + ( (0) * dx, z0/x^4 ), + ( (x^6*z0 + x^4*z1) * dx, z0*z1/x^4 ), + ( (x^5*z0 + x^4*z0) * dx, z0*z1/x^5 ), + ( (x^4*z0 + x^3*z0) * dx, z0*z1/x^6 ), + ( (x^3*z0) * dx, z0*z1/x^7 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l [1 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 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 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 1 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 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 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 1 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 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 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 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 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 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 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 1 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 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 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 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 1 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 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 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 1 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 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 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 1 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 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 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 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 1] + + +[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 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 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 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 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 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 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 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 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 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 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 1 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 1 0 0 0 1 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 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 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 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 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 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 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 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 1 1 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 0] +[1 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 ) +( (x^3) * dx, 0 ) ( (x^3*z1) * dx, z0*z1/x^6 ) ( (x^3*z0) * dx, z0*z1/x^7 ) +[?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[?7lB[?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^3*z0 + x^2*z1) * dx, 0 ), + ( (x^2*z0) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^4*z0 + x^3*z0 + x^3*z1) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (x^5) * dx, 0 ), + ( (x^6) * dx, 0 ), + ( (x^9) * dx, z1/x ), + ( (x^7) * dx, z0/x ), + ( (x^9*z0 + x^8 + x^7*z1 + x^7 + x^5*z1) * dx, z0*z1/x ), + ( (x^8 + 1) * dx, z1/x^2 ), + ( (x^6 + x^4) * dx, z0/x^2 ), + ( (x^8*z0 + x^6*z1 + x^4*z1 + z0) * dx, z0*z1/x^2 ), + ( (x^7) * dx, z1/x^3 ), + ( (0) * dx, z0/x^3 ), + ( (x^7*z0 + x^5*z1 + x^4*z0 + x^3*z0) * dx, z0*z1/x^3 ), + ( (0) * dx, z1/x^4 ), + ( (x^6*z0 + x^4*z1 + x^3*z0) * dx, z0*z1/x^4 ), + ( (x^5*z0 + x^4*z0 + x^3*z0) * dx, z0*z1/x^5 ), + ( (x^4*z0 + x^3*z0) * dx, z0*z1/x^6 ), + ( (x^3*z0) * dx, z0*z1/x^7 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 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 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 1 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 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 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 1 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 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 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 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 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 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 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 1 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 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 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 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 1 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 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 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 1 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 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 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 1 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 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 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 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 1] + + +[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 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 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 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 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 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 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 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 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 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 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 1 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 1 0 0 0 1 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 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 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 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 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 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 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 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 1 1 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 0] +[1 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 ) +( (x^3) * dx, 0 ) ( (x^3*z1) * dx, z0*z1/x^6 ) ( (x^3*z0) * dx, z0*z1/x^7 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^9 + x^7 +z1^2 - z1 = x^11 + x^3 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 0 0] +[0 1 0 0] +[0 0 1 0] +[0 0 0 1] + + +[1 1 0 0] +[0 1 0 0] +[0 0 1 1] +[0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 0 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + + +[1 1 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 1 0 0 0 1 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 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 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^3 ) ( (z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 1 0 0 0 0 1 1] +[0 0 0 0 1 0 0 0 1 0] +[0 0 0 0 0 1 0 1 0 0] +[0 0 0 0 0 0 1 0 1 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] + + +[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 0 0 0 1 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 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 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^3 ) ( (z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 1 0 0 0 0 0 1 0 1] +[0 0 0 0 0 0 1 0 0 1 0 0 1 0] +[0 0 0 0 0 0 0 1 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 1 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 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 1 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 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^4 ) ( (z0) * dx, 0 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 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 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 1 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 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 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 1 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 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 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 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 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 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 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 1 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 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 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 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 1 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 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 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 1 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 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 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 1 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 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 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 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 1] + + +[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 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 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 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 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 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 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 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 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 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 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 1 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 1 0 0 0 1 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 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 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 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 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 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 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 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 1 1 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 0] +[1 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 ) +( (x^3) * dx, 0 ) ( (x^3*z1) * dx, z0*z1/x^6 ) ( (x^3*z0) * dx, z0*z1/x^7 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^6[?7h[?12l[?25h[?25l[?7l= C.z[0]*C.z[1]/C.x^6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^7 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^11*z0 + x^9*z1 + x^7*z1 + x^3*z0 + z0*z1)/x^8) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l. (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7lx (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l* (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om =C.x* (C.z[1]) * C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom =C.x* (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7lsage: om.valuation() +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^9 + x^7 +z1^2 - z1 = x^11 + x^3 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7ld_rham_basis()[?7h[?12l[?25h[?25l[?7lx.valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lsage: C.dx.valuation() +[?7h[?12l[?25h[?2004l[?7h26 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lon()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.z[1].valuation() +[?7h[?12l[?25h[?2004l[?7h-22 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  lo +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [48], line 1 +----> 1 lo + +NameError: name 'lo' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372: +******************************************************************************** +Denominators of fraction field elements are sometimes dropped without warning. +This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. +******************************************************************************** +[ 1 0 1 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 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 1 0 1 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 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 1 a + 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a] +[ 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 1 a + 1 0 0 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 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 1 0 0 0 0 0 0 0 a 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 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 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 1 0 1 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 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 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 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 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 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 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 1] + + +[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 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 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 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 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 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 0 a 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 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 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 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 1 a 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 1 a 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 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 1] +[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 1 0] +[ 0 1 0] +[ 0 0 1], +[ 1 a 1] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 a] +[ 0 0 1], +[ 1 0 a] +[ 0 1 1] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 a^2 0] +[ 0 1 0] +[ 0 0 1], +[ 1 1 a^2] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 a^2] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 a] +[ 0 0 1], +[ 1 0 a] +[ 0 1 1] +[ 0 0 1] +} +{ +[ 1 0 a^2] +[ 0 1 1] +[ 0 0 1], +[ 1 0 a] +[ 0 1 0] +[ 0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, ((a + 1)*z0*z1)/x^6 ) ( (x^2*z0) * dx, z0*z1/x^6 ) +( (x^3) * dx, 0 ) ( (x^3*z1) * dx, ((a + 1)*z0*z1)/x^5 ) ( (x^3*z0) * dx, z0*z1/x^5 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7l= C.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^5 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^5[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn() +[?7h[?12l[?25h[?2004l[?7h((a*x^9*z0 + x^9*z1 + z0*z1)/x^6) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l =C.x* (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l (C.z[1]/C.x^3)* C.dx[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l.(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7lx(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l^(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l3(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l*(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = C.x^3*(C.z[1]) * C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.x^3*(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7l.0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7laluation()[?7h[?12l[?25h[?25l[?7lsage: om.valuation() +[?7h[?12l[?25h[?2004l[?7h-8 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[1].valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (z0) * dx, + (x) * dx, + (x*z1) * dx, + (x*z0) * dx, + (x^2) * dx, + ((a + 1)*x^2*z0 + x^2*z1) * dx, + (x^3) * dx, + ((a + 1)*x^3*z0 + x^3*z1) * dx, + (x^4) * dx, + (x^5) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 1 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 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 1 0 0 0 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 1 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 1 1 0 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 1 1 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 1 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 1 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 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 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 1 0 1 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 1 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 1] + + +[1 1 0 0 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 0 1 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 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 1 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 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 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 1 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 1 1 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 1 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] +[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 1 1 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 1 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 0] +[1 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^6 ) ( (x*z0) * dx, 0 ) +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, (x*z0*z1 + z0*z1)/x^6 ) ( (x^2*z0) * dx, z0*z1/x^6 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  #print(e1, e2, e3) +....:  print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B)) +....:  print(from_coor(e1, B).omega8, from_coor(e2, B).omega8, from_coor(e3, B).omega8)[?7h[?12l[?25h[?25l[?7l....:  print(from_coor(e1, B).omega8, from_coor(e2, B).omega8, from_coor(e3, B).omega8) +....: [?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  #print(e1, e2, e3) +....:  print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B)) +....:  print(from_coor(e1, B).omega8, from_coor(e2, B).omega8, from_coor(e3, B).omega8) +....:  +[?7h[?12l[?25h[?2004l( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(1) * dx (z1) * dx (z0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^6 ) ( (x*z0) * dx, 0 ) +(x) * dx (x^2*z0 + x*z1 + z1) * dx (x*z0) * dx +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, (x*z0*z1 + z0*z1)/x^6 ) ( (x^2*z0) * dx, z0*z1/x^6 ) +(x^2) * dx ((x^9*z0 + x^8*z0 + x^8*z1 + x^7*z1 + x^6*z1 + z0*z1)/x^6) * dx (z1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: 4416 - 3842 +[?7h[?12l[?25h[?2004l[?7h574 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5+14 - 5[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: 574/12 +[?7h[?12l[?25h[?2004l[?7h287/6 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l574/12[?7h[?12l[?25h[?25l[?7l12.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 574/12.n() +[?7h[?12l[?25h[?2004l[?7h47.8333333333333 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^7 +z1^2 - z1 = x^9 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (z0) * dx, + (x) * dx, + (x^2*z0 + x*z1) * dx, + (x*z0) * dx, + (x^2) * dx, + (x^3*z0 + x^2*z1) * dx, + (x^3) * dx, + (x^4) * dx, + (x^5) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ lol ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ lolsage + ┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?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[?7llo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 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 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 1 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 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 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 1 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 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 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 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 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 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 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 1 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 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 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 1 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 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 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 1 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 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 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 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 1] + + +[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 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 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 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 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 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 1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 0] +[1 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 ) +(0) * dx ((x^11*z0 + x^9*z1 + z0*z1)/x^8) * dx (0) * dx +( (x^3) * dx, 0 ) ( (x^3*z1) * dx, (x*z0*z1 + z0*z1)/x^7 ) ( (x^3*z0) * dx, z0*z1/x^7 ) +(0) * dx ((x^12*z0 + x^11*z0 + x^10*z1 + x^9*z1 + z0*z1)/x^8) * dx ((x^11*z0 + x^9*z1 + z0*z1)/x^8) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (z0) * dx, + (x) * dx, + (x*z1) * dx, + (x*z0) * dx, + (x^2) * dx, + (x^3*z0 + x^2*z1) * dx, + (x^2*z0) * dx, + (x^3) * dx, + (x^4*z0 + x^3*z1) * dx, + (x^4) * dx, + (x^5) * dx, + (x^6) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e1 in W.basis():[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^5[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((C.x)^(-6)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[1]/C.x^7 + C.z[0]*((C.x)^(-6) + (C.x)^(-7)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[1]/C.x^7 + C.z[0]*((C.x)^(-6) + (C.x)^(-7))[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.coordinates()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lvaluation()\[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.valuation() +[?7h[?12l[?25h[?2004l[?7h10 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[1]/C.x^7 + C.z[0]*((C.x)^(-6) + (C.x)^(-7))[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[1]/C.x^7 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: ff.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372: +******************************************************************************** +Denominators of fraction field elements are sometimes dropped without warning. +This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. +******************************************************************************** +[ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 0 0 0 1 a + 1 0 0 0 0 0 0 0 0 0 a 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 a 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 1 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 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 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 1 0 0 0 0 0 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0 0 0 0 a 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 1 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 a 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 1 a 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 a^2 a] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 a] +[ 0 1 0] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a^2] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 1 a] +[ 0 1 0] +[ 0 0 1], +[ 1 a 1] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 a] +[ 0 0 1], +[ 1 0 a] +[ 0 1 1] +[ 0 0 1] +} +{ +[ 1 0 a^2] +[ 0 1 a] +[ 0 0 1], +[ 1 0 0] +[ 0 1 a^2] +[ 0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, ((a + 1)*z0*z1)/x^5 ) ( (x*z0) * dx, z0*z1/x^5 ) +(0) * dx ((x^7*z0 + (a + 1)*x^7*z1 + (a + 1)*z0*z1)/x^6) * dx ((a*x^7*z0 + x^7*z1 + z0*z1)/x^6) * dx +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, ((a + 1)*z0*z1)/x^4 ) ( (x^2*z0) * dx, z0*z1/x^4 ) +(0) * dx (x^2*z0 + (a + 1)*x^2*z1) * dx (a*x^2*z0 + x^2*z1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[ 1 0 1 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 1 0 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 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 a a + 1 1 0 0 0 0 0 0 0 0 0 a a + 1] +[ 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 a 0 0] +[ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 a + 1 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 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 1 0 1 a + 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 a 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] + + +[ 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[ 0 0 1 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 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 a + 1 1 1 0 0 0 0 0 0 0 0 0 1 1] +[ 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 1 0 0 0 0 0 0 1 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 1 1 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 a + 1 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0] +[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1] +[ +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2), +RModule of dimension 3 over GF(2^2) +] +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 0] +[ 0 1 1] +[ 0 0 1], +[ 1 0 a] +[ 0 1 a^2] +[ 0 0 1] +} +{ +[ 1 0 a^2] +[ 0 1 a] +[ 0 0 1], +[ 1 0 a] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 0 a^2] +[ 0 1 a^2] +[ 0 0 1], +[ 1 0 1] +[ 0 1 a] +[ 0 0 1] +} +{ +[ 1 0 1] +[ 0 1 0] +[ 0 0 1], +[ 1 1 0] +[ 0 1 0] +[ 0 0 1] +} +{ +[ 1 a^2 0] +[ 0 1 0] +[ 0 0 1], +[ 1 0 a^2] +[ 0 1 0] +[ 0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, ((a + 1)*z0*z1)/x^5 ) ( (x*z0) * dx, z0*z1/x^5 ) +(0) * dx ((x^7*z0 + (a + 1)*x^7*z1 + (a + 1)*x^5*z0 + (a + 1)*z0*z1)/x^6) * dx ((a*x^7*z0 + x^7*z1 + x^5*z0 + z0*z1)/x^6) * dx +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, ((a + 1)*x*z0*z1 + a*z0*z1)/x^5 ) ( (x^2*z0) * dx, (x*z0*z1 + z0*z1)/x^5 ) +(0) * dx ((x^8*z0 + (a + 1)*x^8*z1 + (a + 1)*x^7*z0 + a*x^7*z1 + (a + 1)*x^6*z0 + a*x^5*z0 + a*z0*z1)/x^6) * dx ((a*x^8*z0 + x^8*z1 + a*x^7*z0 + x^7*z1 + x^6*z0 + x^5*z0 + z0*z1)/x^6) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (z0) * dx, + (x) * dx, + (a*x^2*z0 + (a + 1)*x^2*z1 + x*z1) * dx, + ((a + 1)*x^2*z0 + x^2*z1 + x*z0) * dx, + (x^2) * dx, + (x^3) * dx, + (x^4) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372: +******************************************************************************** +Denominators of fraction field elements are sometimes dropped without warning. +This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696. +******************************************************************************** +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Cell In [1], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :64, in coordinates(self, threshold, basis) + +File :64, in (.0) + +File :131, in serre_duality_pairing(self, fct) + +File /ext/sage/9.8/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) + 583 return expression.sum(*args, **kwds) + 584 elif max(len(args),len(kwds)) <= 1: +--> 585 return sum(expression, *args, **kwds) + 586 else: + 587 from sage.symbolic.ring import SR + +File :131, in (.0) + +File :124, in residue(self, place) + +File :39, in expansion_at_infty(self, place) + +File /ext/sage/9.8/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() + 941 5 + 942 """ +--> 943 return self.subs(in_dict,**kwds) + 944 + 945 cpdef _act_on_(self, x, bint self_on_left): + +File /ext/sage/9.8/src/sage/structure/element.pyx:830, in sage.structure.element.Element.subs() + 828 if str(gen) in kwds: + 829 variables.append(kwds[str(gen)]) +--> 830 elif in_dict and gen in in_dict: + 831 variables.append(in_dict[gen]) + 832 else: + +File /ext/sage/9.8/src/sage/structure/element.pyx:1111, in sage.structure.element.Element.__richcmp__() + 1109 return (self)._richcmp_(other, op) + 1110 else: +-> 1111 return coercion_model.richcmp(self, other, op) + 1112 + 1113 cpdef _richcmp_(left, right, int op): + +File /ext/sage/9.8/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp() + 1971 # Coerce to a common parent + 1972 try: +-> 1973 x, y = self.canonical_coercion(x, y) + 1974 except (TypeError, NotImplementedError): + 1975 pass + +File /ext/sage/9.8/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion() + 1309 x_map, y_map = coercions + 1310 if x_map is not None: +-> 1311 x_elt = (x_map)._call_(x) + 1312 else: + 1313 x_elt = x + +File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.8/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 1 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 1 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 1 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 1 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 1 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 1 0 1 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 1 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 1 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 1 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 1 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 1] + + +[1 1 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 1 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 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 1 1 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 1 1 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 1 0 0 0 0 0 0 1 0 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 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 1 1 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 1 1 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 1 1 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 1 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, z0*z1/x^6 ) +(0) * dx (0) * dx ((x^8*z1 + z0)/x^4) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [3], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :392, in de_rham_basis(self, threshold) + +File :380, in lift_to_de_rham(self, fct, threshold) + +ValueError: Increase threshold! +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 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 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 1 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 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 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 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 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 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 1 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 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 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 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 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 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 1 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 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 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 1 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 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 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 1 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 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 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 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 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 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 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 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 1] + + +[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 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 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 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 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 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 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 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 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 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 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 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 0 1 0 0 0 1 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 1 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 1 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 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 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 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 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 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 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 1 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, z0*z1/x^8 ) +(0) * dx (0) * dx ((x^6*z1 + z0)/x^2) * dx +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, 0 ) ( (x^2*z0) * dx, z0*z1/x^7 ) +(0) * dx (0) * dx ((x^13*z1 + x^7*z0 + z0*z1)/x^8) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [5], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [6], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [7], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [8], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [9], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [10], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 = block_matrix([[A1 - I], [A2 - I]])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: C.x_series +[?7h[?12l[?25h[?2004l[?7h{0: t^-4 + t^10 + t^24 + t^26 + t^28 + t^33 + t^38 + t^49 + t^52 + t^54 + t^58 + t^61 + t^65 + t^66 + t^74 + t^77 + t^80 + t^81 + t^94 + t^100 + t^105 + t^107 + t^120 + t^123 + t^133 + t^137 + t^138 + t^145 + t^146 + t^150 + t^153 + t^154 + t^157 + t^164 + t^169 + t^171 + t^178 + t^179 + t^182 + t^185 + t^187 + t^193 + t^201 + t^206 + t^210 + t^212 + t^213 + t^225 + t^227 + t^228 + t^233 + t^235 + t^241 + t^242 + t^245 + t^249 + t^250 + t^255 + t^257 + t^268 + t^269 + t^271 + t^273 + t^274 + t^278 + t^283 + t^289 + t^292 + t^296 + t^297 + t^298 + t^299 + t^301 + t^304 + t^305 + t^306 + t^311 + t^312 + t^313 + t^325 + t^328 + t^329 + t^330 + t^332 + t^338 + t^339 + t^346 + t^347 + t^353 + t^354 + t^356 + t^357 + t^361 + t^362 + t^363 + t^367 + t^368 + t^369 + t^371 + t^377 + t^378 + t^379 + t^380 + t^385 + t^386 + t^390 + t^393 + O(t^396)} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [12], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x_series[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l_series[?7h[?12l[?25h[?25l[?7lsage: C.x_series +[?7h[?12l[?25h[?2004l[?7h{0: t^-4 + t^10 + t^24 + t^26 + t^28 + t^33 + t^38 + t^49 + t^52 + t^54 + t^58 + t^61 + t^65 + t^66 + t^74 + t^77 + t^80 + t^81 + t^94 + t^100 + t^105 + t^107 + t^120 + t^123 + t^133 + t^137 + t^138 + t^145 + t^146 + t^150 + t^153 + t^154 + t^157 + t^164 + t^169 + t^171 + t^178 + t^179 + t^182 + t^185 + t^187 + t^193 + t^201 + t^206 + t^210 + t^212 + t^213 + t^225 + t^227 + t^228 + t^233 + t^235 + t^241 + t^242 + t^245 + t^249 + t^250 + t^255 + t^257 + t^268 + t^269 + t^271 + t^273 + t^274 + t^278 + t^283 + t^289 + t^292 + t^296 + t^297 + t^298 + t^299 + t^301 + t^304 + t^305 + t^306 + t^311 + t^312 + t^313 + t^325 + t^328 + t^329 + t^330 + t^332 + t^338 + t^339 + t^346 + t^347 + t^353 + t^354 + t^356 + t^357 + t^361 + t^362 + t^363 + t^367 + t^368 + t^369 + t^371 + t^377 + t^378 + t^379 + t^380 + t^385 + t^386 + t^390 + t^393 + O(t^396)} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [14], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12 + +File :29, in group_action_matrices_dR(AS, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x_series[?7h[?12l[?25h[?25l[?7l.x_series[?7h[?12l[?25h[?25l[?7lsage: C.x_series +[?7h[?12l[?25h[?2004l[?7h{0: t^-4 + t^10 + t^24 + t^26 + t^28 + t^33 + t^38 + t^49 + t^52 + t^54 + t^58 + t^61 + t^65 + t^66 + t^74 + t^77 + t^80 + t^81 + t^94 + t^100 + t^105 + t^107 + t^120 + t^123 + t^133 + t^137 + t^138 + t^145 + t^146 + t^150 + t^153 + t^154 + t^157 + t^164 + t^169 + t^171 + t^178 + t^179 + t^182 + t^185 + t^187 + t^193 + t^201 + t^206 + t^210 + t^212 + t^213 + t^225 + t^227 + t^228 + t^233 + t^235 + t^241 + t^242 + t^245 + t^249 + t^250 + t^255 + t^257 + t^268 + t^269 + t^271 + t^273 + t^274 + t^278 + t^283 + t^289 + t^292 + t^296 + t^297 + t^298 + t^299 + t^301 + t^304 + t^305 + t^306 + t^311 + t^312 + t^313 + t^325 + t^328 + t^329 + t^330 + t^332 + t^338 + t^339 + t^346 + t^347 + t^353 + t^354 + t^356 + t^357 + t^361 + t^362 + t^363 + t^367 + t^368 + t^369 + t^371 + t^377 + t^378 + t^379 + t^380 + t^385 + t^386 + t^390 + t^393 + O(t^396)} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x_series[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: C.prec +[?7h[?12l[?25h[?2004l[?7h700 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] + + +[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 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 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 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 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 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 1 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 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1] +[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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, z0*z1/x^7 ) +(0) * dx (0) * dx ((x^13*z1 + x^5*z0 + z0*z1)/x^8) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] + + +[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 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 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 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 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 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 1 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 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1] +[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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, z0*z1/x^7 ) +(0) * dx (0) * dx ((x^13*z1 + x^5*z0 + z0*z1)/x^8) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] + + +[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 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 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 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 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 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 1 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 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1] +[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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, z0*z1/x^7 ) +(0) * dx (0) * dx ((x^13*z1 + x^5*z0 + z0*z1)/x^8) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  #print(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(e1, e2, e3) +....: [?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis(): +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1) +....:  e = vector(F, e) +....:  e2 = A3.solve_right(e) +....:  e = list(e1) + n*[0] +....:  e = vector(F, e) +....:  e3 = A3.solve_right(e) +....:  print(e1, e2, e3) +....:  +[?7h[?12l[?25h[?2004l(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, 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, 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, 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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.prec[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.valuation()[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x*z1) * dx, 0 ), + ( (x^5*z1 + x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^2*z1) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^3*z1) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (x^4*z1) * dx, 0 ), + ( (x^5) * dx, 0 ), + ( (x^6) * dx, 0 ), + ( (0) * dx, z1/x ), + ( (x^11) * dx, z0/x ), + ( (x^11*z1 + x^7 + x^3*z0) * dx, z0*z1/x ), + ( (x^2) * dx, z1/x^2 ), + ( (x^10) * dx, z0/x^2 ), + ( (x^10*z1 + x^2*z0) * dx, z0*z1/x^2 ), + ( (x^9) * dx, z0/x^3 ), + ( (x^9*z1 + x^5*z1) * dx, z0*z1/x^3 ), + ( (x^8) * dx, z0/x^4 ), + ( (x^8*z1 + z0) * dx, z0*z1/x^4 ), + ( (x^7) * dx, z0/x^5 ), + ( (x^7*z1) * dx, z0*z1/x^5 ), + ( (x^6*z1) * dx, z0*z1/x^6 ), + ( (x^5*z1) * dx, z0*z1/x^7 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e1 in W.basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l e1 in W.basis():[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e1 in W.basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li in [7, 10, 16, 19, 22, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lin [7, 10, 16, 19, 22, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l5 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l, 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l1, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l3, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]: +....: [?7h[?12l[?25h[?25l[?7lprint(e1, e2, e3)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lis_M3(B[i], BB))[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7l(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l....:  print(is_M32(B[i], BB)) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]: +....:  print(is_M32(B[i], BB)) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [8], line 2 + 1 for i in [Integer(5), Integer(16), Integer(19), Integer(21), Integer(23), Integer(25), Integer(26), Integer(27)]: +----> 2 print(is_M32(B[i], BB)) + +File :27, in is_M32(x, B) + +File :54, in coordinates(self, threshold, basis) + +File :392, in de_rham_basis(self, threshold) + +File :380, in lift_to_de_rham(self, fct, threshold) + +ValueError: Increase threshold! +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  n = len(x.coordinates(basis = B, threshold = 20)) +....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  y1_coor = y1.coordinates(basis = B, threshold = 20) +....:  if y1_coor == vector(n*[0]): +....:  return False +....:  if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio n +....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  y2_coor = y2.coordinates() +....:  if y2_coor == vector(n*[0]): +....:  return False +....:  if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio n +....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence([y1_coor, y2_coor])) > 0: +....:  return False +....:  return True[?7h[?12l[?25h[?25l[?7lFx.curve.base_ring +y1 = x - x.groupaction([0, 1]) +_coor = y1.coordinates(basis = B, threshold = 20) +if y1_coor == vector(n*[0]): +  returnFalse +if(y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio n +([1, 0]) - y1).coordnates(basis = B, threshold = 20) != vector(n*[0]): +  return False +y2= x - x.group_action([1, 0]) +_coor = y2.coordinates() +if y2_coor == vector(n*[0]): +  returnFalse +if(y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio n +([1, 0]) - y2).coordnates(basis = B, threshold = 20) != vector(n*[0]): +  return False +V=F^n +if len(V.linear_dependence([y1_coor, y2_coor])) > 0: +  return False +retun True +[?7h[?12l[?25h[?25l[?7l....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  y1_coor = y1.coordinates(basis = B, threshold = 20) +....:  if y1_coor == vector(n*[0]): +....:  return False +....:  if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio n +....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  y2_coor = y2.coordinates() +....:  if y2_coor == vector(n*[0]): +....:  return False +....:  if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio n +....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence([y1_coor, y2_coor])) > 0: +....:  return False +....:  return True +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  n = len(x.coordinates(basis = B, threshold = 20)) +....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  y1_coor = y1.coordinates(basis = B, threshold = 20) +....:  if y1_coor == vector(n*[0]): +....:  return False +....:  if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio n +....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  y2_coor = y2.coordinates() +....:  if y2_coor == vector(n*[0]): +....:  return False +....:  if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio n +....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence([y1_coor, y2_coor])) > 0: +....:  return False +....:  return True[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: defis_M32(x, B): +nlen(x.coordinates(basis = B, threshold = 20)) +F = x.curve.basering + = x - x.group_action([0, 1]) +y1_coor = y1.coordinates(basis = B, threshold = 20) +ify1_coor== vector(n*[0]): +  return False + if (y1.group_acton([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio n +([1,0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]): +  return False + = x - x.group_action([1, 0]) +y2_coor = y2.coordinates() +ify2_coor== vector(n*[0]): +  return False + if (y2.group_acton([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio n +([1,0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]): +  return False +V = F^n +iflen(V.linear_dependence([y1_coor, y2_coor])) > 0: + eturn False[?7h[?12l[?25h[?25l[?7lfori in [5, 16, 19, 21, 23, 25, 26, 27]: +print(is_M32(B[], BB)) +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]: +....:  print(is_M32(B[i], BB)) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [10], line 2 + 1 for i in [Integer(5), Integer(16), Integer(19), Integer(21), Integer(23), Integer(25), Integer(26), Integer(27)]: +----> 2 print(is_M32(B[i], BB)) + +Cell In [9], line 11, in is_M32(x, B) + 9 return False + 10 y2 = x - x.group_action([Integer(1), Integer(0)]) +---> 11 y2_coor = y2.coordinates() + 12 if y2_coor == vector(n*[Integer(0)]): + 13 return False + +File :54, in coordinates(self, threshold, basis) + +File :392, in de_rham_basis(self, threshold) + +File :380, in lift_to_de_rham(self, fct, threshold) + +ValueError: Increase threshold! +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  n = len(x.coordinates(basis = B, threshold = 20)) +....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  y1_coor = y1.coordinates(basis = B, threshold = 20) +....:  if y1_coor == vector(n*[0]): +....:  return False +....:  if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio n +....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  y2_coor = y2.coordinates(basis = B, threshold = 20) +....:  if y2_coor == vector(n*[0]): +....:  return False +....:  if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio n +....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence([y1_coor, y2_coor])) > 0: +....:  return False +....:  return True[?7h[?12l[?25h[?25l[?7lFx.curve.base_ring +y1 = x - x.groupaction([0, 1]) +_coor = y1.coordinates(basis = B, threshold = 20) +if y1_coor == vector(n*[0]): +  returnFalse +if(y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio n +([1, 0]) - y1).coordnates(basis = B, threshold = 20) != vector(n*[0]): +  return False +y2= x - x.group_action([1, 0]) +_coor = y2.coordinates(basis = B, threshold = 20) +if y2_coor == vector(n*[0]): +  returnFalse +if(y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio n +([1, 0]) - y2).coordnates(basis = B, threshold = 20) != vector(n*[0]): +  return False +V=F^n +if len(V.linear_dependence([y1_coor, y2_coor])) > 0: +  return False +retun True +[?7h[?12l[?25h[?25l[?7l....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  y1_coor = y1.coordinates(basis = B, threshold = 20) +....:  if y1_coor == vector(n*[0]): +....:  return False +....:  if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio n +....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  y2_coor = y2.coordinates(basis = B, threshold = 20) +....:  if y2_coor == vector(n*[0]): +....:  return False +....:  if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio n +....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence([y1_coor, y2_coor])) > 0: +....:  return False +....:  return True +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  n = len(x.coordinates(basis = B, threshold = 20)) +....:  F = x.curve.base_ring +....:  y1 = x - x.group_action([0, 1]) +....:  y1_coor = y1.coordinates(basis = B, threshold = 20) +....:  if y1_coor == vector(n*[0]): +....:  return False +....:  if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio n +....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  y2 = x - x.group_action([1, 0]) +....:  y2_coor = y2.coordinates(basis = B, threshold = 20) +....:  if y2_coor == vector(n*[0]): +....:  return False +....:  if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio n +....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]): +....:  return False +....:  V = F^n +....:  if len(V.linear_dependence([y1_coor, y2_coor])) > 0: +....:  return False +....:  return True[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: defis_M32(x, B): +nlen(x.coordinates(basis = B, threshold = 20)) +F = x.curve.basering + = x - x.group_action([0, 1]) +y1_coor = y1.coordinates(basis = B, threshold = 20) +ify1_coor== vector(n*[0]): +  return False + if (y1.group_acton([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio n +([1,0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]): +  return False + = x - x.group_action([1, 0]) +y2_coor = y2.coordinates(basis = B, threshold = 20) +ify2_coor== vector(n*[0]): +  return False + if (y2.group_acton([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio n +([1,0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]): +  return False +V = F^n +iflen(V.linear_dependence([y1_coor, y2_coor])) > 0: + eturn False[?7h[?12l[?25h[?25l[?7lfori in [5, 16, 19, 21, 23, 25, 26, 27]: +print(is_M32(B[], BB)) +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]: +....:  print(is_M32(B[i], BB)) +....:  +[?7h[?12l[?25h[?2004lTrue +True +True +False +True +False +False +False +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^13 +z1^2 - z1 = x^5 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] + + +[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 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 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 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 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 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 1 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 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1] +[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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, z0*z1/x^7 ) +(0) * dx (0) * dx ((x^13*z1 + x^5*z0 + z0*z1)/x^8) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]: +....:  print(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0 = omega.int()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l....:  gene(B[i]) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]: +....:  gene(B[i]) +....:  +[?7h[?12l[?25h[?2004l( (x^5) * dx, 0 ) ( (x) * dx, 0 ) +( (x^11) * dx, z0/x ) ( (x^3) * dx, z1/x ) +( (x^10) * dx, z0/x^2 ) ( (x^2) * dx, z1/x^2 ) +( (x^9 + x^5) * dx, z0/x^3 ) ( (0) * dx, z1/x^3 ) +( (x^8) * dx, z0/x^4 ) ( (1) * dx, z1/x^4 ) +( (x^7) * dx, z0/x^5 ) ( (0) * dx, z1/x^5 ) +( (x^6) * dx, z0/x^6 ) ( (0) * dx, z1/x^6 ) +( (x^5) * dx, z0/x^7 ) ( (0) * dx, z1/x^7 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]: +....:  gene(B[i])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l6]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l9]:[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l....:  gene(B[i]) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [16, 19]: +....:  gene(B[i]) +....:  +[?7h[?12l[?25h[?2004l( (x^11) * dx, z0/x ) ( (x^3) * dx, z1/x ) +( (x^10) * dx, z0/x^2 ) ( (x^2) * dx, z1/x^2 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x*z1) * dx, 0 ), + ( (x^5*z1 + x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^2*z1) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^3*z1) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (x^4*z1) * dx, 0 ), + ( (x^5) * dx, 0 ), + ( (x^6) * dx, 0 ), + ( (0) * dx, z1/x ), + ( (x^11) * dx, z0/x ), + ( (x^11*z1 + x^7 + x^3*z0) * dx, z0*z1/x ), + ( (x^2) * dx, z1/x^2 ), + ( (x^10) * dx, z0/x^2 ), + ( (x^10*z1 + x^2*z0) * dx, z0*z1/x^2 ), + ( (x^9) * dx, z0/x^3 ), + ( (x^9*z1 + x^5*z1) * dx, z0*z1/x^3 ), + ( (x^8) * dx, z0/x^4 ), + ( (x^8*z1 + z0) * dx, z0*z1/x^4 ), + ( (x^7) * dx, z0/x^5 ), + ( (x^7*z1) * dx, z0*z1/x^5 ), + ( (x^6*z1) * dx, z0*z1/x^6 ), + ( (x^5*z1) * dx, z0*z1/x^7 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^13 +z1^2 - z1 = x^5 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lz[1].valuton()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[1]/C.x).coordinates() +[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]/C.x).cordinates()[?7h[?12l[?25h[?25l[?7l0]/C.x).cordinates()[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]/C.x).coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^).cordinates()[?7h[?12l[?25h[?25l[?7l5).cordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]/C.x^5).coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x^5).coordinates()[?7h[?12l[?25h[?25l[?7l).coordinates()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: for i in [16, 19]: +....:  gene(B[i])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l5, 16, 19, 21, 23, 25, 26, 27]: +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l....:  gene(B[i]) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]: +....:  gene(B[i]) +....:  +[?7h[?12l[?25h[?2004l( (x^5) * dx, 0 ) ( (x) * dx, 0 ) +( (x^11) * dx, z0/x ) ( (x^3) * dx, z1/x ) +( (x^10) * dx, z0/x^2 ) ( (x^2) * dx, z1/x^2 ) +( (x^9 + x^5) * dx, z0/x^3 ) ( (0) * dx, z1/x^3 ) +( (x^8) * dx, z0/x^4 ) ( (1) * dx, z1/x^4 ) +( (x^7) * dx, z0/x^5 ) ( (0) * dx, z1/x^5 ) +( (x^6) * dx, z0/x^6 ) ( (0) * dx, z1/x^6 ) +( (x^5) * dx, z0/x^7 ) ( (0) * dx, z1/x^7 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lsage: lo +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [10], line 1 +----> 1 lo + +NameError: name 'lo' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 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 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 1 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 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 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 1 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 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1] +[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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] + + +[1 1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^7 ) ( (x*z0) * dx, 0 ) +(0) * dx ((x^13*z0 + x^5*z1 + z0*z1)/x^8) * dx (0) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW = V.subspace(Z)[?7h[?12l[?25h[?25l[?7l1 = (A1 - I).transpose().kernel()[?7h[?12l[?25h[?25l[?7l.intersection(W2)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrsection(W2)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lV)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: W1.intersection(W2).intersection(V1).basis() +[?7h[?12l[?25h[?2004l[?7h[ +(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, 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, 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, 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, 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, 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, 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, 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, 1, 0, 0, 0) +] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^5*z0 + x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^2*z0) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^3*z0) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (x^4*z0) * dx, 0 ), + ( (x^5) * dx, 0 ), + ( (x^6) * dx, 0 ), + ( (x^11) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ), + ( (x^10) * dx, z1/x^2 ), + ( (x^2) * dx, z0/x^2 ), + ( (x^10*z0 + x^2*z1) * dx, z0*z1/x^2 ), + ( (x^9) * dx, z1/x^3 ), + ( (x^9*z0 + x^5*z0) * dx, z0*z1/x^3 ), + ( (x^8) * dx, z1/x^4 ), + ( (x^8*z0 + z1) * dx, z0*z1/x^4 ), + ( (x^7) * dx, z1/x^5 ), + ( (x^7*z0) * dx, z0*z1/x^5 ), + ( (x^6*z0) * dx, z0*z1/x^6 ), + ( (x^5*z0) * dx, z0*z1/x^7 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [5, 16, 19, 21, 23, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7le1 in W.basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW1.intersection(W2).intersection(V1).basis()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis(): +....: [?7h[?12l[?25h[?25l[?7lprint(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lfrom_coor(e1, B).omega8, from_coor(e2, B).omega8, from_coor(e3, B).omega8)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(from_coor(e, B)) +....: [?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis(): +....:  print(from_coor(e, B)) +....:  +[?7h[?12l[?25h[?2004l( (1) * dx, 0 ) +( (x) * dx, 0 ) +( (x^2) * dx, 0 ) +( (x^3) * dx, 0 ) +( (x^4) * dx, 0 ) +( (x^5) * dx, 0 ) +( (x^6 + x^2) * dx, z0/x^2 ) +( (x^11) * dx, z1/x ) +( (x^10) * dx, z1/x^2 ) +( (x^9) * dx, z1/x^3 ) +( (x^8) * dx, z1/x^4 ) +( (x^7) * dx, z1/x^5 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e in W1.intersection(W2).intersection(V1).basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: for e in B: +....: [?7h[?12l[?25h[?25l[?7lif len(V.linear_dependence([y1_coor, y2_coor])) > 0:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l32[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e in B: +....: ....: if is_M32(e, B[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l if is_M32(e, BB): + [?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l: if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l +....:  if is_M32(e, BB):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  if is_M32(e, BB): +....: [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(gene(e)) +....: [?7h[?12l[?25h[?25l[?7lsage: for e in B: +....:  if is_M32(e, BB): +....:  print(gene(e)) +....:  +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Cell In [18], line 2 + 1 for e in B: +----> 2 if is_M32(e, BB): + 3 print(gene(e)) + +File :33, in is_M32(x, B) + +File :61, in coordinates(self, threshold, basis) + +File :61, in (.0) + +File :131, in serre_duality_pairing(self, fct) + +File /ext/sage/9.8/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) + 583 return expression.sum(*args, **kwds) + 584 elif max(len(args),len(kwds)) <= 1: +--> 585 return sum(expression, *args, **kwds) + 586 else: + 587 from sage.symbolic.ring import SR + +File :131, in (.0) + +File :124, in residue(self, place) + +File :39, in expansion_at_infty(self, place) + +File /ext/sage/9.8/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute() + 941 5 + 942 """ +--> 943 return self.subs(in_dict,**kwds) + 944 + 945 cpdef _act_on_(self, x, bint self_on_left): + +File /ext/sage/9.8/src/sage/structure/element.pyx:830, in sage.structure.element.Element.subs() + 828 if str(gen) in kwds: + 829 variables.append(kwds[str(gen)]) +--> 830 elif in_dict and gen in in_dict: + 831 variables.append(in_dict[gen]) + 832 else: + +File /ext/sage/9.8/src/sage/structure/element.pyx:1111, in sage.structure.element.Element.__richcmp__() + 1109 return (self)._richcmp_(other, op) + 1110 else: +-> 1111 return coercion_model.richcmp(self, other, op) + 1112 + 1113 cpdef _richcmp_(left, right, int op): + +File /ext/sage/9.8/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp() + 1971 # Coerce to a common parent + 1972 try: +-> 1973 x, y = self.canonical_coercion(x, y) + 1974 except (TypeError, NotImplementedError): + 1975 pass + +File /ext/sage/9.8/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion() + 1309 x_map, y_map = coercions + 1310 if x_map is not None: +-> 1311 x_elt = (x_map)._call_(x) + 1312 else: + 1313 x_elt = x + +File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.8/src/sage/rings/fraction_field.py:534, in FractionField_generic._element_constructor_(self, x, y, coerce) + 522  """ + 523  Return if ``self`` is exact which is if the underlying ring is exact. + 524 + (...) + 530  False + 531  """ + 532 return self.ring().is_exact() +--> 534 def _element_constructor_(self, x, y=None, coerce=True): + 535  """ + 536  Construct an element of this fraction field. + 537 + (...) + 629  -1/2/(a^2 + a) + 630  """ + 631 if isinstance(x, (list, tuple)) and len(x) == 1: + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e in B: +....:  if is_M32(e, BB): +....:  print(gene(e))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7legene(e)[?7h[?12l[?25h[?25l[?7l,gene(e)[?7h[?12l[?25h[?25l[?7l gene(e)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(e, gene(e)) +....: [?7h[?12l[?25h[?25l[?7lsage: for e in B: +....:  if is_M32(e, BB): +....:  print(e, gene(e)) +....:  +[?7h[?12l[?25h[?2004l( (x) * dx, 0 ) ( (x^5) * dx, 0 ) +( (x^5*z0 + x*z1) * dx, 0 ) None +( (x^3) * dx, z0/x ) ( (x^11) * dx, z1/x ) +( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ) None +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Cell In [19], line 2 + 1 for e in B: +----> 2 if is_M32(e, BB): + 3 print(e, gene(e)) + +File :27, in is_M32(x, B) + +File :91, in coordinates(self, threshold, basis) + +File :92, in coordinates(self, basis) + +File :139, in holomorphic_differentials_basis(self, threshold) + +File :425, in holomorphic_combinations(S) + +File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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 :75, in __rmul__(self, constant) + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def gene(x): +....:  y1 = x - x.group_action([0, 1]) +....:  y2 = x - x.group_action([1, 0]) +....:  return(y1, y2)[?7h[?12l[?25h[?25l[?7l....:  return(y1, y2) +....: [?7h[?12l[?25h[?25l[?7lsage: def gene(x): +....:  y1 = x - x.group_action([0, 1]) +....:  y2 = x - x.group_action([1, 0]) +....:  return(y1, y2) +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def gene(x): +....:  y1 = x - x.group_action([0, 1]) +....:  y2 = x - x.group_action([1, 0]) +....:  return(y1, y2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfore in B: +  if is_M32(e, BB): +    print(e, gene(e)) + [?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for e in B: +....:  if is_M32(e, BB): +....:  print(e, gene(e)) +....:  +[?7h[?12l[?25h[?2004l( (x^5*z0 + x*z1) * dx, 0 ) (( (x) * dx, 0 ), ( (x^5) * dx, 0 )) +( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ) (( (x^3) * dx, z0/x ), ( (x^11) * dx, z1/x )) +( (x^10*z0 + x^2*z1) * dx, z0*z1/x^2 ) (( (x^2) * dx, z0/x^2 ), ( (x^10) * dx, z1/x^2 )) +( (x^8*z0 + z1) * dx, z0*z1/x^4 ) (( (1) * dx, z0/x^4 ), ( (x^8) * dx, z1/x^4 )) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e in B:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lW1.intersection(W2).intersection(V1).basis():[?7h[?12l[?25h[?25l[?7l1.intersection(W2).intersection(V1).basis():[?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis(): +....: [?7h[?12l[?25h[?25l[?7lprint(from_coor(e, B))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(from_coor(e, B))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l(from_coor(e, B))[?7h[?12l[?25h[?25l[?7l....:  print(from_coor(e, B)) +....: [?7h[?12l[?25h[?25l[?7l....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = n*[0] + list(e1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7l[]list(e1)[?7h[?12l[?25h[?25l[?7l[list(e1)[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +print(fromcoo(e, B)) +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = list(e) +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7llen[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l() +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l....:  e = list(e) + n*[0] +....: [?7h[?12l[?25h[?25l[?7le3 = A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l = vector(F, e)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lvector(F, e)[?7h[?12l[?25h[?25l[?7l....:  e = vector(F, e) +....: [?7h[?12l[?25h[?25l[?7lprint(from_coor(e, B))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()r[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print('e2', A3.solve_right(e)) +....: [?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis(): +....:  n = len(list(e)) +....:  print(from_coor(e, B)) +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = list(e) + n*[0] +....:  e = vector(F, e) +....:  print('e2', A3.solve_right(e)) +....:  +[?7h[?12l[?25h[?2004l( (1) * dx, 0 ) +e2 (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) +( (x) * dx, 0 ) +e2 (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, 0 ) +e2 (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) +( (x^3) * dx, 0 ) +e2 (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) +( (x^4) * dx, 0 ) +e2 (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) +( (x^5) * dx, 0 ) +e2 (0, 0, 0, 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^6 + x^2) * dx, z0/x^2 ) +e2 (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) +( (x^11) * dx, z1/x ) +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [22], line 7 + 5 e = list(e) + n*[Integer(0)] + 6 e = vector(F, e) +----> 7 print('e2', A3.solve_right(e)) + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right() + 903 + 904 if not self.is_square(): +--> 905 X = self._solve_right_general(C, check=check) + 906 else: + 907 try: + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general() + 1026 # Have to check that we actually solved the equation. + 1027 if self*X != B: +-> 1028 raise ValueError("matrix equation has no solutions") + 1029 return X + 1030 + +ValueError: matrix equation has no solutions +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis(): +....:  n = len(list(e)) +....:  print(from_coor(e, B)) +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = list(e) + n*[0] +....:  e = vector(F, e) +....:  print('e2', A3.solve_right(e))[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +....:  +....:  print('e2', A3.solve_right(e))[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltry[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l print('e2', A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l print('e2', A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l print('e2', A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l print('e2', A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfA3.solve_right(e)[?7h[?12l[?25h[?25l[?7lrA3.solve_right(e)[?7h[?12l[?25h[?25l[?7loA3.solve_right(e)[?7h[?12l[?25h[?25l[?7lmA3.solve_right(e)[?7h[?12l[?25h[?25l[?7l_A3.solve_right(e)[?7h[?12l[?25h[?25l[?7lcA3.solve_right(e)[?7h[?12l[?25h[?25l[?7loA3.solve_right(e)[?7h[?12l[?25h[?25l[?7loA3.solve_right(e)[?7h[?12l[?25h[?25l[?7lrA3.solve_right(e)[?7h[?12l[?25h[?25l[?7l(A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(([0;38;5;210;48;5;88m))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print('e2', from_coor(A3.solve_right(e), B)) +....: [?7h[?12l[?25h[?25l[?7l....:  +....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le = vector(F, e)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lexcept[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l +....: [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lpass[?7h[?12l[?25h[?25l[?7l....:  pass +....: [?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis(): +....:  n = len(list(e)) +....:  print(from_coor(e, B)) +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = list(e) + n*[0] +....:  e = vector(F, e) +....:  try: +....:  print('e2', from_coor(A3.solve_right(e), B)) +....:  except: +....:  pass +....:  +[?7h[?12l[?25h[?2004l( (1) * dx, 0 ) +e2 ( (z0) * dx, 0 ) +( (x) * dx, 0 ) +e2 ( (x*z0) * dx, 0 ) +( (x^2) * dx, 0 ) +e2 ( (x^2*z0) * dx, 0 ) +( (x^3) * dx, 0 ) +e2 ( (x^3*z0) * dx, 0 ) +( (x^4) * dx, 0 ) +e2 ( (x^4*z0) * dx, 0 ) +( (x^5) * dx, 0 ) +e2 ( (x^5*z0) * dx, z0*z1/x^7 ) +( (x^6 + x^2) * dx, z0/x^2 ) +e2 ( (x^6*z0 + x^2*z0) * dx, z0*z1/x^6 ) +( (x^11) * dx, z1/x ) +( (x^10) * dx, z1/x^2 ) +( (x^9) * dx, z1/x^3 ) +e2 ( (x^9*z0) * dx, (x^4*z0*z1 + z0*z1)/x^7 ) +( (x^8) * dx, z1/x^4 ) +e2 ( (x^8*z0) * dx, z0*z1/x^4 ) +( (x^7) * dx, z1/x^5 ) +e2 ( (x^7*z0) * dx, z0*z1/x^5 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^5*z0 + x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^2*z0) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^3*z0) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (x^4*z0) * dx, 0 ), + ( (x^5) * dx, 0 ), + ( (x^6) * dx, 0 ), + ( (x^11) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ), + ( (x^10) * dx, z1/x^2 ), + ( (x^2) * dx, z0/x^2 ), + ( (x^10*z0 + x^2*z1) * dx, z0*z1/x^2 ), + ( (x^9) * dx, z1/x^3 ), + ( (x^9*z0 + x^5*z0) * dx, z0*z1/x^3 ), + ( (x^8) * dx, z1/x^4 ), + ( (x^8*z0 + z1) * dx, z0*z1/x^4 ), + ( (x^7) * dx, z1/x^5 ), + ( (x^7*z0) * dx, z0*z1/x^5 ), + ( (x^6*z0) * dx, z0*z1/x^6 ), + ( (x^5*z0) * dx, z0*z1/x^7 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^5 +z1^2 - z1 = x^13 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lz[1].valuton()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[1]*C.x*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[1]*C.x*C.dx).valuation() +[?7h[?12l[?25h[?2004l[?7h-4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx.divides(x^2)[?7h[?12l[?25h[?25l[?7li.omega0.r()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^*C.dx,[?7h[?12l[?25h[?25l[?7l8*C.dx,[?7h[?12l[?25h[?25l[?7l*C.dx,[?7h[?12l[?25h[?25l[?7l9*C.dx,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, C.z[1]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, C.z[1]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.omega0.r()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates(basis = B, threshold = 20) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [28], line 1 +----> 1 xi.coordinates(basis = B, threshold = Integer(20)) + +TypeError: superelliptic_cech.coordinates() got an unexpected keyword argument 'basis' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates(basis = B, threshold = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7l(threshold = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega0.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.omega8.valuation() +[?7h[?12l[?25h[?2004l[?7h-36 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8.valuation()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi +[?7h[?12l[?25h[?2004l[?7h((x^9*z1) * dx, (x^4*z0*z1 + z0*z1)/x^7, ((x^17*z0 + x^17*z1 + x^13*z0 + x^9*z1 + x^5*z1 + x^4*z0*z1 + z0*z1)/x^8) * dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7l.omega8.valuation()[?7h[?12l[?25h[?25l[?7lcoordinates(basis = B, threshold = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, C.z[1]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l0]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, C.z[0]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, C.z[0]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega8.valuation()[?7h[?12l[?25h[?25l[?7lsage: xi.omega8.valuation() +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8.valuation()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: xi.omega8 +[?7h[?12l[?25h[?2004l[?7h((x^13*z0 + x^9*z1 + x^5*z1 + x^4*z0*z1 + z0*z1)/x^8) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lz[1].valuton()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^3*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[1]/C.x^3*C.dx).valuation() +[?7h[?12l[?25h[?2004l[?7h12 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (z0) * dx, + (x) * dx, + (x^5*z0 + x*z1) * dx, + (x*z0) * dx, + (x^2) * dx, + (x^2*z0) * dx, + (x^3) * dx, + (x^3*z0) * dx, + (x^4) * dx, + (x^4*z0) * dx, + (x^5) * dx, + (x^6) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7lx. = PolynomialRing(F[?7h[?12l[?25h[?25l[?7l. = PolynomialRing(F)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(2)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e in W1.intersection(W2).intersection(V1).basis():[?7h[?12l[?25h[?25l[?7l =x^3 + x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lsage: f = x^6 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^6[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.nth_root(2) +[?7h[?12l[?25h[?2004l[?7hx^3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 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 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 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 1 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 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 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 1 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 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1] +[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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] + + +[1 1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^7 ) ( (x*z0) * dx, 0 ) +(0) * dx ((x^13*z0 + x^5*z1 + z0*z1)/x^8) * dx (0) * dx +--------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [4], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :87 + +File :83, in alpha(C) + +AttributeError: 'as_cover' object has no attribute 'list_of_functions' +[?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[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() + C.a_number C.branch_points C.de_rham_basis   + C.at_most_poles C.cartier_matrix C.dx   + C.at_most_poles_forms C.characteristic C.dx_series > + C.base_ring C.cohomology_of_structure_sheaf_basis C.exponent_of_different   + [?7h[?12l[?25h[?25l[?7la_number + C.a_number  + + + + [?7h[?12l[?25h[?25l[?7lbranch_points + C.a_number  C.branch_points [?7h[?12l[?25h[?25l[?7lde_rham_basi + C.branch_points  C.de_rham_basis [?7h[?12l[?25h[?25l[?7lexponent_of_different_prim + branch_pointsde_rham_basiexponent_of_different_prim + cartiermatrixdx fct_field +<characeristic dx_seris function + cohomoloy_of_structure_sheaf_basisexpnent_of_different genus [?7h[?12l[?25h[?25l[?7lgroup +de_rham_basiexponent_of_different_primgroup  +dx fct_fieldheight  +dx_seris functionholomorphic_differentials_basis +expnent_of_different genus ith_ramification_gp[?7h[?12l[?25h[?25l[?7ljumps +exponent_of_different_primgroup jumps +fct_fieldheight lift_o_de_rham +functionholomorphic_differentials_basismagical_element  +genus ith_ramification_gpnb_of_pts_at_nfty [?7h[?12l[?25h[?25l[?7lone +group jumpsone  +height lift_o_de_rhamprec  +holomorphic_differentials_basismagical_element pseudo_magical_element +ith_ramification_gpnb_of_pts_at_nfty quotien [?7h[?12l[?25h[?25l[?7lramification_jumps +jumpsone ramification_jumps +lift_o_de_rhamprec uniformizer +magical_element pseudo_magical_elementx  +nb_of_pts_at_nfty quotien x_series[?7h[?12l[?25h[?25l[?7ly +one ramification_jumpsy   +prec uniformizery_series   +pseudo_magical_elementx z  +quotien x_seriesz  [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lramification_jumps + C.ramification_jumps  C.y [?7h[?12l[?25h[?25l[?7lone + C.one  C.ramification_jumps [?7h[?12l[?25h[?25l[?7ljumps +jumpsone ramification_jumps  +lift_to_de_rhamprec uniformizer  +magical_element pseudo_magical_elementx> +nb_of_ps_at_inftyquotientx  [?7h[?12l[?25h[?25l[?7lgroup +groupjumpsone  +heigh lift_to_de_rhamprec  +holomorphic_differentials_basismagical_element pseudo_magical_element +ith_ramificaton_gpnb_of_ps_at_inftyquotient[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim +exponent_of_different_primgroupjumps +fct_fieldheigh lift_to_de_rham +functions holomorphic_differentials_basismagical_element  +genus ith_ramificaton_gpnb_of_ps_at_infty[?7h[?12l[?25h[?25l[?7lde_rham_basis +de_rham_basis exponent_of_different_primgroup +dx fct_fieldheigh  +dx_seriefunctions holomorphic_differentials_basis +exponent_of_differentgenus ith_ramificaton_gp[?7h[?12l[?25h[?25l[?7lbranch_point +branch_pointde_rham_basis exponent_of_different_prim +cartier_matrixdx fct_field +charactristicdx_seriefunctions  +cohmology_of_structure_sheaf_basisexponent_of_differentgenus [?7h[?12l[?25h[?25l[?7la_number + a_number branch_pointde_rham_basis  + at_mostpoles cartier_matrixdx  + at_mos_poles_formscharactristicdx_serie + base_rin cohmology_of_structure_sheaf_basisexponent_of_different[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + + + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 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 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 1 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 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 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 1 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 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1] +[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 1 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 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 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 1 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 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 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 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 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 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 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 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 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 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 1] + + +[1 1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^7 ) ( (x*z0) * dx, 0 ) +(0) * dx ((x^13*z0 + x^5*z1 + z0*z1)/x^8) * dx (0) * dx +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [5], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :87 + +File :85, in alpha(C) + +File :9, in __init__(self, C, g) + +AttributeError: 'as_cover' object has no attribute 'polynomial' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def alpha(C): +....:  f1, f2 = C.functions +....:  f1, f2 = f1.function, f2.function +....:  return superelliptic_function(C, (f2/f1).nth_root(2))[?7h[?12l[?25h[?25l[?7l....:  return superelliptic_function(C, (f2/f1).nth_root(2)) +....: [?7h[?12l[?25h[?25l[?7lsage: def alpha(C): +....:  f1, f2 = C.functions +....:  f1, f2 = f1.function, f2.function +....:  return superelliptic_function(C, (f2/f1).nth_root(2)) +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.nth_root(p)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: alpha(C) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [7], line 1 +----> 1 alpha(C) + +Cell In [6], line 4, in alpha(C) + 2 f1, f2 = C.functions + 3 f1, f2 = f1.function, f2.function +----> 4 return superelliptic_function(C, (f2/f1).nth_root(Integer(2))) + +File :9, in __init__(self, C, g) + +AttributeError: 'as_cover' object has no attribute 'polynomial' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def alpha(C): +....:  f1, f2 = C.functions +....:  f1, f2 = f1.function, f2.function +....:  print(f1, f2, (f2/f1).nth_root(2)) +....:  return superelliptic_function(C, (f2/f1).nth_root(2))[?7h[?12l[?25h[?25l[?7l....:  return superelliptic_function(C, (f2/f1).nth_root(2)) +....: [?7h[?12l[?25h[?25l[?7lsage: def alpha(C): +....:  f1, f2 = C.functions +....:  f1, f2 = f1.function, f2.function +....:  print(f1, f2, (f2/f1).nth_root(2)) +....:  return superelliptic_function(C, (f2/f1).nth_root(2)) +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha(C)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: alpha(C) +[?7h[?12l[?25h[?2004lx^5 x^13 x^4 +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [9], line 1 +----> 1 alpha(C) + +Cell In [8], line 5, in alpha(C) + 3 f1, f2 = f1.function, f2.function + 4 print(f1, f2, (f2/f1).nth_root(Integer(2))) +----> 5 return superelliptic_function(C, (f2/f1).nth_root(Integer(2))) + +File :9, in __init__(self, C, g) + +AttributeError: 'as_cover' object has no attribute 'polynomial' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lspan(v1, v2)[?7h[?12l[?25h[?25l[?7lum(floor(305/5^n) for n in range(1, 10))[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def alpha(C): +....:  f1, f2 = C.functions +....:  f1, f2 = f1.function, f2.function +....:  Fxyz, Rxyz, x, y, z = C.fct_field +....:  print(f1, f2, (f2/f1).nth_root(2)) +....:  return superelliptic_function(C, Fxyz((f2/f1).nth_root(2)))[?7h[?12l[?25h[?25l[?7l....:  return superelliptic_function(C, Fxyz((f2/f1).nth_root(2))) +....: [?7h[?12l[?25h[?25l[?7lsage: def alpha(C): +....:  f1, f2 = C.functions +....:  f1, f2 = f1.function, f2.function +....:  Fxyz, Rxyz, x, y, z = C.fct_field +....:  print(f1, f2, (f2/f1).nth_root(2)) +....:  return superelliptic_function(C, Fxyz((f2/f1).nth_root(2))) +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha(C)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: alpha(C) +[?7h[?12l[?25h[?2004lx^5 x^13 x^4 +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [11], line 1 +----> 1 alpha(C) + +Cell In [10], line 6, in alpha(C) + 4 Fxyz, Rxyz, x, y, z = C.fct_field + 5 print(f1, f2, (f2/f1).nth_root(Integer(2))) +----> 6 return superelliptic_function(C, Fxyz((f2/f1).nth_root(Integer(2)))) + +File :9, in __init__(self, C, g) + +AttributeError: 'as_cover' object has no attribute 'polynomial' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension()) +[?7h[?12l[?25h[?2004lTrue +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [12], line 8 + 6 BASIS += [aux] + 7 # +----> 8 aux = superelliptic_cech(C, C.z[Integer(1)]*C.x**i*C.dx, C.z[Integer(0)]*C.z[Integer(1)]*alpha/(C.x**(M - Integer(1) - i) + alpha * C.x**(m - Integer(1) - i))) + 9 print(aux.omega8.valuation() > Integer(0)) + 10 BASIS += [aux] + +TypeError: unsupported operand type(s) for /: 'NoneType' and 'as_function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha = x^((M - m)/2)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: alpha +[?7h[?12l[?25h[?2004l[?7hx^4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension()) +[?7h[?12l[?25h[?2004lTrue +True +True +True +True +True +True +True +True +False +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [14], line 41 + 39 lista = [] + 40 for a in BASIS: +---> 41 lista += a.coordinates(basis = BB) + 43 V = F**(Integer(2)*C.genus()) + 44 print(V.subspace(lista).dimension()) + +NameError: name 'BB' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS = [][?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS = [][?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS = [][?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: BB BOmega = C.holomorphic_differentials_basis() +....: BOX = C.cohomology_of_structure_sheaf_basis() +....: BB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB BOmega = C.holomorphic_differentials_basis() +....: BOX = C.cohomology_of_structure_sheaf_basis() +....: BB = [BOmega, BOX, B] +[?7h[?12l[?25h[?2004l Cell In [15], line 1 + BB BOmega = C.holomorphic_differentials_basis() + ^ +SyntaxError: invalid syntax + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis() +....: BOX = C.cohomology_of_structure_sheaf_basis() +....: BB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis() +....: BOX = C.cohomology_of_structure_sheaf_basis() +....: BB = [BOmega, BOX, B] +[?7h[?12l[?25h[?2004l +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension()) +[?7h[?12l[?25h[?2004lTrue +True +True +True +True +True +True +True +True +False +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [17], line 41 + 39 lista = [] + 40 for a in BASIS: +---> 41 lista += a.coordinates(basis = BB) + 43 V = F**(Integer(2)*C.genus()) + 44 print(V.subspace(lista).dimension()) + +TypeError: superelliptic_cech.coordinates() got an unexpected keyword argument 'basis' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension()) +[?7h[?12l[?25h[?2004lTrue +True +True +True +True +True +True +True +True +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [18], line 17 + 14 BASIS += [aux] + 16 for i in range((m-Integer(1))/Integer(2), m - Integer(1)): +---> 17 aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i)) + 18 print(aux.omega8.valuation() > Integer(0)) + 19 BASIS += [aux] + +File :18, in __init__(self, C, omega, f) + +ValueError: cech cocycle not regular +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension()) +[?7h[?12l[?25h[?2004l1A, 0 True +1B, 0 True +1C, 0 True +1A, 1 True +1B, 1 True +1C, 1 True +2A, 2 True +2B, 2 True +2C, 2 True +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [19], line 17 + 14 BASIS += [aux] + 16 for i in range((m-Integer(1))/Integer(2), m - Integer(1)): +---> 17 aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i)) + 18 print("2A, ", i, aux.omega8.valuation() > Integer(0)) + 19 BASIS += [aux] + +File :18, in __init__(self, C, omega, f) + +ValueError: cech cocycle not regular +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in range((m-1)/2, m - 1): +....:  try: +....:  aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +....:  print("2A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +....:  print("2B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  except: +....:  pass[?7h[?12l[?25h[?25l[?7l....:  pass +....: [?7h[?12l[?25h[?25l[?7lsage: for i in range((m-1)/2, m - 1): +....:  try: +....:  aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +....:  print("2A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +....:  print("2B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  except: +....:  pass +....:  +[?7h[?12l[?25h[?2004l2A, 2 True +2B, 2 True +2C, 2 True +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in range((m-1)/2, m - 1): +....:  #aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +....:  #print("2A, ", i, aux.omega8.valuation() > 0) +....:  #BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +....:  print("2B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux][?7h[?12l[?25h[?25l[?7l....:  BASIS += [aux] +....: [?7h[?12l[?25h[?25l[?7lsage: for i in range((m-1)/2, m - 1): +....:  #aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +....:  #print("2A, ", i, aux.omega8.valuation() > 0) +....:  #BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +....:  print("2B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +[?7h[?12l[?25h[?2004l2B, 2 True +2C, 2 True +2B, 3 True +2C, 3 True +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-3], BB)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: i = 3 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7lmC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7l C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7l=C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7l C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range((m-1)/2, m - 1):[?7h[?12l[?25h[?25l[?7lf.coordintes)[?7h[?12l[?25h[?25l[?7lf.valuation()[?7h[?12l[?25h[?25l[?7l = C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l[]C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l[C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l()C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l[]C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l[C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^(m-1-i) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om - fff.diffn() +[?7h[?12l[?25h[?2004l[?7h(z0*z1/x^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - fff.diffn()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(om - f.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (om - fff.diffn()).valuation() +[?7h[?12l[?25h[?2004l[?7h-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = [][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: lift + lift  + lift_form_to_drw + lift_to_sl2z  + + [?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS = [][?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (x) * dx, 0 ), + ( (x^5*z0 + x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (x^2*z0) * dx, 0 ), + ( (x^3) * dx, 0 ), + ( (x^3*z0) * dx, 0 ), + ( (x^4) * dx, 0 ), + ( (x^4*z0) * dx, 0 ), + ( (x^5) * dx, 0 ), + ( (x^6) * dx, 0 ), + ( (x^11) * dx, z1/x ), + ( (0) * dx, z0/x ), + ( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ), + ( (x^10) * dx, z1/x^2 ), + ( (x^2) * dx, z0/x^2 ), + ( (x^10*z0 + x^2*z1) * dx, z0*z1/x^2 ), + ( (x^9) * dx, z1/x^3 ), + ( (x^9*z0 + x^5*z0) * dx, z0*z1/x^3 ), + ( (x^8) * dx, z1/x^4 ), + ( (x^8*z0 + z1) * dx, z0*z1/x^4 ), + ( (x^7) * dx, z1/x^5 ), + ( (x^7*z0) * dx, z0*z1/x^5 ), + ( (x^6*z0) * dx, z0*z1/x^6 ), + ( (x^5*z0) * dx, z0*z1/x^7 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l(om - fff.diffn()).valuation()[?7h[?12l[?25h[?25l[?7lom - f.difn()[?7h[?12l[?25h[?25l[?7l(om - f.difn()).valuation()[?7h[?12l[?25h[?25l[?7lom - f.difn()[?7h[?12l[?25h[?25l[?7lsage: om - fff.diffn() +[?7h[?12l[?25h[?2004l[?7h(z0*z1/x^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(om - fff.diffn()).valuation()[?7h[?12l[?25h[?25l[?7lC.z[1]/Cx^3*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[1]/C.x^5).diffn() +[?7h[?12l[?25h[?2004l[?7h((x^13 + z1)/x^6) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^5).diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l6)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.z[1]/C.x^6)*C.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l(*)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: ((C.z[1]/C.x^6)*C.dx).valuation() +[?7h[?12l[?25h[?2004l[?7h24 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx_series[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^7*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x^7*C.dx).valuation() +[?7h[?12l[?25h[?2004l[?7h-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l.C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lzC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[]C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[]0C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[]C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0]C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]*C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l.C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lzC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l1C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[]C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[]/C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l.C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lxC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l^C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l2C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l+C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lX + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l. + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7ld + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lx + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]*C.z[1]/C.x^2*C.dx + C.x^7*C.dx).valuation() +[?7h[?12l[?25h[?2004l[?7h3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1]/C.x^2*C.dx + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^2*C.dx + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]*C.z[1] + alpha*f1).valuation() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [33], line 1 +----> 1 (C.z[Integer(0)]*C.z[Integer(1)] + alpha*f1).valuation() + +File :23, in __add__(self, other) + +AttributeError: 'NoneType' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1] + alpha*f1).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7lC).valuation()[?7h[?12l[?25h[?25l[?7l.).valuation()[?7h[?12l[?25h[?25l[?7lx).valuation()[?7h[?12l[?25h[?25l[?7l^).valuation()[?7h[?12l[?25h[?25l[?7lm).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]*C.z[1] + alpha*C.x^m).valuation() +[?7h[?12l[?25h[?2004l[?7h-31 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: -m - 2*M +[?7h[?12l[?25h[?2004l[?7h-31 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-m - 2*M[?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1] + alpha*C.x^m).valuation()[?7h[?12l[?25h[?25l[?7lf1).valution()[?7h[?12l[?25h[?25l[?7l/C.x^2*C.dx + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lx^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^6)*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC.z[1]/C.x^5).diffn()[?7h[?12l[?25h[?25l[?7lom - fff.diffn()[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l(om - fff.diffn()).valuation()[?7h[?12l[?25h[?25l[?7lom - f.difn()[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lom = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7li = 3[?7h[?12l[?25h[?25l[?7lsage: for i in range((m-1)/2, m - 1): +....:  #aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +....:  #print("2A, ", i, aux.omega8.valuation() > 0) +....:  #BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +....:  print("2B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l +try: + aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) + print("2A, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + # + aux = as_cech(C, C.x^(M - m + )*C.dx, C.z[1]/C.x^(m-1-i)) + print("2B, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + # + aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  except: +....:  pass[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) +BASIS += [ux] + +foriin range((m-1)/2, M - (m+3)/2 + 1): +aux= as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuaton() > 0) +BASIS += [aux] +# +aux= as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + + +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3B, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB) + +V = F^(2*C.genus))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3B, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB) +[?7h[?12l[?25h[?25l[?7lprint("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3B, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB)[?7h[?12l[?25h[?25l[?7laux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3B, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS:[?7h[?12l[?25h[?25l[?7l# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3B, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [][?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3B, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +[?7h[?12l[?25h[?25l[?7lprint("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3B, ", i, aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3B, ", i, aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3B, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lprint("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print("3A, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7lprint("1B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux] +[?7h[?12l[?25h[?25l[?7laux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7l# +aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i)) +print("2C, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lprint("1A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7laux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range(0, (m-1)/2): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print("2B, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lBASIS= [] +fori in range(0, (m-1)/2): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lsage: alphaC.x^((M - m)/2) +BASIS= [] +fori in range(0, (m-1)/2): +aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print("1B, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = as_cech(CC.^i*C.dx, 0*C.x) +print("1C, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print("2A, ", i, aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7l....:  ux= as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) + print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux =as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] + + +lista = [] +aBASIS: +lista+= a.oordinates(basis = BB) + +V=F^(2*C.genus()) +print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l[] +()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l[] +()[?7h[?12l[?25h[?25l[?7l# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB) + +V = F^(2*C.genus))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB) +[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB)[?7h[?12l[?25h[?25l[?7laux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS:[?7h[?12l[?25h[?25l[?7l# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [][?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = s_cech(C, C.x^i*C.dx,0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l# +aux = s_cech(C, C.x^i*C.dx,0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] +[?7h[?12l[?25h[?25l[?7l# +aux =as_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =as_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux =as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) + print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = s_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7laux =as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =as_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =as_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux =as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux][?7h[?12l[?25h[?25l[?7lfori in range(0, (m-1)/2): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lBASIS= [] +fori in range(0, (m-1)/2): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lsage: alphaC.x^((M - m)/2) +BASIS= [] +fori in range(0, (m-1)/2): +aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = s_cech(C, C.x^i*C.dx,0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7l....:  ux= superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) + print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - (m+3)/2 + 1): +aux =superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] + + +lista = [] +aBASIS: +lista+= a.oordinates(basis = BB) + +V=F^(2*C.genus()) +print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB) + +V = F^(2*C.genus))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB) +[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB)[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS:[?7h[?12l[?25h[?25l[?7l# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [][?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] +[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =superelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux =superelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =superelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) + print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lfori in range(0, (m-1)/2): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS= [] +fori in range(0, (m-1)/2): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lsage: alphaC.x^((M - m)/2) +BASIS= [] +fori in range(0, (m-1)/2): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis() +OX =C.cohomology_of_structure_sheaf_basis() +BB = [BOmega, BOX, B] +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB BOmega = C.holomorphic_differentials_basis() + +[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:   aux =supereliptic_ech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) + print(aux.omega8.valuation() > 0) +  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB) + +V = F^(2*C.genus))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB) +[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB)[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS:[?7h[?12l[?25h[?25l[?7l# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [][?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] +[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =superelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux =superelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =superelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) + print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lfori in range(0, (m-1)/2): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS= [] +fori in range(0, (m-1)/2): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lsage: alphaC.x^((M - m)/2) +BASIS= [] +fori in range(0, (m-1)/2): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7l +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7l....:  ux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print(aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l() +[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB) + +V = F^(2*C.genus))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB) +[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS: + lista += a.coordinates(basis = BB)[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [] +fora in BASIS:[?7h[?12l[?25h[?25l[?7l# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + + +list= [][?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) + BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, M - m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) + BASIS += [aux] +[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =superelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) + BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux =superelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =superelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS+= [aux] +# +aux =superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) + print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lfori in range(0, (m-1)/2): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS= [] +fori in range(0, (m-1)/2): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +#[?7h[?12l[?25h[?25l[?7lsage: alphax^((M - m)/2) +BASIS= [] +fori in range(0, (m-1)/2): +aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i))) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# + aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i ) +)) +print(aux.omega8.valuation() > 0) +BASIS += [aux] +# +aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x) +print(aux.omega8.valuation() > 0) +BASIS += [aux] + +fori in range((m-1)/2, m - 1): +aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)) +print(aux.omega8.valuation() > 0) +BASIS += [aux][?7h[?12l[?25h[?25l[?7l(C) +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7ldef alpha(C): +....:  f1, f2 = C.functions +....:  f1, f2 = f1.function, f2.function +....:  Fxyz, Rxyz, x, y, z = C.fct_field +....:  print(f1, f2, (f2/f1).nth_root(2)) +....:  return superelliptic_function(C, Fxyz((f2/f1).nth_root(2)))[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha(C) +  +  +  +  + [?7h[?12l[?25h[?25l[?7ldef alpha(C): +....:  f1, f2 = C.functions +....:  f1, f2 = f1.function, f2.function +....:  print(f1, f2, (f2/f1).nth_root(2)) +....:  return superelliptic_function(C, (f2/f1).nth_root(2))[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha(C) +  +  +  + [?7h[?12l[?25h[?25l[?7ldef alpha(C): +....:  f1, f2 = C.functions +....:  f1, f2 = f1.function, f2.function +....:  return superelliptic_function(C, (f2/f1).nth_root(2))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage') +  +  + [?7h[?12l[?25h[?25l[?7lf.nth_root(2)[?7h[?12l[?25h[?25l[?7l = x^6[?7h[?12l[?25h[?25l[?7lRx.<> = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7lC.holomorphic_differetials_basis()[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^3*C.dx).valution()[?7h[?12l[?25h[?25l[?7lxiomega8[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7l = superelipc_cech(C, C.z[0]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega8.valuation()[?7h[?12l[?25h[?25l[?7lcoordinates(basis = B, threshold = 20)[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, C.z[1]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l(C.z[1]*C.x*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lfor e in W1.intersection(W2).intersection(V1).basis(): +....:  n = len(list(e)) +....:  print(from_coor(e, B)) +....:  A3 = block_matrix([[A1 - I], [A2 - I]]) +....:  e = list(e) + n*[0] +....:  e = vector(F, e) +....:  try: +....:  print('e2', from_coor(A3.solve_right(e), B)) +....:  except: +....:  pass[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + + + + + +print('e2', A3.solve_right(e)) +  +  + [?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l[] +()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lB: +   if is_M32(e, BB): + print(e, gene(e)) +  +  +  + [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldefgene(x): +y1=x - x.group_action([0, 1]) +y2=x-x.group_action([1, 0]) +....:  return(y1, y2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfore in B: +  if is_M32(e, BB): +    print(e, gene(e)) + [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + +(gene(e))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B] +  + [?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lfor e in B: +....:  if is_M32(e, BB): +....:  print(gene(e))[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7le, gene(e))[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7ldefgene(x): +y1=x - x.group_action([0, 1]) +y2=x-x.group_action([1, 0]) +....:  return(y1, y2)[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7lfore in B: +  if is_M32(e, BB): +    print(e, gene(e)) + [?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7lprint(e, gene(e)[?7h[?12l[?25h[?25l[?7lprint(e, gene(e)[?7h[?12l[?25h[?25l[?7lprint(e, gene(e)[?7h[?12l[?25h[?25l[?7lprint(e, gene(e)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^13*z0 + x^5*z1 + z0*z1)/x^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lfff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff +[?7h[?12l[?25h[?2004l[?7hz0*z1/x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7li = 3[?7h[?12l[?25h[?25l[?7lsage: i +[?7h[?12l[?25h[?2004l[?7h3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension()) +[?7h[?12l[?25h[?2004l1A, 0 True +1B, 0 True +1C, 0 True +1A, 1 True +1B, 1 True +1C, 1 True +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [39], line 17 + 14 BASIS += [aux] + 16 for i in range((m-Integer(1))/Integer(2), m - Integer(1)): +---> 17 aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*f1/C.x**(i+Integer(1) - M - m)) + 18 print("2A, ", i, aux.omega8.valuation() > Integer(0)) + 19 BASIS += [aux] + +TypeError: unsupported operand type(s) for /: 'NoneType' and 'as_function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print("2A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +....:  print("2B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....: [?7h[?12l[?25h[?25l[?7l....:  print("2A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i)) +....:  print("2B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +[?7h[?12l[?25h[?2004l1A, 0 True +1B, 0 True +1C, 0 True +1A, 1 True +1B, 1 True +1C, 1 True +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [40], line 17 + 14 BASIS += [aux] + 16 for i in range((m-Integer(1))/Integer(2), m - Integer(1)): +---> 17 ff1 = as_function(C, f1.polynomial) + 18 aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - m)) + 19 print("2A, ", i, aux.omega8.valuation() > Integer(0)) + +AttributeError: 'superelliptic_function' object has no attribute 'polynomial' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension()) +[?7h[?12l[?25h[?2004l1A, 0 True +1B, 0 True +1C, 0 True +1A, 1 True +1B, 1 True +1C, 1 True +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [41], line 18 + 16 for i in range((m-Integer(1))/Integer(2), m - Integer(1)): + 17 ff1 = as_function(C, f1.function) +---> 18 aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - m)) + 19 print("2A, ", i, aux.omega8.valuation() > Integer(0)) + 20 BASIS += [aux] + +File :18, in __init__(self, C, omega, f) + +ValueError: cech cocycle not regular +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = 3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: i = 3 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Intege r +....: (1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - m))[?7h[?12l[?25h[?25l[?7l( +)a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lsage: aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Intege r +....: (1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - m))aaed +[?7h[?12l[?25h[?2004l Cell In [43], line 1 + aux = as_cech(C, C.z[Integer(Integer(1))]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(Integer(0))]*C.dx, C.z[Integer(Integer(0))]*C.z[Integer(Integer(1))]/C.x**(m-Integer(Integer(1))-i) + C.z[Integer(Integer(1))]*alpha*ff1/C.x**(i+Integer(Integer(1)) - M - m))aaed + ^ +SyntaxError: invalid syntax + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - fff.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: fff = C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - +....: m)[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - +....: m) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M -   +....: m)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn() + [?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M -   +....: m)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff +[?7h[?12l[?25h[?2004l[?7h(x^24*z1 + z0*z1)/x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^5 +z1^2 - z1 = x^13 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Intege r +....: (1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - m))aaed[?7h[?12l[?25h[?25l[?7llpha= C.x^(M - m)/2) + [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: alpha +[?7h[?12l[?25h[?2004l[?7hx^4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: ff0 +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [49], line 1 +----> 1 ff0 + +NameError: name 'ff0' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff0[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: ff1 +[?7h[?12l[?25h[?2004l[?7hx^5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff1[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^37 + x^24*z1 + x^13*z0 + x^5*z1 + z0*z1)/x^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: alpha*f0 +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [52], line 1 +----> 1 alpha*f0 + +NameError: name 'f0' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha*f0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: alpha*ff1 +[?7h[?12l[?25h[?2004l[?7hx^9 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M -   +....: m)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1 + [?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[1]/C.x^6 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[1]/C.x^6[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.diffn() +[?7h[?12l[?25h[?2004l[?7h(x^6) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.diffn()[?7h[?12l[?25h[?25l[?7l = C.z[1]/C.x^6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]C.x^6[?7h[?12l[?25h[?25l[?7l[]*C.x^6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[1]*C.x^23 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[1]*C.x^23[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.diffn() +[?7h[?12l[?25h[?2004l[?7h(x^35 + x^22*z1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.diffn()[?7h[?12l[?25h[?25l[?7l = C.z[1]*C.x^23[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]C.x^23[?7h[?12l[?25h[?25l[?7l[]/C.x^23[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[1]/C.x^5 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[1]/C.x^5[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^13 + z1)/x^6) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:  aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i)) +....:  print("2C, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....: for i in range((m-1)/2, M - (m+3)/2 + 1): +....:  aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3A, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  # +....:  aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1))) +....:  print("3B, ", i, aux.omega8.valuation() > 0) +....:  BASIS += [aux] +....:  +....:  +....: lista = [] +....: for a in BASIS: +....:  lista += a.coordinates(basis = BB) +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension()) +[?7h[?12l[?25h[?2004l1A, 0 True +1B, 0 True +1C, 0 True +1A, 1 True +1B, 1 True +1C, 1 True +2A, 2 True +2B, 2 True +2C, 2 True +2A, 3 True +2B, 3 True +2C, 3 True +3A, 2 True +3B, 2 True +3A, 3 True +3B, 3 True +3A, 4 True +3B, 4 True +3A, 5 True +3B, 5 True +3A, 6 True +3B, 6 True +3A, 7 True +3B, 7 True +3A, 8 True +3B, 8 True +3A, 9 True +3B, 9 True +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +File /ext/sage/9.8/src/sage/modules/free_module.py:6488, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized, category) + 6487 try: +-> 6488 basis = [ambient(x) for x in basis] + 6489 except TypeError: + 6490 # That failed, try the ambient vector space instead + +File /ext/sage/9.8/src/sage/modules/free_module.py:6488, in (.0) + 6487 try: +-> 6488 basis = [ambient(x) for x in basis] + 6489 except TypeError: + 6490 # That failed, try the ambient vector space instead + +File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__() + 895 if no_extra_args: +--> 896 return mor._call_(x) + 897 else: + +File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + +File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + +File /ext/sage/9.8/src/sage/modules/free_module.py:6355, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds) + 6354 pass +-> 6355 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds) + +File /ext/sage/9.8/src/sage/modules/free_module.py:2161, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check) + 2160 if isinstance(self, FreeModule_ambient): +-> 2161 return self.element_class(self, x, coerce, copy) + 2162 try: + +File /ext/sage/9.8/src/sage/modules/vector_mod2_dense.pyx:213, in sage.modules.vector_mod2_dense.Vector_mod2_dense.__init__() + 212 elif x != 0: +--> 213 raise TypeError("can't initialize vector from nonzero non-list") + 214 elif self._degree: + +TypeError: can't initialize vector from nonzero non-list + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +File /ext/sage/9.8/src/sage/modules/free_module.py:6494, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized, category) + 6493 try: +-> 6494 basis = [V(x) for x in basis] + 6495 except TypeError: + +File /ext/sage/9.8/src/sage/modules/free_module.py:6494, in (.0) + 6493 try: +-> 6494 basis = [V(x) for x in basis] + 6495 except TypeError: + +File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__() + 895 if no_extra_args: +--> 896 return mor._call_(x) + 897 else: + +File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + +File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + +File /ext/sage/9.8/src/sage/modules/free_module.py:6355, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds) + 6354 pass +-> 6355 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds) + +File /ext/sage/9.8/src/sage/modules/free_module.py:2161, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check) + 2160 if isinstance(self, FreeModule_ambient): +-> 2161 return self.element_class(self, x, coerce, copy) + 2162 try: + +File /ext/sage/9.8/src/sage/modules/vector_mod2_dense.pyx:213, in sage.modules.vector_mod2_dense.Vector_mod2_dense.__init__() + 212 elif x != 0: +--> 213 raise TypeError("can't initialize vector from nonzero non-list") + 214 elif self._degree: + +TypeError: can't initialize vector from nonzero non-list + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Cell In [60], line 45 + 42 lista += a.coordinates(basis = BB) + 44 V = F**(Integer(2)*C.genus()) +---> 45 print(V.subspace(lista).dimension()) + +File /ext/sage/9.8/src/sage/modules/free_module.py:4663, in FreeModule_generic_field.subspace(self, gens, check, already_echelonized) + 4620 def subspace(self, gens, check=True, already_echelonized=False): + 4621  """ + 4622  Return the subspace of ``self`` spanned by the elements of gens. + 4623 + (...) + 4661  ArithmeticError: argument gens (= [[1, 1, 0]]) does not generate a submodule of self + 4662  """ +-> 4663 return self.submodule(gens, check=check, already_echelonized=already_echelonized) + +File /ext/sage/9.8/src/sage/modules/free_module.py:1745, in Module_free_ambient.submodule(self, gens, check, already_echelonized) + 1743 if isinstance(gens, Module_free_ambient): + 1744 gens = gens.gens() +-> 1745 V = self.span(gens, check=check, already_echelonized=already_echelonized) + 1746 if check: + 1747 if not V.is_submodule(self): + +File /ext/sage/9.8/src/sage/modules/free_module.py:1660, in Module_free_ambient.span(self, gens, base_ring, check, already_echelonized) + 1658 gens = gens.gens() + 1659 if base_ring is None or base_ring is self.base_ring(): +-> 1660 return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized) + 1662 # The base ring has changed + 1663 try: + +File /ext/sage/9.8/src/sage/modules/free_module.py:7914, in FreeModule_submodule_field.__init__(self, ambient, gens, check, already_echelonized, category) + 7912 if is_FreeModule(gens): + 7913 gens = gens.gens() +-> 7914 FreeModule_submodule_with_basis_field.__init__(self, ambient, basis=gens, check=check, + 7915  echelonize=not already_echelonized, already_echelonized=already_echelonized, + 7916  category=category) + +File /ext/sage/9.8/src/sage/modules/free_module.py:7714, in FreeModule_submodule_with_basis_field.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized, category) + 7698 def __init__(self, ambient, basis, check=True, + 7699 echelonize=False, echelonized_basis=None, already_echelonized=False, + 7700 category=None): + 7701  """ + 7702  Create a vector space with given basis. + 7703 + (...) + 7712  [4 5 6] + 7713  """ +-> 7714 FreeModule_submodule_with_basis_pid.__init__( + 7715  self, ambient, basis=basis, check=check, echelonize=echelonize, + 7716  echelonized_basis=echelonized_basis, already_echelonized=already_echelonized, + 7717  category=category) + +File /ext/sage/9.8/src/sage/modules/free_module.py:6496, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized, category) + 6494 basis = [V(x) for x in basis] + 6495 except TypeError: +-> 6496 raise TypeError("each element of basis must be in " + 6497 "the ambient vector space") + 6499 if echelonize and not already_echelonized: + 6500 basis = self._echelonized_basis(ambient, basis) + +TypeError: each element of basis must be in the ambient vector space +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = [][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7lsage: lista +[?7h[?12l[?25h[?2004l[?7h[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, + 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, + 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, + 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, + 1, + 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, + 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, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 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, + 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, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 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, + 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, + 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, + 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, + 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, + 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, + 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, + 1, + 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, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 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, + 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, + 1, + 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, + 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, + 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, + 1, + 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, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7len(Z[0])[?7h[?12l[?25h[?25l[?7llen[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: len(lista) +[?7h[?12l[?25h[?2004l[?7h784 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(lista)[?7h[?12l[?25h[?25l[?7lista[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lsage: lista2 = [ +....: [?7h[?12l[?25h[?25l[?7l[ +][?7h[?12l[?25h[?25l[?7lsage: lista2 = [ +....: ] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista2 = [[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 2*C.genus() +[?7h[?12l[?25h[?2004l[?7h28 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7*2 + 1[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l784.[?7h[?12l[?25h[?25l[?7l784[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: 784/28 +[?7h[?12l[?25h[?2004l[?7h28 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lista = [] +....: for a in BASIS: +....:  lista += [a.coordinates(basis = BB)] +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7lsage: lista = [] +....: for a in BASIS: +....:  lista += [a.coordinates(basis = BB)] +....:  +....: V = F^(2*C.genus()) +....: print(V.subspace(lista).dimension()) +[?7h[?12l[?25h[?2004l28 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS = [][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: BASIS +[?7h[?12l[?25h[?2004l[?7h[( (z0) * dx, z0*z1/(x^12 + x^8) ), + ( (z1) * dx, z0*z1/(x^8 + x^4) ), + ( (1) * dx, 0 ), + ( (x*z0) * dx, z0*z1/(x^11 + x^7) ), + ( (x*z1) * dx, z0*z1/(x^7 + x^3) ), + ( (x) * dx, 0 ), + ( (x^10*z0 + x^2*z1) * dx, (x^4*z0*z1 + z1)/x^6 ), + ( (x^10) * dx, z1/x^2 ), + ( (x^2) * dx, z0/x^2 ), + ( (x^11*z0 + x^3*z1) * dx, (x^4*z0*z1 + z1)/x^5 ), + ( (x^11) * dx, z1/x ), + ( (x^3) * dx, z0/x ), + ( (x^2*z0) * dx, z0*z1/(x^10 + x^6) ), + ( (x^2) * dx, z1/(x^10 + x^6) ), + ( (x^3*z0) * dx, z0*z1/(x^9 + x^5) ), + ( (x^3) * dx, z1/(x^9 + x^5) ), + ( (x^4*z0) * dx, z0*z1/(x^8 + x^4) ), + ( (x^4) * dx, z1/(x^8 + x^4) ), + ( (x^5*z0) * dx, z0*z1/(x^7 + x^3) ), + ( (x^5) * dx, z1/(x^7 + x^3) ), + ( (x^6*z0) * dx, z0*z1/(x^6 + x^2) ), + ( (x^6) * dx, z1/(x^6 + x^2) ), + ( (x^7*z0) * dx, z0*z1/(x^5 + x) ), + ( (x^7) * dx, z1/(x^5 + x) ), + ( (x^8*z0) * dx, z0*z1/(x^4 + 1) ), + ( (x^8) * dx, z1/(x^4 + 1) ), + ( (x^9*z0) * dx, x*z0*z1/(x^4 + 1) ), + ( (x^9) * dx, x*z1/(x^4 + 1) )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lin BASIS:[?7h[?12l[?25h[?25l[?7lsage: for a in BASIS: +....: [?7h[?12l[?25h[?25l[?7lprint("3B, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7laux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(a.f.coordinates(basis = BOX)) +....: [?7h[?12l[?25h[?25l[?7lsage: for a in BASIS: +....:  print(a.f.coordinates(basis = BOX)) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [68], line 2 + 1 for a in BASIS: +----> 2 print(a.f.coordinates(basis = BOX)) + +File :149, in coordinates(self, prec, basis) + +TypeError: 'as_function' object is not iterable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in BASIS: +....:  print(a.f.coordinates(basis = BOX))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(a.f.coordinates()) +....: [?7h[?12l[?25h[?25l[?7lsage: for a in BASIS: +....:  print(a.f.coordinates()) +....:  +[?7h[?12l[?25h[?2004l[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 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, 1, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 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, 1, 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, 1, 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, 1, 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, 1, 0, 0, 0, 0, 0, 1] +[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la in BASIS:[?7h[?12l[?25h[?25l[?7lsage: for a in BASIS: +....: [?7h[?12l[?25h[?25l[?7lif len(V.linear_dependence([y1_coor, y2_coor])) > 0:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +....: for a in BASIS: +....:  if a.f.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv28*[0][?7h[?12l[?25h[?25l[?7le28*[0][?7h[?12l[?25h[?25l[?7lc28*[0][?7h[?12l[?25h[?25l[?7lt28*[0][?7h[?12l[?25h[?25l[?7lo28*[0][?7h[?12l[?25h[?25l[?7lr28*[0][?7h[?12l[?25h[?25l[?7l(28*[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF28*[0])[?7h[?12l[?25h[?25l[?7l,28*[0])[?7h[?12l[?25h[?25l[?7l 28*[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()"[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:  if a.f.coordinates() == vector(F, 28*[0]): +....: [?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l....:  licz += 1 +....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l +....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: licz = 0 +....: for a in BASIS: +....:  if a.f.coordinates() == vector(F, 28*[0]): +....:  licz += 1 +....: print(licz) +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: licz = 0 +....: for a in BASIS: +....:  if a.f.coordinates() == vector(F, 28*[0]): +....:  licz += 1 +....: print(licz)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lla.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7lia.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7lsa.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7lta.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7llist(a.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7llista.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7la.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7la.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7la.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7la.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[0]):[?7h[?12l[?25h[?25l[?7l*[0]):[?7h[?12l[?25h[?25l[?7l1*[0]):[?7h[?12l[?25h[?25l[?7l4*[0]):[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: licz = 0 +....: for a in BASIS: +....:  if a.f.coordinates() == vector(F, 14*[0]): +....:  licz += 1 +....: print(licz) +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: licz = 0 +....: for a in BASIS: +....:  if a.f.coordinates() == vector(F, 14*[0]): +....:  licz += 1 +....: print(licz)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]:[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lla.f.cordinates() = 14*[0]:[?7h[?12l[?25h[?25l[?7lia.f.cordinates() = 14*[0]:[?7h[?12l[?25h[?25l[?7lsa.f.cordinates() = 14*[0]:[?7h[?12l[?25h[?25l[?7lta.f.cordinates() = 14*[0]:[?7h[?12l[?25h[?25l[?7llist(a.f.cordinates() = 14*[0]:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()) = 14*[0]:[?7h[?12l[?25h[?25l[?7l() +[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: licz = 0 +....: for a in BASIS: +....:  if list(a.f.coordinates()) == 14*[0]: +....:  licz += 1 +....: print(licz) +[?7h[?12l[?25h[?2004l12 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: licz = 0 +....: for a in BASIS: +....:  if list(a.f.coordinates()) == 14*[0]: +....:  licz += 1 +....: print(licz)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + +a.f.coordinates() == vector(F, 14*[0]): + +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + +28 + +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS: + print(a.f.coordinates()) +  +  + [?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for a in BASIS: +....:  print(a.f.coordinates()) +....:  +[?7h[?12l[?25h[?2004l[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 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, 1, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0] +[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 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, 1, 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, 1, 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, 1, 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, 1, 0, 0, 0, 0, 0, 1] +[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[4] +[?7h[?12l[?25h[?2004l[?7h( (x*z1) * dx, z0*z1/(x^7 + x^3) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[4][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[-10] +[?7h[?12l[?25h[?2004l[?7h( (x^5*z0) * dx, z0*z1/(x^7 + x^3) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicz = 0[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 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 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 1 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 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 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 1 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 1 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 1 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 1 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 1 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 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 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 1 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 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 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 1 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 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 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 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 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 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 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 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 1] + + +[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 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 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 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 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 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 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 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 1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 0] +[1 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^8 ) ( (x*z0) * dx, 0 ) +(0) * dx ((x^6*z0 + z1)/x^2) * dx (0) * dx +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 ) +(0) * dx ((x^13*z0 + x^7*z1 + z0*z1)/x^8) * dx (0) * dx +1A, 0 True +1B, 0 True +1C, 0 True +1A, 1 True +1B, 1 True +1C, 1 True +1A, 2 True +1B, 2 True +1C, 2 True +2A, 3 True +2B, 3 True +2C, 3 True +2A, 4 False +2B, 4 True +2C, 4 True +2A, 5 True +2B, 5 True +2C, 5 True +3A, 3 True +3B, 3 True +3A, 4 True +3B, 4 True +3A, 5 True +3B, 5 True +3A, 6 True +3B, 6 True +3A, 7 True +3B, 7 True +3A, 8 True +3B, 8 True +30 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[-10][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l`[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[12] +[?7h[?12l[?25h[?2004l[?7h( (x^10*z0 + x^4*z1) * dx, (x^3*z0*z1 + z1)/x^5 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[12][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: BASIS[12].omega8.valuation() >= 0 +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l in BASIS:[?7h[?12l[?25h[?25l[?7lsage: for a in BASIS: +....: [?7h[?12l[?25h[?25l[?7lprint(a.f.coordinates())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lprint(a.f.coordinates())[?7h[?12l[?25h[?25l[?7l....:  print(a.f.coordinates()) +....: [?7h[?12l[?25h[?25l[?7lsage: for a in BASIS: +....:  print(a.f.coordinates()) +....:  +[?7h[?12l[?25h[?2004l[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 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, 1, 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, 0] +[0, 0, 0, 0, 0, 0, 1, 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, 1, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0] +[1, 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, 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, 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, 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, 1, 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, 1, 0, 0, 1, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[12].omega8.valuation() >= 0[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-10][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[-10] +[?7h[?12l[?25h[?2004l[?7h( (x^4*z0) * dx, z0*z1/(x^8 + x^5) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[-10][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[4] +[?7h[?12l[?25h[?2004l[?7h( (x*z1) * dx, z0*z1/(x^8 + x^5) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 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 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 1 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 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 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 1 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 1 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 1 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 1 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 1 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 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 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 1 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 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 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 1 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 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 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 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 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 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 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 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 1] + + +[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 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 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 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 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 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 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 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 1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^8 ) ( (x*z0) * dx, 0 ) +(0) * dx ((x^6*z0 + z1)/x^2) * dx (0) * dx +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 ) +(0) * dx ((x^13*z0 + x^7*z1 + z0*z1)/x^8) * dx (0) * dx +1A, 0 True +1B, 0 True +1C, 0 True +1A, 1 True +1B, 1 True +1C, 1 True +1A, 2 True +1B, 2 True +1C, 2 True +2A, 3 True +2B, 3 True +2C, 3 True +2A, 4 True +2B, 4 True +2C, 4 True +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [82], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :109 + +File :18, in __init__(self, C, omega, f) + +ValueError: cech cocycle not regular +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 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 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 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 1 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 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 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 1 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] +[0 0 0 0 0 0 0 1 0 0 0 0 1 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 1 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 1 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 1 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 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 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 1 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 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 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 1 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 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 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 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 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 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 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 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 1] + + +[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 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 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 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 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 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] +[0 0 0 0 0 0 0 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 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 1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 1] +[ +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 2 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2), +RModule of dimension 3 over GF(2) +] +{ +[1 0] +[1 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1] +[0 1], +[1 0] +[0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 1 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 1 0] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 1] +[0 1 0] +[0 0 1], +[1 0 1] +[0 1 1] +[0 0 1] +} +{ +[1 0 0] +[0 1 1] +[0 0 1], +[1 0 1] +[0 1 0] +[0 0 1] +} +( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 ) +(0) * dx (0) * dx (0) * dx +( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^8 ) ( (x*z0) * dx, 0 ) +(0) * dx ((x^6*z0 + z1)/x^2) * dx (0) * dx +( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 ) +(0) * dx ((x^13*z0 + x^7*z1 + z0*z1)/x^8) * dx (0) * dx +1A, 0 True +1B, 0 True +1C, 0 True +1A, 1 True +1B, 1 True +1C, 1 True +1A, 2 True +1B, 2 True +1C, 2 True +2A, 3 True +2B, 3 True +2C, 3 True +2A, 4 True +2B, 4 True +2C, 4 True +2A, 5 True +2B, 5 True +2C, 5 True +3A, 3 True +3B, 3 True +3A, 4 True +3B, 4 True +3A, 5 True +3B, 5 True +3A, 6 True +3B, 6 True +3A, 7 True +3B, 7 True +3A, 8 True +3B, 8 True +30 +[?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[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus() +[?7h[?12l[?25h[?2004l[?7h15 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [1], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :18 + +NameError: name 'A1' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1A, 0 True +1B, 0 True +1C, 0 True +1A, 1 True +1B, 1 True +1C, 1 True +1A, 2 True +1B, 2 True +1C, 2 True +2A, 3 True +2B, 3 True +2C, 3 True +2A, 4 True +2B, 4 True +2C, 4 True +2A, 5 True +2B, 5 True +2C, 5 True +3A, 3 True +3B, 3 True +3A, 4 True +3B, 4 True +3A, 5 True +3B, 5 True +3A, 6 True +3B, 6 True +3A, 7 True +3B, 7 True +3A, 8 True +3B, 8 True +Tyle form powinno być: 15 Tyle jest: 14 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[4][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: BASIS +[?7h[?12l[?25h[?2004l[?7h[( (z0) * dx, z0*z1/(x^12 + x^9) ), + ( (z1) * dx, z0*z1/(x^9 + x^6) ), + ( (1) * dx, 0 ), + ( (x*z0) * dx, z0*z1/(x^11 + x^8) ), + ( (x*z1) * dx, z0*z1/(x^8 + x^5) ), + ( (x) * dx, 0 ), + ( (x^2*z0) * dx, z0*z1/(x^10 + x^7) ), + ( (x^2*z1) * dx, z0*z1/(x^7 + x^4) ), + ( (x^2) * dx, 0 ), + ( (x^9*z0 + x^3*z1) * dx, (x^3*z0*z1 + z1)/x^6 ), + ( (x^9) * dx, z1/x^3 ), + ( (x^3) * dx, z0/x^3 ), + ( (x^10*z0 + x^4*z1) * dx, (x^3*z0*z1 + z1)/x^5 ), + ( (x^10) * dx, z1/x^2 ), + ( (x^4) * dx, z0/x^2 ), + ( (x^11*z0 + x^5*z1) * dx, (x^3*z0*z1 + z1)/x^4 ), + ( (x^11) * dx, z1/x ), + ( (x^5) * dx, z0/x ), + ( (x^3*z0) * dx, z0*z1/(x^9 + x^6) ), + ( (x^3) * dx, z1/(x^9 + x^6) ), + ( (x^4*z0) * dx, z0*z1/(x^8 + x^5) ), + ( (x^4) * dx, z1/(x^8 + x^5) ), + ( (x^5*z0) * dx, z0*z1/(x^7 + x^4) ), + ( (x^5) * dx, z1/(x^7 + x^4) ), + ( (x^6*z0) * dx, z0*z1/(x^6 + x^3) ), + ( (x^6) * dx, z1/(x^6 + x^3) ), + ( (x^7*z0) * dx, z0*z1/(x^5 + x^2) ), + ( (x^7) * dx, z1/(x^5 + x^2) ), + ( (x^8*z0) * dx, z0*z1/(x^4 + x) ), + ( (x^8) * dx, z1/(x^4 + x) )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (z0) * dx, + (x) * dx, + (x^4*z0 + x*z1) * dx, + (x*z0) * dx, + (x^2) * dx, + (x^5*z0 + x^2*z1) * dx, + (x^2*z0) * dx, + (x^3) * dx, + (x^3*z0) * dx, + (x^4) * dx, + (x^5) * dx, + (x^6) * dx, + (x^7) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lbC.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1:[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: for b in BASIS: +....: [?7h[?12l[?25h[?25l[?7lprint(a.f.coordinates())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lif list(a.f.coordinates()) == 14*[0]:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:  if b.f.valuation() >= 0: +....: [?7h[?12l[?25h[?25l[?7lpass[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreturn False[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l"2C, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l("2C, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l("2C, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print(b.omega0) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in BASIS: +....:  if b.f.valuation() >= 0: +....:  print(b.omega0) +....:  +[?7h[?12l[?25h[?2004l(z0) * dx +(1) * dx +(x*z0) * dx +(x) * dx +(x^2*z0) * dx +(x^2) * dx +(x^3) * dx +(x^4) * dx +(x^5) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: BASIS +[?7h[?12l[?25h[?2004l[?7h[( (z0) * dx, z0*z1/(x^12 + x^9) ), + ( (z1) * dx, z0*z1/(x^9 + x^6) ), + ( (1) * dx, 0 ), + ( (x*z0) * dx, z0*z1/(x^11 + x^8) ), + ( (x*z1) * dx, z0*z1/(x^8 + x^5) ), + ( (x) * dx, 0 ), + ( (x^2*z0) * dx, z0*z1/(x^10 + x^7) ), + ( (x^2*z1) * dx, z0*z1/(x^7 + x^4) ), + ( (x^2) * dx, 0 ), + ( (x^9*z0 + x^3*z1) * dx, (x^3*z0*z1 + z1)/x^6 ), + ( (x^9) * dx, z1/x^3 ), + ( (x^3) * dx, z0/x^3 ), + ( (x^10*z0 + x^4*z1) * dx, (x^3*z0*z1 + z1)/x^5 ), + ( (x^10) * dx, z1/x^2 ), + ( (x^4) * dx, z0/x^2 ), + ( (x^11*z0 + x^5*z1) * dx, (x^3*z0*z1 + z1)/x^4 ), + ( (x^11) * dx, z1/x ), + ( (x^5) * dx, z0/x ), + ( (x^3*z0) * dx, z0*z1/(x^9 + x^6) ), + ( (x^3) * dx, z1/(x^9 + x^6) ), + ( (x^4*z0) * dx, z0*z1/(x^8 + x^5) ), + ( (x^4) * dx, z1/(x^8 + x^5) ), + ( (x^5*z0) * dx, z0*z1/(x^7 + x^4) ), + ( (x^5) * dx, z1/(x^7 + x^4) ), + ( (x^6*z0) * dx, z0*z1/(x^6 + x^3) ), + ( (x^6) * dx, z1/(x^6 + x^3) ), + ( (x^7*z0) * dx, z0*z1/(x^5 + x^2) ), + ( (x^7) * dx, z1/(x^5 + x^2) ), + ( (x^8*z0) * dx, z0*z1/(x^4 + x) ), + ( (x^8) * dx, z1/(x^4 + x) )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor b in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb in BASIS:[?7h[?12l[?25h[?25l[?7lsage: for b in BASIS: +....: [?7h[?12l[?25h[?25l[?7lprint(a.f.coordinates())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lbserre_uality_pairing(om))[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(b.f.coordinates()) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in BASIS: +....:  print(b.f.coordinates()) +....:  +[?7h[?12l[?25h[?2004l[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 0, 0, 0, 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, 1, 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, 0] +[0, 0, 0, 0, 0, 0, 1, 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, 1, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +[0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0] +[1, 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, 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, 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, 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, 1, 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, 1, 0, 0, 1, 0] +[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lIS[?7h[?12l[?25h[?25l[?7l[4][?7h[?12l[?25h[?25l[?7l12].omega8.valuation() >= 0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[11] +[?7h[?12l[?25h[?2004l[?7h( (x^3) * dx, z0/x^3 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[11][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[-0][?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[-5] +[?7h[?12l[?25h[?2004l[?7h( (x^6) * dx, z1/(x^6 + x^3) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[-5][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: BASIS[11].f.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[11].f.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].f.cordinates()[?7h[?12l[?25h[?25l[?7l].f.cordinates()[?7h[?12l[?25h[?25l[?7l-].f.cordinates()[?7h[?12l[?25h[?25l[?7l5].f.cordinates()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: BASIS[-5].f.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[-5].f.coordinates()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: BASIS[9].f.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[9].f.coordinates()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[9] +[?7h[?12l[?25h[?2004l[?7h( (x^9*z0 + x^3*z1) * dx, (x^3*z0*z1 + z1)/x^6 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[9][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: BASIS +[?7h[?12l[?25h[?2004l[?7h[( (z0) * dx, z0*z1/(x^12 + x^9) ), + ( (z1) * dx, z0*z1/(x^9 + x^6) ), + ( (1) * dx, 0 ), + ( (x*z0) * dx, z0*z1/(x^11 + x^8) ), + ( (x*z1) * dx, z0*z1/(x^8 + x^5) ), + ( (x) * dx, 0 ), + ( (x^2*z0) * dx, z0*z1/(x^10 + x^7) ), + ( (x^2*z1) * dx, z0*z1/(x^7 + x^4) ), + ( (x^2) * dx, 0 ), + ( (x^9*z0 + x^3*z1) * dx, (x^3*z0*z1 + z1)/x^6 ), + ( (x^9) * dx, z1/x^3 ), + ( (x^3) * dx, z0/x^3 ), + ( (x^10*z0 + x^4*z1) * dx, (x^3*z0*z1 + z1)/x^5 ), + ( (x^10) * dx, z1/x^2 ), + ( (x^4) * dx, z0/x^2 ), + ( (x^11*z0 + x^5*z1) * dx, (x^3*z0*z1 + z1)/x^4 ), + ( (x^11) * dx, z1/x ), + ( (x^5) * dx, z0/x ), + ( (x^3*z0) * dx, z0*z1/(x^9 + x^6) ), + ( (x^3) * dx, z1/(x^9 + x^6) ), + ( (x^4*z0) * dx, z0*z1/(x^8 + x^5) ), + ( (x^4) * dx, z1/(x^8 + x^5) ), + ( (x^5*z0) * dx, z0*z1/(x^7 + x^4) ), + ( (x^5) * dx, z1/(x^7 + x^4) ), + ( (x^6*z0) * dx, z0*z1/(x^6 + x^3) ), + ( (x^6) * dx, z1/(x^6 + x^3) ), + ( (x^7*z0) * dx, z0*z1/(x^5 + x^2) ), + ( (x^7) * dx, z1/(x^5 + x^2) ), + ( (x^8*z0) * dx, z0*z1/(x^4 + x) ), + ( (x^8) * dx, z1/(x^4 + x) )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^7 +z1^2 - z1 = x^13 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha = C.x^((M - m)/2)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: alpha +[?7h[?12l[?25h[?2004l[?7hx^3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1A, 0 True +1B, 0 True +1C, 0 True +1A, 1 True +1B, 1 True +1C, 1 True +1A, 2 True +1B, 2 True +1C, 2 True +2A, 3 True +2B, 3 True +2C, 3 True +2A, 4 True +2B, 4 True +2C, 4 True +2A, 5 True +2B, 5 True +2C, 5 True +3A, 3 True +3B, 3 True +3A, 4 True +3B, 4 True +3A, 5 True +3B, 5 True +3A, 6 True +3B, 6 True +3A, 7 True +3B, 7 True +3A, 8 True +3B, 8 True +Tyle form powinno być: 15 Tyle jest: 20 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lchlogy_of_structure_hef_basis()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis() + C.cartier_matrix C.cohomology_of_structure_sheaf_basis + C.characteristic C.crystalline_cohomology_basis  + + + [?7h[?12l[?25h[?25l[?7lartier_matrix + C.cartier_matrix  + + [?7h[?12l[?25h[?25l[?7lharacteristc + C.cartier_matrix  + C.characteristic [?7h[?12l[?25h[?25l[?7lrystalline_cohomology_basis + + C.characteristic  C.crystalline_cohomology_basis [?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lCrys of C: +( [0] d[x] + [1] d[y] + V((x^5 + x^3) dy) + dV(0), V(((x^2 + 1)/x)*y) ) +( [0] d[x] + [x] d[y] + V((x^8 + 2*x^6 + 1) dy) + dV(0), [2/x*y] + V((x^4 + x^2 + 1)*y) ) +Crys of C1: +( [0] d[x] + [2] d[y] + V((2*x^3 + 2*x) dy) + dV(0), V(((x^6 + x^4 + 2)/x^3)*y) ) +( [0] d[x] + [2*x] d[y] + V((2*x^14 + 2*x^12 + 2*x^6 + 2*x^4 + x^2) dy) + dV(0), V(((x^10 + x^8 + 2*x^4 + x^2 + 2)/x^4)*y) ) +( [0] d[x] + [2*x^2] d[y] + V((x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3) dy) + dV(0), V(((x^12 + x^10 + 2*x^6 + x^4 + 2*x^2 + 1)/x^3)*y) ) +( [0] d[x] + [2*x^3] d[y] + V((2*x^12 + 2*x^10 + x^8 + x^6 + 2*x^4 + 1) dy) + dV(0), V(((x^16 + x^14 + 2*x^10 + x^8 + 2*x^6 + x^4 + x^2 + 1)/x^4)*y) ) +( [0] d[x] + [2*x^7 + 2*x] d[y] + V((2*x^32 + 2*x^30 + 2*x^24 + 2*x^22 + x^20 + x^16 + x^12 + x^10 + 2*x^8 + 2*x^2 + 1) dy) + dV(0), [2/x*y] + V(((x^26 + x^24 + 2*x^20 + x^18 + 2*x^16 + x^14 + x^12 + x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 1)/x^2)*y) ) +( [0] d[x] + [x^6 + 1] d[y] + V((x^21 + x^19 + 2*x^17 + 2*x^15 + x^13 + x^11 + 2*x^9 + x^7) dy) + dV(0), [2/x^2*y] + V(((2*x^24 + 2*x^22 + x^18 + 2*x^16 + x^14 + 2*x^12 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^4 + x^2 + 2)/x^3)*y) ) +( [0] d[x] + [0] d[y] + V((2*x^8 + x^2 + 1) dy) + dV(0), [2/x^3*y] ) +( [0] d[x] + [2*x^4] d[y] + V((2*x^23 + 2*x^21 + 2*x^15 + 2*x^13 + x^11 + x^7 + 2*x^3 + x) dy) + dV(0), [2/x^4*y] + V(((x^16 + x^14 + 2*x^10 + x^8 + 2*x^6 + x^4 + x^2 + 1)/x)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpsp(3, 31)> jprime(2*6, 2)^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: p] +[?7h[?12l[?25h[?2004l Cell In [3], line 1 + p] + ^ +SyntaxError: unmatched ']' + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp][?7h[?12l[?25h[?25l[?7lsage: p +[?7h[?12l[?25h[?2004l[?7h3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1] + alpha*C.x^m).valuation()[?7h[?12l[?25h[?25l[?7lx^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3).quo_rem(x^3 - x) +[?7h[?12l[?25h[?2004l[?7h(x^14 + 2*x^12 + 2*x^10 + 2*x^8 + x^6 + x^2, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha[?7h[?12l[?25h[?25l[?7ldic_expansion_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1), x^3 - x)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: adic_expansion + adic_expansion  + adic_expansion_polynomial + + + [?7h[?12l[?25h[?25l[?7l_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1), x^3 - x)[?7h[?12l[?25h[?25l[?7l_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1), x^3 - x) + +[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lx^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3, x^3 - x) +[?7h[?12l[?25h[?2004l[?7hx^2*t^5 + 2*x*t^4 + 2*x*t^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lxi.omega8[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x^2*((x^3 - x)^5 + (x^3 - x)^3) +[?7h[?12l[?25h[?2004l[?7hx^17 + x^15 + x^13 + 2*x^9 + 2*x^7 + 2*x^5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lx^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx^17 + x^15 + x^13 + 2*x^9 + 2*x^7 + 2*x^5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3 - (x^17 + x^15 + x^13 + 2*x^9 + 2*x^7 + 2*x^5) +[?7h[?12l[?25h[?2004l[?7h2*x^13 + 2*x^5 + 2*x^3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l2*13 + 2*x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(2*x^13 + 2*x^5 + 2*x^3, x^3 - x) +[?7h[?12l[?25h[?2004l[?7h2*x*t^4 + 2*x^2*t^3 + 2*x*t^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^13 + 2*x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1 +Crys of C: +( [0] d[x] + [1] d[y] + V((x^5 + x^3 + 2*x^2 + 2) dy) + dV(0), V(((x^2 + 2*x + 1)/x)*y) ) +( [0] d[x] + [x] d[y] + V((x^8 + 2*x^6 + x^5 + 2*x^3 + x^2 + x + 1) dy) + dV(0), [2/x*y] + V(((x^5 + 2*x^4 + x^3 + x^2 + 2*x + 2)/x)*y) ) + +Crys of C1: +( [0] d[x] + [2] d[y] + V((2*x^3 + 2*x + 2) dy) + dV(0), V(((x^6 + x^4 + x^3 + 2)/x^3)*y) ) +( [0] d[x] + [2*x] d[y] + V((2*x^14 + 2*x^12 + 2*x^11 + 2*x^6 + 2*x^4 + 2*x^3 + x^2) dy) + dV(0), V(((x^10 + x^8 + x^7 + 2*x^4 + x^2 + x + 2)/x^4)*y) ) +( [0] d[x] + [2*x^2] d[y] + V((x^17 + x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + 1) dy) + dV(0), V(((x^11 + x^9 + x^8 + 2*x^5 + x^3 + x^2 + 2*x + 1)/x^2)*y) ) +( [0] d[x] + [2*x^3] d[y] + V((2*x^12 + 2*x^10 + 2*x^9 + x^8 + x^6 + 2*x^4 + 2*x^3 + x + 1) dy) + dV(0), V(((x^16 + x^14 + x^13 + 2*x^10 + x^8 + x^7 + 2*x^6 + x^5 + x^2 + x + 1)/x^4)*y) ) +( [0] d[x] + [2*x^7 + 2*x] d[y] + V((2*x^32 + 2*x^30 + 2*x^29 + 2*x^24 + 2*x^22 + 2*x^21 + x^20 + 2*x^17 + x^16 + 2*x^14 + x^13 + x^12 + 2*x^11 + x^10 + x^8 + 2*x^7 + 2*x^5 + x^4 + x^3 + x + 1) dy) + dV(0), [2/x*y] + V(((x^28 + x^26 + x^25 + 2*x^22 + x^20 + x^19 + 2*x^18 + x^17 + x^14 + x^13 + x^12 + 2*x^11 + 2*x^10 + x^9 + 2*x^8 + 2*x^7 + 2*x^6 + x^5 + x^4 + x^3 + 2*x^2 + 2*x + 2)/x^4)*y) ) +( [0] d[x] + [x^6 + 1] d[y] + V((x^21 + x^19 + x^18 + 2*x^17 + 2*x^15 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + 2*x^4 + x^3 + x) dy) + dV(0), [2/x^2*y] + V(((2*x^25 + 2*x^23 + 2*x^22 + x^19 + 2*x^17 + 2*x^16 + x^15 + 2*x^14 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + 2*x^6 + x^5 + x^4 + x^3 + 2*x^2 + 2)/x^4)*y) ) +( [0] d[x] + [0] d[y] + V((2*x^8 + x^2 + 1) dy) + dV(0), [2/x^3*y] ) +( [0] d[x] + [2*x^4] d[y] + V((2*x^23 + 2*x^21 + 2*x^20 + 2*x^15 + 2*x^13 + 2*x^12 + x^11 + 2*x^8 + x^7 + 2*x^5 + x^4 + 2*x^3 + x) dy) + dV(0), [2/x^4*y] + V(((x^19 + x^17 + x^16 + 2*x^13 + x^11 + x^10 + 2*x^9 + x^8 + x^5 + x^4 + x^3 + 2*x^2 + x + 1)/x^4)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lx^17 + x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + 1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: (x^17 + x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + 1) - x^2 * 1 +[?7h[?12l[?25h[?2004l[?7hx^17 + x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = G1.irreducible_characters()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: X = x^3 - x +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX = x^3 - x[?7h[?12l[?25h[?25l[?7l(x^17 +x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + 1) - x^2 * 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 1[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx^5 + x^3 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2 + 2)[?7h[?12l[?25h[?25l[?7lX^2 + 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^3 + 2*X^2 + 2)[?7h[?12l[?25h[?25l[?7lX^3 + 2*X^2 + 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^5 + X^3 + 2*X^2 + 2)[?7h[?12l[?25h[?25l[?7lX^5 + X^3 + 2*X^2 + 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^17 + x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + 1) - x^2 * (X^5 + X^3 + 2*X^2 + 2) +[?7h[?12l[?25h[?2004l[?7hx^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^13 + 2*x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(2*x^13 + 2*x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lx^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^3 - x) +[?7h[?12l[?25h[?2004l[?7h(x^2 + 2*x + 1)*t^4 + (2*x^2 + x)*t^3 + (2*x^2 + 2*x + 1)*t^2 + x*t + 2*x^2 + 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lclass test:[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lclass test:[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = crys[0].regular_form() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = crys[0].regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lsage: om.valuation() + om.capitalize om.encode om.format om.isalpha om.isidentifier om.isspace om.ljust om.partition om.rfind om.rsplit om.startswith   + om.casefold om.endswith om.format_map om.isascii om.islower om.istitle om.lower om.removeprefix om.rindex om.rstrip om.strip   + om.center om.expandtabs om.index om.isdecimal om.isnumeric om.isupper om.lstrip om.removesuffix om.rjust om.split om.swapcase > + om.count om.find om.isalnum om.isdigit om.isprintable om.join om.maketrans om.replace om.rpartition om.splitlines om.title   + [?7h[?12l[?25h[?25l[?7lcapitalize + om.capitalize  + + + + [?7h[?12l[?25h[?25l[?7lencode + om.capitalize  om.encode [?7h[?12l[?25h[?25l[?7lformat + om.encode  om.format [?7h[?12l[?25h[?25l[?7lisalpha + om.format  om.isalpha [?7h[?12l[?25h[?25l[?7lidentifier + om.isalpha  om.isidentifier[?7h[?12l[?25h[?25l[?7lspace + om.isidentifier om.isspace [?7h[?12l[?25h[?25l[?7lljust + om.isspace  om.ljust [?7h[?12l[?25h[?25l[?7lpartition + om.ljust  om.partition [?7h[?12l[?25h[?25l[?7lrfind + om.partition  om.rfind [?7h[?12l[?25h[?25l[?7lsplit + om.rfind  om.rsplit [?7h[?12l[?25h[?25l[?7lstartswith + om.rsplit  om.startswith [?7h[?12l[?25h[?25l[?7ltrnslate + encode formatisalphaidentifierspace ljust partitionrfind splitstartswithtrnslate   + endswithformat_mapisascii lowertitlelower removeprefixindex stripstrip upper  +<expandtabsindex scimalnumericupp ltrip removesuffixjust spliwapcasezfill   + find isalnumdigitprinablejoin maketransreplace partitionslilinestitle    [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstrtswith + om.startswith  om.translate [?7h[?12l[?25h[?25l[?7lrsplit + om.rsplit  om.startswith [?7h[?12l[?25h[?25l[?7lfind + om.rfind  om.rsplit [?7h[?12l[?25h[?25l[?7lpartition + om.partition  om.rfind [?7h[?12l[?25h[?25l[?7lljust + om.ljust  om.partition [?7h[?12l[?25h[?25l[?7lisspace + om.isspace  om.ljust [?7h[?12l[?25h[?25l[?7lidentifier + om.isidentifier om.isspace [?7h[?12l[?25h[?25l[?7lalpha + om.isalpha  om.isidentifier[?7h[?12l[?25h[?25l[?7lformat + om.format  om.isalpha [?7h[?12l[?25h[?25l[?7lencode + om.encode  om.format [?7h[?12l[?25h[?25l[?7lcapitalize + capitalizeencodeformat alpha identifierisspaceljust partitionfind rsplit strtswith  + casefoldendswith format_mapasciiloweristitlelower emoveprefixindexrstripstrip  + center expandtabsnx decimalnumiciupperlstrip emovesuffixrjusplit swapcase> + countfind alnumdigi isprintablejoin maketranseplace raritionsplitlines om.title   [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + + + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = crys[0].regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om +[?7h[?12l[?25h[?2004l[?7h'( [0] d[x] + [1] d[y] + V((x^5 + x^3 + 2*x^2 + 2) dy) + dV(0), V(((x^2 + 2*x + 1)/x)*y) )' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lclass test:[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(crys1[2][?7h[?12l[?25h[?25l[?7l-crys1[2][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (-crys1[2]).regular_form() +[?7h[?12l[?25h[?2004l[?7h'( [0] d[x] + [x^2] d[y] + V((2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2) dy) + dV(0), V(((2*x^11 + 2*x^9 + 2*x^8 + x^5 + 2*x^3 + 2*x^2 + x + 2)/x^2)*y) )' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7l|[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX = x^3 - x[?7h[?12l[?25h[?25l[?7lsage: X +[?7h[?12l[?25h[?2004l[?7hx^3 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 -[?7h[?12l[?25h[?25l[?7l 2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 -[?7h[?12l[?25h[?25l[?7l=2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 -[?7h[?12l[?25h[?25l[?7l 2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A = 2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 - x^6*(X^5+X^3 + 2*X^2 + 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = 2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 - x^6*(X^5+X^3 + 2*X^2 + 2)[?7h[?12l[?25h[?25l[?7lsage: A +[?7h[?12l[?25h[?2004l[?7h2*x^21 + 2*x^19 + x^17 + 2*x^15 + 2*x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^9 + x^8 + x^7 + 2*x^6 + 2*x^5 + x^3 + 2*x^2 + 2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor n in range(n0 + 1, 30):[?7h[?12l[?25h[?25l[?7lsage: f +[?7h[?12l[?25h[?2004l[?7hx^3 + 2*x + 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: A/f +[?7h[?12l[?25h[?2004l[?7h(2*x^21 + 2*x^19 + x^17 + 2*x^15 + 2*x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^9 + x^8 + x^7 + 2*x^6 + 2*x^5 + x^3 + 2*x^2 + 2)/(x^3 + 2*x + 1) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(x^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^3 - x)[?7h[?12l[?25h[?25l[?7l.nth_root(p)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA/f[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.quo_rem(f) +[?7h[?12l[?25h[?2004l[?7h(2*x^18 + x^16 + x^15 + 2*x^14 + x^10 + x^9 + 2*x^8 + x^7 + 2*x^3 + 2*x^2 + 2*x + 1, + 2*x^2 + 2*x + 1) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(x^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(x^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l(, f)[?7h[?12l[?25h[?25l[?7lA, f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(A, f) +[?7h[?12l[?25h[?2004l[?7h2*t^7 + (x + 1)*t^6 + (x^2 + 2)*t^5 + (2*x + 1)*t^4 + x^2*t^3 + (2*x^2 + x + 1)*t^2 + 2*x^2 + 2*x + 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega.cartier()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = a*omega[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: omega = C1.x^2*C1.dy +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [25], line 1 +----> 1 omega = C1.x**Integer(2)*C1.dy + +AttributeError: 'superelliptic' object has no attribute 'dy' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C1.x^2*C1.dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega = C1.x^2*C1.y.diffn() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C1.x^2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega +[?7h[?12l[?25h[?2004l[?7h((-x^2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(omega)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift_form0(omega) +[?7h[?12l[?25h[?2004l[?7h[(2*x^2/(x^9 + x^3 + x + 1))*y] d[x] + V(((-x^35 - x^33 - x^32 + x^29 - x^26 - x^25 - x^23 - x^20 + x^19 + x^16 + x^15 - x^13 + x^10 - x^9 + x^8 - x^7 - x^6)/(x^18*y - x^12*y - x^10*y - x^9*y + x^6*y - x^4*y - x^3*y + x^2*y - x*y + y)) dx) + dV([((2*x^27 + 2*x^25 + 2*x^24 + 2*x^21 + x^19 + x^18 + 2*x^17 + x^16 + 2*x^15 + 2*x^13 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + 2*x^7)/(x^18 + 2*x^12 + 2*x^10 + 2*x^9 + x^6 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1))*y]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(omega)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift_form0(omega).regular_form() +[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [x^2] d[y] + V((0) dy) + dV(0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(omega).regular_form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(omega)[?7h[?12l[?25h[?25l[?7l8(omega)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7l = C1.x^2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ldy[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(A, f)[?7h[?12l[?25h[?25l[?7lomega = C1.x^2*C1.dy[?7h[?12l[?25h[?25l[?7ly.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(omega).regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]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$ p = 3 + m = 2 + F = GF(p) + Rx. = PolynomialRing(F) + f = x^3 - x + C = superelliptic(f, m) +bash: p: command not found +bash: m: command not found +bash: syntax error near unexpected token `(' +bash: syntax error near unexpected token `(' +bash: f: command not found +bash: syntax error near unexpected token `(' +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: p = 3 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: f = x^3 - x +....: C = superelliptic(f, m)[?7h[?12l[?25h[?25l[?7lsage: p = 3 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: f = x^3 - x +....: C = superelliptic(f, m) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [1], line 6 + 4 Rx = PolynomialRing(F, names=('x',)); (x,) = Rx._first_ngens(1) + 5 f = x**Integer(3) - x +----> 6 C = superelliptic(f, m) + +NameError: name 'superelliptic' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: p = 3 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: f = x^3 - x +....: C = superelliptic(f, m)[?7h[?12l[?25h[?25l[?7lsage: p = 3 +....: m = 2 +....: F = GF(p) +....: Rx. = PolynomialRing(F) +....: f = x^3 - x +....: C = superelliptic(f, m) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(f, m)[?7h[?12l[?25h[?25l[?7l.holomophic_dfferentials_basis()[?7h[?12l[?25h[?25l[?7lx_series[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: C.x_series +[?7h[?12l[?25h[?2004l[?7h[t^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lafty/[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(3) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [6], line 1 +----> 1 at_most_poles_superelliptic(Integer(3)) + +TypeError: at_most_poles_superelliptic() missing 1 required positional argument: 'pole_order' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC3)[?7h[?12l[?25h[?25l[?7l,3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [7], line 1 +----> 1 at_most_poles_superelliptic(C,Integer(3)) + +File :17, in at_most_poles_superelliptic(self, pole_order, threshold) + +AttributeError: 'superelliptic' object has no attribute 'height' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7lC,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [9], line 1 +----> 1 at_most_poles_superelliptic(C,Integer(3)) + +File :17, in at_most_poles_superelliptic(self, pole_order, threshold) + +AttributeError: 'superelliptic' object has no attribute 'prec' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [11], line 1 +----> 1 at_most_poles_superelliptic(C,Integer(3)) + +File :17, in at_most_poles_superelliptic(self, pole_order, threshold, prec) + +AttributeError: 'superelliptic' object has no attribute 'quotient' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [13], line 1 +----> 1 at_most_poles_superelliptic(C,Integer(3)) + +File :26, in at_most_poles_superelliptic(self, pole_order, threshold, prec) + +TypeError: 'function' object cannot be interpreted as an integer +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [15], line 1 +----> 1 at_most_poles_superelliptic(C,Integer(3)) + +File :32, in at_most_poles_superelliptic(self, pole_order, threshold, prec) + +File :219, in holomorphic_combinations_fcts(S, pole_order) + +AttributeError: 'superelliptic' object has no attribute 'prec' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [17], line 1 +----> 1 at_most_poles_superelliptic(C,Integer(3)) + +File :32, in at_most_poles_superelliptic(self, pole_order, threshold, prec) + +File :238, in holomorphic_combinations_fcts(S, pole_order) + +File :6, in __init__(self, C, g) + +AttributeError: 'superelliptic' object has no attribute 'height' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [19], line 1 +----> 1 at_most_poles_superelliptic(C,Integer(3)) + +File :32, in at_most_poles_superelliptic(self, pole_order, threshold, prec) + +File :64, in holomorphic_combinations_fct_superelliptic(S, pole_order) + +File :6, in __init__(self, C, g) + +AttributeError: 'superelliptic' object has no attribute 'height' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3) +[?7h[?12l[?25h[?2004l[?7h[1, y, x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.quo_rem(f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.quo_rem(f)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lC][?7h[?12l[?25h[?25l[?7l.][?7h[?12l[?25h[?25l[?7ly,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7lC][?7h[?12l[?25h[?25l[?7l.][?7h[?12l[?25h[?25l[?7lx][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y, C.x]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y, C.x])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 with the equations: +z0^3 - z0 = y +z1^3 - z1 = x + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element() +[?7h[?12l[?25h[?2004l[?7h[x*z0^2*z1^2 + x^2*z1^2 + y*z0*z1^2, + x^2*z0*z1^2 + y*z0^2*z1^2 + x*y*z1^2, + x^2*z0^2*z1^2 + x^3*z1^2 + x*y*z0*z1^2, + x^3*z0*z1^2 + x*y*z0^2*z1^2 + x^2*y*z1^2, + x^3*z0^2*z1^2 + x^4*z1^2 + x^2*y*z0*z1^2, + x^4*z0*z1^2 + x^2*y*z0^2*z1^2 + x^3*y*z1^2, + x^4*z0^2*z1^2 + x^5*z1^2 + x^3*y*z0*z1^2, + x^5*z0*z1^2 + x^3*y*z0^2*z1^2 + x^4*y*z1^2, + x^5*z0^2*z1^2 + x^6*z1^2 + x^4*y*z0*z1^2, + x^6*z0*z1^2 + x^4*y*z0^2*z1^2 + x^5*y*z1^2, + x^6*z0^2*z1^2 + x^7*z1^2 + x^5*y*z0*z1^2, + x^7*z0*z1^2 + x^5*y*z0^2*z1^2 + x^6*y*z1^2, + x^7*z0^2*z1^2 + x^8*z1^2 + x^6*y*z0*z1^2, + x^8*z0*z1^2 + x^6*y*z0^2*z1^2 + x^7*y*z1^2, + x^8*z0^2*z1^2 + x^9*z1^2 + x^7*y*z0*z1^2, + x^9*z0*z1^2 + x^7*y*z0^2*z1^2 + x^8*y*z1^2, + x^9*z0^2*z1^2 + x^10*z1^2 + x^8*y*z0*z1^2, + x^10*z0*z1^2 + x^8*y*z0^2*z1^2 + x^9*y*z1^2, + x^10*z0^2*z1^2 + x^11*z1^2 + x^9*y*z0*z1^2, + x^11*z0*z1^2 + x^9*y*z0^2*z1^2 + x^10*y*z1^2, + x^11*z0^2*z1^2 + x^12*z1^2 + x^10*y*z0*z1^2, + x^12*z0*z1^2 + x^10*y*z0^2*z1^2 + x^11*y*z1^2, + x^12*z0^2*z1^2 + x^13*z1^2 + x^11*y*z0*z1^2, + x^13*z0*z1^2 + x^11*y*z0^2*z1^2 + x^12*y*z1^2, + x^13*z0^2*z1^2 + x^14*z1^2 + x^12*y*z0*z1^2, + x^14*z0*z1^2 + x^12*y*z0^2*z1^2 + x^13*y*z1^2, + x^14*z0^2*z1^2 + x^15*z1^2 + x^13*y*z0*z1^2, + x^15*z0*z1^2 + x^13*y*z0^2*z1^2 + x^14*y*z1^2, + x^15*z0^2*z1^2 + x^16*z1^2 + x^14*y*z0*z1^2, + x^16*z0*z1^2 + x^14*y*z0^2*z1^2 + x^15*y*z1^2, + x^16*z0^2*z1^2 + x^17*z1^2 + x^15*y*z0*z1^2, + x^17*z0*z1^2 + x^15*y*z0^2*z1^2 + x^16*y*z1^2, + x^17*z0^2*z1^2 + x^18*z1^2 + x^16*y*z0*z1^2, + x^18*z0*z1^2 + x^16*y*z0^2*z1^2 + x^17*y*z1^2, + x^18*z0^2*z1^2 + x^19*z1^2 + x^17*y*z0*z1^2, + x^19*z0*z1^2 + x^17*y*z0^2*z1^2 + x^18*y*z1^2, + x^19*z0^2*z1^2 + x^20*z1^2 + x^18*y*z0*z1^2, + x^20*z0*z1^2 + x^18*y*z0^2*z1^2 + x^19*y*z1^2, + x^20*z0^2*z1^2 + x^21*z1^2 + x^19*y*z0*z1^2, + x^21*z0*z1^2 + x^19*y*z0^2*z1^2 + x^20*y*z1^2, + x^21*z0^2*z1^2 + x^22*z1^2 + x^20*y*z0*z1^2, + x^22*z0*z1^2 + x^20*y*z0^2*z1^2 + x^21*y*z1^2, + x^22*z0^2*z1^2 + x^23*z1^2 + x^21*y*z0*z1^2, + x^23*z0*z1^2 + x^21*y*z0^2*z1^2 + x^22*y*z1^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lzAS.magical_element()[?7h[?12l[?25h[?25l[?7l AS.magical_element()[?7h[?12l[?25h[?25l[?7l=AS.magical_element()[?7h[?12l[?25h[?25l[?7l AS.magical_element()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z = AS.magical_element()[0] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: z.trace() +[?7h[?12l[?25h[?2004l[?7hx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz.trace()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: z.valuation() +[?7h[?12l[?25h[?2004l[?7h+Infinity +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz.valuation()[?7h[?12l[?25h[?25l[?7lsage: z +[?7h[?12l[?25h[?2004l[?7hx*z0^2*z1^2 + x^2*z1^2 + y*z0*z1^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: z.valuation(prec = 200) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [29], line 1 +----> 1 z.valuation(prec = Integer(200)) + +TypeError: as_function.valuation() got an unexpected keyword argument 'prec' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz.valuation(prec = 200)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7ltrace()[?7h[?12l[?25h[?25l[?7l = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7lAS.magicl_elemnt()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y, C.x])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y, C.x], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz.valuation(prec = 200)[?7h[?12l[?25h[?25l[?7l = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lAS.magical_element()[0][?7h[?12l[?25h[?25l[?7lsage: z = AS.magical_element()[0] +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Cell In [31], line 1 +----> 1 z = AS.magical_element()[Integer(0)] + +IndexError: list index out of range +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_lement()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_lement()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h12 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS. + AS.a_number AS.branch_points  + AS.at_most_poles AS.cartier_matrix  + AS.at_most_poles_forms AS.characteristic > + AS.base_ring AS.cohomology_of_structure_sheaf_basis  + [?7h[?12l[?25h[?25l[?7la_number + AS.a_number  + + + + [?7h[?12l[?25h[?25l[?7lbranch_points + AS.a_number  AS.branch_points [?7h[?12l[?25h[?25l[?7lde_rham_basi + branch_pointsde_rham_basi + cartiermatrixdx  +<characeristic dx_seris  + cohomoloy_of_structure_sheaf_basisexpnent_of_different [?7h[?12l[?25h[?25l[?7lexponent_of_different_prim +de_rham_basiexponent_of_different_prim +dx fct_field +dx_seris function +expnent_of_different genus [?7h[?12l[?25h[?25l[?7lgroup +exponent_of_different_primgroup  +fct_fieldheight  +functionholomorphic_differentials_basis +genus ith_ramification_gp[?7h[?12l[?25h[?25l[?7ljumps +group jumps +height lift_o_de_rham +holomorphic_differentials_basismagical_element  +ith_ramification_gpnb_of_pts_at_nfty [?7h[?12l[?25h[?25l[?7llift_to_de_rham + AS.jumps  + AS.lift_to_de_rham [?7h[?12l[?25h[?25l[?7lheigh + + AS.height  AS.lift_to_de_rham [?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis + + AS.height  + AS.holomorphic_differentials_basis [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx, + ((x*z0^2 + x^2 + y*z0 - x*z1)/y) * dx, + (1/y) * dx, + (z1/y) * dx, + (z1^2/y) * dx, + (z0/y) * dx, + (z0*z1/y) * dx, + (z0*z1^2/y) * dx, + (z0^2/y) * dx, + ((z0^2*z1 - x*z1)/y) * dx, + ((z0^2*z1^2 - x*z1^2 + x*z1)/y) * dx, + (x/y) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x_series[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l(it.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7l_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3) +[?7h[?12l[?25h[?2004l[?7h[1, x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7lz = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lz.valuatin(prec= 200)[?7h[?12l[?25h[?25l[?7lAS = as_cver(C,[C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y, C.x], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element() +[?7h[?12l[?25h[?2004l[?7h[] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x_series[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (x/y) dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (z1^2) * dx, + (z0) * dx, + ((x^3*z1^2 + x^2*z0^2 + y*z0*z1)/y) * dx, + (1/y) * dx, + (z1/y) * dx, + (z1^2/y) * dx, + (z0/y) * dx, + (z0*z1/y) * dx, + (z0*z1^2/y) * dx, + (z0^2/y) * dx, + (z0^2*z1/y) * dx, + (z0^2*z1^2/y) * dx, + ((-x^2*z0*z1^2 + x*y)/y) * dx, + (x/y) * dx, + (x*z1/y) * dx, + (x*z1^2/y) * dx, + (x*z0/y) * dx, + (x*z0*z1/y) * dx, + (x*z0*z1^2/y) * dx, + (x*z0^2/y) * dx, + (x*z0^2*z1/y) * dx, + (x*z0^2*z1^2/y) * dx, + (x^2/y) * dx, + (x^2*z1/y) * dx, + (x^2*z1^2/y) * dx, + (x^2*z0/y) * dx, + (x^2*z0*z1/y) * dx, + (x^3/y) * dx, + (x^3*z1/y) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() + AS.a_number AS.branch_points  + AS.at_most_poles AS.cartier_matrix  + AS.at_most_poles_forms AS.characteristic > + AS.base_ring AS.cohomology_of_structure_sheaf_basis  + [?7h[?12l[?25h[?25l[?7la_number + AS.a_number  + + + + [?7h[?12l[?25h[?25l[?7lbranch_points + AS.a_number  AS.branch_points [?7h[?12l[?25h[?25l[?7lde_rham_basi + branch_pointsde_rham_basi + cartiermatrixdx  +<characeristic dx_seris  + cohomoloy_of_structure_sheaf_basisexpnent_of_different [?7h[?12l[?25h[?25l[?7lexponent_of_different_prim +de_rham_basiexponent_of_different_prim +dx fct_field +dx_seris function +expnent_of_different genus [?7h[?12l[?25h[?25l[?7lgroup +exponent_of_different_primgroup  +fct_fieldheight  +functionholomorphic_differentials_basis +genus ith_ramification_gp[?7h[?12l[?25h[?25l[?7ljumps +group jumps +height lift_o_de_rham +holomorphic_differentials_basismagical_element  +ith_ramification_gpnb_of_pts_at_nfty [?7h[?12l[?25h[?25l[?7lone +jumpsone  +lift_o_de_rhamprec  +magical_element pseudo_magical_element +nb_of_pts_at_nfty quotien [?7h[?12l[?25h[?25l[?7lramification_jumps +one ramification_jumps +prec uniformizer +pseudo_magical_elementx  +quotien x_series[?7h[?12l[?25h[?25l[?7lone + AS.one  AS.ramification_jumps [?7h[?12l[?25h[?25l[?7lprc + AS.one  + AS.prec [?7h[?12l[?25h[?25l[?7lsudo_magical_element + + AS.prec  + AS.pseudo_magical_element [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element() +[?7h[?12l[?25h[?2004l[?7h[z0^2*z1^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l6)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,6) +[?7h[?12l[?25h[?2004l[?7h[1, y, x, x^2, x^3] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,6)[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_elemen()[?7h[?12l[?25h[?25l[?7lholomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l = as_covr(C, [C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7lx, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l^, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l2, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x^2, C.x], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x^2, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element() +[?7h[?12l[?25h[?2004l[?7h[z0^2*z1^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x^2, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x^2, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lat_mostpls_superelliptic(C6)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l9)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,9) +[?7h[?12l[?25h[?2004l[?7h[1, y, x, x*y, x^2, x^2*y, x^3, x^4] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,9)[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_elemen()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x^2, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l*, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l., C.x], prec = 20)[?7h[?12l[?25h[?25l[?7ly, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x*C.y, C.x], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x*C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element() +[?7h[?12l[?25h[?2004l[?7h[z0^2*z1^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x*C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x*C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lat_mostpls_superelliptic(C,9)[?7h[?12l[?25h[?25l[?7lAS = ascvr(C, [C.x*C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7l.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7l.x], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element() +[?7h[?12l[?25h[?2004l[?7h[z0^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l^], prec = 20)[?7h[?12l[?25h[?25l[?7l3], prec = 20)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x^3], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x^3], prec = 200)[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element() +[?7h[?12l[?25h[?2004l[?7h[x^2 + x*z0 + z0^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x^3], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l4], prec = 20)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x^4], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x^4], prec = 200)[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element() +[?7h[?12l[?25h[?2004l[?7h[z0^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,9)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_most_poles_superelliptic(C,9)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,12) +[?7h[?12l[?25h[?2004l[?7h[1, y, x, x*y, x^2, x^2*y, x^3, x^3*y, x^4, x^5, x^6] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx_series[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.valuation() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [55], line 1 +----> 1 C.x.valuation() + +AttributeError: 'superelliptic_function' object has no attribute 'valuation' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.valuation()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion + C.x.expansion  + C.x.expansion_at_infty + + + [?7h[?12l[?25h[?25l[?7l + C.x.expansion  + + [?7h[?12l[?25h[?25l[?7l_at_infty + C.x.expansion  + C.x.expansion_at_infty[?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^6 + 2*t^30 + t^54 + 2*t^78 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ly.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^3 + t^11 + t^27 + t^35 + 2*t^51 + t^75 + 2*t^83 + O(t^95) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,12)[?7h[?12l[?25h[?25l[?7lt_most_poles_superelliptic(C,12)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,5) +[?7h[?12l[?25h[?2004l[?7h[1, y, x, x^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x^4], prec = 200)[?7h[?12l[?25h[?25l[?7l= as_cover(C, [C.x^4], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l,], prec = 20)[?7h[?12l[?25h[?25l[?7l ], prec = 20)[?7h[?12l[?25h[?25l[?7lC], prec = 20)[?7h[?12l[?25h[?25l[?7l.], prec = 20)[?7h[?12l[?25h[?25l[?7ly], prec = 20)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x, C.y], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x, C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lpseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element() +[?7h[?12l[?25h[?2004l[?7h[] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphicdifferentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (x/y) dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lpseudo_magical_element()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 15) +[?7h[?12l[?25h[?2004l[?7h[] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 15)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 30) +[?7h[?12l[?25h[?2004l[?7h[] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[((-x^2*z1 + y)/y) * dx, + ((2*x^2*z1^2 + 2*x^3 + y*z1)/y) * dx, + ((-2*x^2*z1^3 - x^3*z1 + y*z1^2 + 2*x*y)/y) * dx, + ((x^2*z1^4 + x^3*z1^2 + x^4 - x^2*z0^2 + y*z1^3 + x*y*z1)/y) * dx, + ((-x^2*z0*z1 + y*z0)/y) * dx, + ((2*x^2*z0*z1^2 + 2*x^3*z0 - 2*x^2*z0^2 + y*z0*z1)/y) * dx, + ((-2*x^2*z0*z1^3 - 2*x*z0^2*z1^3 - x^3*z0*z1 + 2*x^2*z0^2*z1 + y*z0*z1^2 + 2*x*y*z0 + x^2*z1)/y) * dx, + ((x^2*z0*z1^4 + x*z0^2*z1^4 + x^3*z0*z1^2 - 2*x^2*z0^2*z1^2 + x^4*z0 + x^3*z0^2 + 2*x^2*z0^3 + y*z0*z1^3 + x*y*z0*z1 - x^2*z1^2 + x^3)/y) * dx, + ((-2*x*z0^2*z1^3 + x^2*z0^2*z1 + y*z0^2)/y) * dx, + ((2*x*z0^2*z1^4 - 2*x^2*z0^2*z1^2 - x^3*z0^2 + y*z0^2*z1)/y) * dx, + ((-2*x*z0^3*z1^3 + x^2*z0^3*z1 + y*z0^3)/y) * dx, + ((2*x*z0^3*z1^4 - 2*x^2*z0^3*z1^2 - x^3*z0^3 + y*z0^3*z1 + 2*x^2*z0^2)/y) * dx, + ((-2*x*z0^4*z1^3 + x^2*z0^4*z1 + x*z0^2*z1^3 + y*z0^4 - x^2*z0^2*z1 - x^2*z1)/y) * dx, + ((2*x*z0^4*z1^4 - 2*x^2*z0^4*z1^2 - x^3*z0^4 - x*z0^2*z1^4 + y*z0^4*z1 + 2*x^2*z0^2*z1^2 - x^3*z0^2 + 2*x^2*z0^3 + 2*x^2*z1^2 - 2*x^3)/y) * dx, + (1/y) * dx, + (z1/y) * dx, + (z1^2/y) * dx, + (z1^3/y) * dx, + (z1^4/y) * dx, + (z0/y) * dx, + (z0*z1/y) * dx, + (z0*z1^2/y) * dx, + (z0*z1^3/y) * dx, + (z0*z1^4/y) * dx, + (z0^2/y) * dx, + (z0^2*z1/y) * dx, + (z0^2*z1^2/y) * dx, + (z0^2*z1^3/y) * dx, + ((z0^2*z1^4 - x^2*z0^2)/y) * dx, + (z0^3/y) * dx, + (z0^3*z1/y) * dx, + (z0^3*z1^2/y) * dx, + (z0^3*z1^3/y) * dx, + ((z0^3*z1^4 - x^2*z0^3)/y) * dx, + (z0^4/y) * dx, + (z0^4*z1/y) * dx, + (z0^4*z1^2/y) * dx, + (z0^4*z1^3/y) * dx, + ((z0^4*z1^4 - x^2*z0^4 + x^2*z0^2)/y) * dx, + (x/y) * dx, + (x*z1/y) * dx, + (x*z1^2/y) * dx, + ((x*z1^3 - x^2*z1)/y) * dx, + ((x*z1^4 - 2*x^2*z1^2 + x^3)/y) * dx, + (x*z0/y) * dx, + (x*z0*z1/y) * dx, + (x*z0*z1^2/y) * dx, + ((x*z0*z1^3 - x^2*z0*z1)/y) * dx, + ((x*z0*z1^4 - 2*x^2*z0*z1^2 + x^3*z0 + x^2*z0^2)/y) * dx, + (x*z0^2/y) * dx, + (x*z0^2*z1/y) * dx, + ((x*z0^2*z1^2 - x^2*z0^2)/y) * dx, + (x*z0^3/y) * dx, + (x*z0^3*z1/y) * dx, + ((x*z0^3*z1^2 - x^2*z0^3)/y) * dx, + (x*z0^4/y) * dx, + (x*z0^4*z1/y) * dx, + ((x*z0^4*z1^2 - x^2*z0^4 - 2*x^2*z0^2)/y) * dx, + (x^2/y) * dx, + (x^2*z0/y) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h60 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 2[?7h[?12l[?25h[?25l[?7lagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: matrix + matrix  + matrix_plot + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(C); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(C); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7lS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Cell In [67], line 1 +----> 1 A, B = group_action_matrices_dR(AS) + +File :29, in group_action_matrices_dR(AS, threshold) + +File :345, in cohomology_of_structure_sheaf_basis(self, threshold) + +File :345, in (.0) + +File :131, in serre_duality_pairing(self, fct) + +File /ext/sage/9.8/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) + 583 return expression.sum(*args, **kwds) + 584 elif max(len(args),len(kwds)) <= 1: +--> 585 return sum(expression, *args, **kwds) + 586 else: + 587 from sage.symbolic.ring import SR + +File :131, in (.0) + +File :124, in residue(self, place) + +File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:618, in sage.rings.laurent_series_ring_element.LaurentSeries.residue() + 616 Integer Ring + 617 """ +--> 618 return self[-1] + 619 + 620 def exponents(self): + +File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() + 542 return type(self)(self._parent, f, self.__n) + 543 +--> 544 return self.__u[i - self.__n] + 545 + 546 def __iter__(self): + +File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() + 451 return self.base_ring().zero() + 452 else: +--> 453 raise IndexError("coefficient not known") + 454 return self.__f[n] + 455 + +IndexError: coefficient not known +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_holo(AS) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 2[?7h[?12l[?25h[?25l[?7lagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A1, A2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B) +[?7h[?12l[?25h[?2004l[?7h[ +RModule of dimension 10 over GF(5), +RModule of dimension 25 over GF(5), +RModule of dimension 25 over GF(5) +] +{ +[1 0 0 1 1 2 4 2 0 1] +[0 1 0 3 0 2 0 3 0 0] +[0 0 1 0 0 0 1 0 0 0] +[0 0 0 1 0 0 0 1 0 0] +[0 0 0 0 1 0 3 0 0 0] +[0 0 0 0 0 1 0 4 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 3] +[0 0 0 4 0 3 0 3 0 1], +[3 2 0 4 2 1 3 4 1 3] +[0 1 2 3 4 2 3 1 0 0] +[0 0 1 3 0 0 0 0 0 0] +[0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 1 1 1 1 0 0] +[0 0 0 0 0 1 2 3 0 0] +[0 0 0 0 0 0 1 3 0 0] +[0 0 0 0 0 0 0 1 0 0] +[1 3 2 4 2 1 1 1 4 0] +[0 0 0 0 2 1 4 3 0 1] +} +{ +[1 0 2 0 4 0 4 3 2 1 3 0 0 2 1 4 0 2 1 2 2 1 4 2 1] +[0 1 0 0 3 3 3 1 2 1 0 3 0 4 2 4 0 4 2 1 4 2 2 4 2] +[0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0] +[0 0 0 1 2 0 2 2 2 4 1 1 0 0 1 2 0 0 1 4 0 1 1 0 1] +[0 0 0 0 3 4 2 3 0 1 2 0 0 0 0 4 0 0 0 3 0 0 1 0 0] +[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 3 0 0] +[0 0 0 0 3 1 4 2 3 4 4 0 0 0 0 1 0 0 0 2 0 0 4 0 0] +[0 0 0 0 0 0 0 1 0 3 0 1 0 0 0 0 0 0 0 3 0 0 1 0 0] +[0 0 0 0 0 0 0 0 1 0 4 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 4 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 2 0 0 0 2 1 0 0 0 1 0 0 3 0 0 1 0 0] +[0 0 0 0 3 0 3 0 2 0 2 0 0 1 0 0 0 2 0 0 3 0 0 4 0] +[0 0 0 0 3 2 3 4 2 1 2 1 0 0 1 0 0 0 2 0 0 3 0 0 4] +[0 0 0 0 3 3 3 1 2 4 2 4 0 0 0 1 0 0 0 0 0 0 0 0 0] +[0 0 0 0 0 1 0 2 0 3 0 3 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 3 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 3 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 4 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 4 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 4] +[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 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], +[1 2 3 3 4 0 2 2 2 4 0 2 3 1 1 1 1 2 2 0 0 0 0 0 0] +[0 1 3 3 3 1 0 1 3 4 4 3 4 0 0 0 0 2 2 0 0 0 0 0 0] +[0 0 1 0 4 0 4 0 0 2 3 0 0 4 4 4 4 1 1 0 0 0 0 0 0] +[0 0 0 1 0 1 3 1 0 2 3 4 4 1 1 1 1 2 2 0 0 0 0 0 0] +[0 0 0 0 3 1 2 1 2 4 3 1 1 0 0 0 0 1 1 0 0 0 0 0 0] +[0 0 0 0 1 0 1 3 1 2 4 3 0 0 0 0 0 3 3 0 0 0 0 0 0] +[0 0 0 0 3 2 4 0 3 1 2 4 4 0 0 0 0 4 4 0 0 0 0 0 0] +[0 0 0 0 2 3 2 2 2 4 3 1 0 0 0 0 0 1 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 0 2 3 2 1 2 4 3 1 1 0 0 0 0 1 1 0 0 0 0 0 0] +[0 0 0 0 1 3 1 1 3 1 3 4 0 1 2 3 4 0 0 0 0 0 0 0 0] +[0 0 0 0 2 3 2 1 3 4 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0] +[0 0 0 0 0 4 0 3 4 4 1 3 0 0 0 0 0 1 2 0 0 0 0 0 0] +[0 0 0 0 2 3 2 1 3 4 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] +[0 0 0 0 0 0 0 0 2 1 1 2 0 0 0 0 0 0 0 1 1 1 0 0 0] +[0 0 0 0 0 0 0 0 0 3 2 2 0 0 0 0 0 0 0 0 1 2 0 0 0] +[0 0 0 0 0 0 0 0 2 1 4 2 0 0 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 1 1 1] +[0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 1 2] +[0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1] +} +{ +[1 0 0 0 1 0 0 1 1 2 3 4 0 0 0 0 0 1 0 2 1 3 1 0 4] +[0 1 0 0 0 1 1 1 1 3 3 0 2 1 0 0 0 0 0 1 4 0 1 3 4] +[0 0 1 0 0 0 3 1 2 2 0 0 2 2 0 0 0 2 0 0 3 0 4 1 0] +[0 0 0 1 0 0 2 3 2 4 3 1 3 1 0 0 0 0 0 3 0 2 1 0 1] +[0 0 0 0 1 0 1 0 3 0 2 0 3 0 0 0 0 0 0 0 0 0 4 2 0] +[0 0 0 0 0 1 4 3 4 3 1 2 1 3 0 0 0 0 0 1 0 4 1 0 2] +[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 1 0] +[0 0 0 0 0 0 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 1 0 3 0 1 0 0 0 0 0 0 0 2 0 0 4 0] +[0 0 0 0 0 0 0 0 0 1 0 3 0 1 0 0 0 0 0 0 0 0 4 0 0] +[0 0 0 0 0 0 0 0 0 0 1 0 4 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 4 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 1 0 0 0 0 0 0 0 0 0 0 0] +[0 0 0 1 0 2 0 3 0 4 0 4 0 2 1 0 1 1 0 1 3 0 4 3 4] +[0 0 0 0 0 0 3 0 3 0 2 4 2 3 0 1 0 0 1 2 0 3 1 0 4] +[0 0 0 3 0 1 4 3 4 4 1 0 1 2 0 0 1 0 0 1 3 4 4 1 2] +[0 0 0 0 0 0 1 3 1 1 4 4 4 4 0 0 0 1 0 0 1 0 0 2 0] +[0 0 0 0 0 0 0 2 0 4 0 1 0 1 0 0 0 0 1 0 0 0 3 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 3 2 0 1] +[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 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 4] +[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 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], +[1 1 1 1 0 0 0 4 0 3 2 4 4 0 0 0 0 0 2 4 3 3 0 0 0] +[0 1 2 3 0 0 4 2 4 4 2 4 1 1 0 3 0 2 4 2 0 0 0 0 0] +[0 0 1 3 0 0 2 1 2 2 1 1 2 3 0 3 0 0 0 2 1 1 0 0 0] +[0 0 0 1 0 0 3 0 3 0 2 2 0 3 0 0 0 2 4 4 3 3 0 0 0] +[0 0 0 0 1 1 1 1 0 0 4 4 4 4 0 0 0 2 1 2 1 1 0 0 0] +[0 0 0 0 0 1 4 1 2 1 4 3 1 0 0 0 0 4 3 0 4 4 0 0 0] +[0 0 0 0 0 0 3 4 2 2 3 3 3 3 0 0 0 0 0 2 0 0 0 0 0] +[0 0 0 0 0 0 0 1 0 0 4 4 2 0 0 0 0 0 0 0 3 3 0 0 0] +[0 0 0 0 0 0 3 4 4 4 2 2 2 2 0 0 0 0 0 3 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 1 3 3 4 0 0 0 0 0 0 0 1 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0] +[0 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 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 1 0 0 0 0 0 0 0 0 0 0 0] +[4 2 3 1 1 3 2 3 4 0 1 0 0 4 1 3 0 4 0 0 3 3 0 0 0] +[0 0 0 0 0 0 2 0 2 0 2 2 2 2 0 1 0 3 1 1 0 0 0 0 0] +[0 0 0 0 4 2 0 3 2 4 4 0 0 3 0 0 1 0 4 4 2 2 0 0 0] +[0 0 0 0 0 0 4 2 4 4 1 1 1 1 0 0 0 1 4 4 0 0 0 0 0] +[0 0 0 0 0 0 0 0 0 0 1 1 3 0 0 0 0 0 1 0 2 2 0 0 0] +[0 0 0 0 0 0 4 1 4 2 0 2 3 3 0 0 0 0 0 1 3 3 0 0 0] +[0 0 0 0 0 0 0 0 0 0 2 2 4 4 0 0 0 0 0 0 1 2 0 0 0] +[0 0 0 0 0 0 0 0 0 0 4 2 3 4 0 0 0 0 0 0 0 1 0 0 0] +[0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 1 1 1] +[0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 1 2] +[0 0 0 0 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: C1 = super + super superelliptic_drw/ superelliptic_function  + superelliptic superelliptic_drw_cech superelliptic_regular_drw_form  + superelliptic/ superelliptic_drw_form superelliptic_regular_form > + superelliptic_cech superelliptic_form superelliptic_witt  + [?7h[?12l[?25h[?25l[?7l + super  + + + + [?7h[?12l[?25h[?25l[?7lsuperelliptic + super  + superelliptic [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(1, x) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:2447, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__() + 2446 try: +-> 2447 right = Integer(right) + 2448 except TypeError: + +File /ext/sage/9.8/src/sage/rings/integer.pyx:655, in sage.rings.integer.Integer.__init__() + 654 if otmp is not None: +--> 655 set_from_Integer(self, otmp(the_integer_ring)) + 656 return + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:1396, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion() + 1395 if self.degree() > 0: +-> 1396 raise TypeError("cannot convert nonconstant polynomial") + 1397 return R(self.get_coeff_c(0)) + +TypeError: cannot convert nonconstant polynomial + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Cell In [70], line 1 +----> 1 C1 = superelliptic(Integer(1), x) + +File :20, in __init__(self, f, m, prec) + +File :14, in __init__(self, C, g) + +File :260, in reduction(C, g) + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:2449, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__() + 2447 right = Integer(right) + 2448 except TypeError: +-> 2449 raise TypeError("non-integral exponents not supported") + 2450 + 2451 d = self.degree() + +TypeError: non-integral exponents not supported +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(1, x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(x, 1) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1 +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lx.expansionat_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^6 + 2*t^14 + 4*t^30 + 2*t^38 + t^46 + t^70 + t^78 + 3*t^86 + 2*t^94 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ly.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^3 + 4*t^19 + 2*t^27 + 2*t^35 + 2*t^43 + 3*t^67 + t^75 + t^83 + O(t^95) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lC][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l.][?7h[?12l[?25h[?25l[?7lx][?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l([)][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l^][?7h[?12l[?25h[?25l[?7l2][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7lC][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l.][?7h[?12l[?25h[?25l[?7lx][?7h[?12l[?25h[?25l[?7l^][?7h[?12l[?25h[?25l[?7l(][?7h[?12l[?25h[?25l[?7l-][?7h[?12l[?25h[?25l[?7l5][?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: AS1 = as_cover(C1, [C1.x^2, C1.x^(-5)]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^(-5)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^(-5)])[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_holoAS[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1= group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1= group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS1) +[?7h[?12l[?25h[?2004lIncrease precision. +Increase precision. +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [76], line 1 +----> 1 A1, B1 = group_action_matrices_holo(AS1) + +File :20, in group_action_matrices_holo(AS) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :99, in coordinates(self, basis) + +File :16, in linear_representation_polynomials(polynomial, list_of_polynomials) + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right() + 903 + 904 if not self.is_square(): +--> 905 X = self._solve_right_general(C, check=check) + 906 else: + 907 try: + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general() + 1026 # Have to check that we actually solved the equation. + 1027 if self*X != B: +-> 1028 raise ValueError("matrix equation has no solutions") + 1029 return X + 1030 + +ValueError: matrix equation has no solutions +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lS1= as_cover(C1, [C1.x^2, C1.x^(-5)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS1 = as_cover(C1, [C1.x^2, C1.x^(-5)], prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^(-5)], prec = 100)[?7h[?12l[?25h[?25l[?7l1,B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS1) +[?7h[?12l[?25h[?2004lIncrease precision. +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Cell In [78], line 1 +----> 1 A1, B1 = group_action_matrices_holo(AS1) + +File :20, in group_action_matrices_holo(AS) + +File :139, in holomorphic_differentials_basis(self, threshold) + +File :426, in holomorphic_combinations(S) + +File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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 :78, in __rmul__(self, constant) + +File :10, in __init__(self, C, g) + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:655, in PolynomialRing(base_ring, *args, **kwds) + 653 for arg in args: + 654 try: +--> 655 k = Integer(arg) + 656 except TypeError: + 657 # Interpret arg as names + 658 if names is not None: + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lS1= as_cover(C1, [C1.x^2, C1.x^(-5)], prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l], prec = 10)[?7h[?12l[?25h[?25l[?7l], prec = 10)[?7h[?12l[?25h[?25l[?7l], prec = 10)[?7h[?12l[?25h[?25l[?7l], prec = 10)[?7h[?12l[?25h[?25l[?7l5], prec = 10)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS1 = as_cover(C1, [C1.x^2, C1.x^5], prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^5], prec = 100)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^5], prec = 100)[?7h[?12l[?25h[?25l[?7l1,B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS1) +[?7h[?12l[?25h[?2004lIncrease precision. +Increase precision. +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [80], line 1 +----> 1 A1, B1 = group_action_matrices_holo(AS1) + +File :20, in group_action_matrices_holo(AS) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :99, in coordinates(self, basis) + +File :16, in linear_representation_polynomials(polynomial, list_of_polynomials) + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right() + 903 + 904 if not self.is_square(): +--> 905 X = self._solve_right_general(C, check=check) + 906 else: + 907 try: + +File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general() + 1026 # Have to check that we actually solved the equation. + 1027 if self*X != B: +-> 1028 raise ValueError("matrix equation has no solutions") + 1029 return X + 1030 + +ValueError: matrix equation has no solutions +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lS1= as_cover(C1, [C1.x^2, C1.x^5], prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l30)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS1 = as_cover(C1, [C1.x^2, C1.x^5], prec = 300) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^5], prec = 300)[?7h[?12l[?25h[?25l[?7l1,B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS1) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lmathis(A, B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1) +[?7h[?12l[?25h[?2004l[?7h[ +RModule M of dimension 10 over GF(5) +] +{ +[1 1 1 1 1 0 0 0 0 0] +[0 1 2 3 4 0 0 0 0 0] +[0 0 1 3 1 0 0 0 0 0] +[0 0 0 1 4 0 0 0 0 0] +[0 0 0 0 1 0 0 0 0 0] +[0 0 0 0 0 1 1 1 1 1] +[0 0 0 0 0 0 1 2 3 4] +[0 0 0 0 0 0 0 1 3 1] +[0 0 0 0 0 0 0 0 1 4] +[0 0 0 0 0 0 0 0 0 1], +[1 0 0 0 4 1 0 4 0 2] +[0 1 0 0 0 0 1 0 2 0] +[0 0 1 0 0 0 0 1 0 4] +[0 0 0 1 0 0 0 0 1 0] +[0 0 0 0 1 0 0 0 0 1] +[0 0 0 0 3 1 0 3 0 1] +[0 0 0 0 0 0 1 0 4 0] +[0 0 0 0 0 0 0 1 0 3] +[0 0 0 0 0 0 0 0 1 0] +[0 0 0 0 0 0 0 0 0 1] +} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + + +  + + + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lS1= as_cover(C1, [C1.x^2, C1.x^5], prec = 300)[?7h[?12l[?25h[?25l[?7l.genu()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lmification_jump[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: AS.jumps +[?7h[?12l[?25h[?2004l[?7h{0: [2, 1]} +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + + + [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^5 + x + 1 over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,5) +[?7h[?12l[?25h[?2004l[?7h[1, y, x, x^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + + + + [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-5 + t^3 + t^5 + t^11 + 2*t^15 + t^23 + t^25 + t^27 + t^29 + 2*t^33 + t^35 + 2*t^45 + t^47 + 2*t^49 + t^51 + t^69 + 2*t^71 + t^75 + t^77 + t^83 + t^85 + 2*t^87 + 2*t^93 + O(t^95) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + + [?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x, C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l= as_cover(C, [C.x, C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7l.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7l[C.y], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [90], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7 + +File :43, in __init__(self, f, m, prec) + +TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + x + 1 over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ly.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + t + t^2 + 2*t^5 + 2*t^6 + t^7 + t^8 + t^11 + 2*t^13 + t^15 + 2*t^18 + t^20 + 2*t^24 + t^25 + t^29 + 2*t^33 + t^35 + 2*t^37 + t^41 + 2*t^43 + t^45 + t^47 + t^49 + 2*t^54 + t^56 + 2*t^60 + 2*t^64 + t^68 + 2*t^72 + t^74 + t^76 + t^79 + t^80 + t^83 + 2*t^87 + t^89 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3) +[?7h[?12l[?25h[?2004l[?7h[1, y, x, x*y, x^2, x^3] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.y).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-3 + 2 + 2*t + t^3 + 2*t^5 + 2*t^6 + 2*t^8 + t^13 + 2*t^17 + 2*t^20 + t^22 + 2*t^27 + 2*t^35 + t^37 + 2*t^39 + t^41 + t^47 + t^49 + t^53 + 2*t^56 + t^58 + t^60 + t^64 + 2*t^66 + t^68 + 2*t^72 + 2*t^74 + 2*t^78 + 2*t^81 + 2*t^87 + 2*t^89 + O(t^97) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7l.C.y], prec = 20)[?7h[?12l[?25h[?25l[?7lxC.y], prec = 20)[?7h[?12l[?25h[?25l[?7l*C.y], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x*C.y], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.jumps[?7h[?12l[?25h[?25l[?7lpseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7leudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 30) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [97], line 1 +----> 1 AS.pseudo_magical_element(threshold = Integer(30)) + +File :206, in pseudo_magical_element(self, threshold) + +File :192, in at_most_poles(self, pole_order, threshold) + +File :192, in (.0) + +TypeError: as_function.expansion_at_infty() got an unexpected keyword argument 'place' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x*C.y], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 30) +[?7h[?12l[?25h[?2004l[?7h[-x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + z0^2, + -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + y, + x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 + y*z0, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^47 + x^45*y*z0 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^42*y*z0 - x^42*z0 + x^41*z0^2 + x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^33*y*z0 + x^33*z0 - x^32*z0^2 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*y + x^27 + y*z0^2, + -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + x*z0, + -x^55 + x^53*z0^2 - x^54 + x^53*y - x^53*z0 + x^52*z0^2 - x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^49*y*z0^2 - x^51 + x^50*z0 + x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y + x^48*z0 + x^47*y*z0 - x^47*z0^2 + x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*y - x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^42*z0^2 - x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^42 - x^41*z0 + x^40*z0^2 + x^40*z0 - x^39*z0^2 + x^38*y*z0^2 + x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^37*y*z0 + x^36*y*z0^2 - x^38 + x^37*y + x^37*z0 + x^36*y*z0 + x^36*y + x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^33*z0^2 + x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^33 + x^32*z0 - x^31*z0^2 - x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^30*z0 - x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y - x^26*z0^2 + x^27 - x^26*z0 + x*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 + x^41 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 - x^32 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x*y, + x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^51*y - x^51*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^47*y - x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 - x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 + x^45*y + x^44*y*z0 - x^44*y + x^44*z0 - x^43*y*z0 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y + x^41*y*z0 - x^41*z0^2 + x^40*y*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 - x^39*z0^2 - x^40 + x^39*z0 + x^38*z0^2 - x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*z0 - x^36*z0^2 - x^36*z0 - x^35*y*z0 - x^36 + x^35*y + x^34*y*z0 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 - x^31*y*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*z0 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 + x^26*y + x*y*z0^2, + -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + x^2, + x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 + x^2*z0, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^47 + x^45*y*z0 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^42*y*z0 - x^42*z0 + x^41*z0^2 + x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^33*y*z0 + x^33*z0 - x^32*z0^2 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*y + x^27 + x^2*z0^2, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*y + x^26*z0 + x^2*y, + x^54*z0 + x^53*z0^2 + x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y + x^46*z0 - x^44*y*z0^2 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^42*y*z0 - x^41*y*z0^2 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^38*z0 + x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^35*y*z0 - x^34*y*z0^2 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^34*y - x^33*y*z0 + x^32*y*z0^2 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y + x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^26*y*z0 - x^26*y + x^26*z0 + x^2*y*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y + x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 + x^51 - x^50*y + x^50*z0 + x^48*y*z0^2 - x^49*z0 + x^47*y*z0^2 - x^49 + x^48*y + x^47*y*z0 + x^47*z0 - x^46*y*z0 - x^46*z0^2 - x^47 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^44*z0^2 + x^45 + x^44*z0 - x^42*y*z0^2 + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*y + x^41*z0 - x^40*z0^2 + x^41 - x^39*z0^2 - x^40 + x^38*z0^2 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^35*y*z0 + x^36 + x^33*y*z0^2 - x^35 - x^34*z0 - x^33*z0^2 - x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 + x^32*y - x^32*z0 - x^31*z0^2 - x^32 + x^30*z0^2 + x^29*y*z0^2 + x^31 - x^29*z0^2 + x^28*y*z0 + x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^2*y*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 + x^41 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 - x^32 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^3, + -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^47*y - x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*y + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 - x^45 - x^44*z0 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*z0^2 + x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^40*y*z0^2 + x^42 - x^41*y - x^41*z0 - x^41 - x^39*z0^2 - x^40 + x^39*y + x^38*z0^2 + x^39 - x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*z0 + x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 - x^33*z0^2 - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^31*y*z0^2 - x^33 + x^32*y + x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*y - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y - x^28*y*z0 + x^28*z0^2 + x^28*z0 - x^27*y*z0 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^26*z0^2 - x^26*y + x^26*z0 + x^3*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 - x^27 - x^26*z0 + x^3*y, + x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 - x^41*y*z0^2 - x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y + x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^37*y*z0 + x^37*z0^2 - x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^35*y*z0 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^32*y*z0^2 + x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^32 - x^31*z0 + x^30*y*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 + x^26*y*z0 + x^26*y - x^26*z0 + x^3*y*z0, + x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*y*z0 + x^50*y*z0^2 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 - x^44*y*z0 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 - x^44 + x^43*y - x^42*z0^2 + x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^40*z0^2 + x^41 - x^40*z0 - x^40 + x^39*y - x^39*z0 - x^38*y*z0 - x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^36*y - x^36*z0 - x^35*y*z0 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^35 - x^34*y + x^33*z0^2 - x^32*y*z0^2 - x^33*y + x^33*z0 + x^32*y*z0 + x^33 - x^32*z0 + x^31*z0^2 + x^30*y*z0^2 - x^32 + x^31*z0 + x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^30 - x^29*y + x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^28 - x^27*y - x^26*z0^2 + x^27 + x^26*z0 + x^3*y*z0^2, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*y + x^26*z0 + x^4, + -x^55 + x^53*z0^2 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^46*y*z0^2 - x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^28*y*z0 - x^28*z0^2 + x^29 + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27*z0 - x^27 - x^26*z0 + x^4*z0, + x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 + x^52*z0^2 + x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^50*y*z0^2 - x^52 - x^51*y - x^51*z0 + x^50*y*z0 - x^50*z0^2 - x^51 + x^49*y*z0 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 + x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*z0^2 - x^48 - x^47*y + x^47*z0 - x^46*y*z0 - x^45*y*z0^2 - x^47 + x^45*z0^2 + x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^45 + x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y - x^43*z0 - x^42*y*z0 - x^42*z0^2 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 + x^42 - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^38*y*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^39 - x^38*y + x^38*z0 + x^37*y*z0 + x^37*z0^2 - x^38 + x^37*y - x^36*y*z0 + x^36*z0^2 + x^37 - x^35*z0^2 + x^36 + x^35*z0 + x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 - x^33 + x^32*z0 + x^31*z0^2 + x^32 + x^31*z0 + x^30*z0^2 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^30 + x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^26*z0 + x^4*z0^2, + -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y + x^27 + x^26*z0 + x^4*y, + x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*z0^2 - x^52 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y + x^31*y*z0 - x^32 + x^31*z0 + x^30*z0^2 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y - x^27*z0 - x^27 + x^26*y + x^26*z0 + x^4*y*z0, + x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 - x^52*z0^2 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^50*y*z0^2 - x^52 + x^51*y - x^51*z0 - x^50*y*z0 - x^51 + x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^47 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^43*y*z0^2 + x^45 + x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^39 - x^38*y + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 - x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 - x^35*z0^2 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^33*z0^2 - x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 - x^33 - x^32*y + x^32*z0 - x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^30 + x^29*y - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 - x^28*y - x^27*y*z0 - x^26*y*z0^2 + x^28 - x^26*z0^2 + x^26*y - x^26*z0 + x^4*y*z0^2, + -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*z0^2 + x^52 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 + x^45*y + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^39*y*z0 + x^39*z0^2 - x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y - x^32*z0 - x^30*z0^2 + x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^26*y*z0 - x^26*y + x^5*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 - x^52*y + x^52*z0 + x^51*z0^2 + x^51*z0 - x^50*y*z0 - x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 + x^48*z0^2 - x^48*y + x^47*y*z0 + x^46*y*z0^2 - x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^45*y*z0 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 - x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^44 - x^43*y - x^42*y*z0 - x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*z0^2 + x^42 + x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^38*y*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 - x^35 + x^34*y + x^33*y*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 - x^33 + x^32 + x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 - x^28*z0^2 + x^27*y*z0^2 + x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^28 + x^27*y + x^26*z0^2 - x^27 + x^5*z0^2, + x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*y - x^26*z0 + x^5*y, + -x^55 + x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^44*z0^2 + x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*z0^2 + x^42 + x^40*z0 - x^39*z0^2 + x^40 + x^39*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^31*z0 + x^30*z0^2 - x^31 + x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 - x^26*z0 + x^5*y*z0, + -x^55 + x^53*z0^2 + x^53*y + x^52*z0^2 - x^51*y*z0^2 - x^52*z0 - x^50*y*z0^2 - x^52 + x^50*y*z0 - x^50*z0^2 - x^50*y + x^50*z0 - x^49*z0^2 + x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*z0 + x^47*y*z0 - x^47*z0^2 - x^48 + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 - x^45*z0 + x^44*z0^2 + x^45 + x^43*z0^2 - x^44 - x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^41*y - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 - x^40 + x^39*y - x^38*y*z0 + x^38*z0^2 + x^39 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^35*z0 + x^34*y - x^34*z0 - x^33*y*z0 - x^34 + x^33*y + x^33*z0 + x^32*z0^2 + x^32*y - x^31*z0^2 + x^32 + x^31*z0 + x^29*y*z0^2 + x^31 - x^30*y + x^29*y*z0 - x^29*z0^2 - x^30 + x^29*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 - x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^26*z0 + x^5*y*z0^2, + x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*z0 - x^44*y*z0^2 + x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y + x^41*z0 + x^41 + x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^27 + x^26*y + x^6, + x^55 + x^54*z0 - x^54 - x^53*y - x^52*y*z0 + x^52*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*z0^2 - x^50*y*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^49*y*z0^2 + x^51 - x^50*y + x^49*y*z0 - x^49*z0^2 + x^50 - x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^48*y - x^48*z0 - x^47*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^47 - x^46*y + x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^42*z0 + x^40*y*z0^2 - x^42 - x^41*y + x^39*y*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*z0^2 - x^39 + x^38*y - x^38*z0 + x^36*y*z0^2 + x^38 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^33*z0 + x^33 + x^32*y - x^30*y*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^29 + x^27*y*z0 + x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y - x^26*z0 + x^6*z0^2, + x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0 + x^6*y, + -x^54*z0 - x^53*z0^2 - x^54 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 - x^51*z0^2 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 - x^41 - x^40*z0 - x^39*y*z0 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32 + x^30*y*z0 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 + x^28*y - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27 - x^26*z0 + x^6*y*z0, + -x^55 - x^54*z0 + x^53*y + x^52*y*z0 + x^52*z0^2 - x^50*y*z0^2 - x^52 - x^51*z0 + x^50*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^48*y*z0^2 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*z0 + x^47*y*z0 - x^48 - x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 - x^46*y + x^46*z0 + x^45*z0^2 - x^45*z0 - x^44*y*z0 + x^45 + x^44*z0 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^41*z0^2 - x^41*y - x^40*z0^2 - x^39*y*z0^2 - x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^39 + x^37*y + x^37*z0 + x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^34*y + x^34*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^32*y + x^30*y*z0^2 + x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 - x^28*z0^2 + x^29 - x^28*y + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y - x^26*z0 + x^6*y*z0^2, + x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^52 + x^51*y + x^50*y*z0 - x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 + x^50 + x^48*y*z0 + x^47*y*z0^2 - x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^48 + x^47*y + x^47*z0 + x^47 - x^46*y - x^46*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^42*y*z0 - x^42*z0^2 + x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 + x^41*y*z0 + x^40*y*z0^2 + x^42 - x^41*z0 - x^40*z0^2 - x^41 + x^39*z0^2 - x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 + x^33*z0^2 + x^34 + x^33*y + x^33*z0 - x^32*y*z0 - x^31*y*z0^2 - x^33 + x^32*z0 + x^31*z0^2 + x^32 - x^30*z0^2 - x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 + x^26*z0^2 + x^27 - x^26*z0 + x^7*z0^2, + x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^46*y - x^46*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41*z0 - x^40*y - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^27*y + x^27*z0 - x^26*y*z0 + x^27 + x^26*y + x^7*y, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 + x^51*y + x^51*z0 - x^49*y*z0^2 - x^50*y - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 - x^48*y*z0 - x^49 + x^48*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 - x^47*y + x^46*y*z0 + x^46*z0^2 + x^46*y - x^46*z0 - x^45*y*z0 - x^46 + x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^44*z0 + x^42*y*z0^2 + x^42*y*z0 - x^42*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 - x^42 + x^41*y - x^41*z0 + x^40*z0^2 - x^40*z0 - x^39*z0^2 - x^40 + x^39*y - x^38*y*z0 + x^38*y - x^38*z0 + x^37*y*z0 + x^36*y*z0^2 + x^37*y - x^37 - x^36*y + x^36*z0 - x^35*y*z0 + x^35*z0^2 + x^36 + x^35*y + x^35*z0 - x^33*y*z0^2 + x^35 - x^33*y*z0 - x^34 + x^33*y - x^32*y*z0 + x^31*y*z0^2 + x^33 - x^32*y + x^32*z0 - x^31*z0^2 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^29*y*z0 - x^29*z0^2 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*z0^2 - x^28 - x^27*y + x^26*y - x^26*z0 + x^7*y*z0^2, + -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^27 + x^26*y + x^8, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^47*y*z0 + x^46*y*z0^2 - x^48 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 - x^26*y*z0 + x^26*z0 + x^8*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^52 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^49*y*z0 + x^49*z0^2 - x^50 + x^48*z0^2 - x^49 + x^48*y - x^48*z0 + x^46*y*z0^2 - x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^41*y*z0^2 + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 + x^38 + x^36*y*z0 + x^36*z0^2 - x^37 - x^36*z0 + x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*z0 + x^32*y*z0^2 - x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^32*z0 - x^30*y*z0^2 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^8*z0^2, + x^54*z0 + x^53*z0^2 - x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*z0 + x^51*z0^2 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^48*z0^2 + x^47*y*z0^2 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^44*y*z0^2 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*z0 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^36*z0 - x^34*y*z0^2 + x^35*y - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^32*y*z0^2 + x^33*y + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^29 + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y - x^26*y + x^8*y*z0, + x^55 - x^53*z0^2 - x^53*y + x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^50 + x^49*y + x^49*z0 - x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 - x^43*y + x^43 - x^42*z0 - x^41*y*z0 + x^41*z0 - x^40*z0^2 - x^41 - x^40*z0 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 - x^37*y*z0^2 + x^39 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^34*y - x^33*z0^2 - x^34 + x^33*z0 + x^32*y*z0 - x^32*z0 - x^31*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^26*z0^2 + x^26*z0 + x^8*y*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^52*y + x^51*y*z0 - x^51*z0^2 - x^52 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^40*y*z0 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 - x^37*z0^2 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^31*y*z0 - x^31*z0 + x^30*y*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^26*y*z0 + x^27 + x^26*y + x^26*z0 + x^9*z0, + -x^54 + x^52*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 - x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 - x^45*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^43*z0^2 - x^42*y*z0^2 + x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^42*y - x^42*z0 - x^40*y*z0^2 - x^42 + x^41*y + x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y - x^38*z0 - x^38 + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*z0 + x^35*y*z0 + x^35*z0 - x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 + x^33*y + x^33*z0 - x^31*y*z0^2 + x^33 - x^32*y + x^30*y*z0^2 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 + x^26*y + x^26*z0 + x^9*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 + x^51*z0^2 + x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^37*z0^2 + x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y + x^36*z0 - x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^33*y*z0 + x^32*y*z0^2 + x^32*y*z0 - x^32*z0^2 + x^33 + x^32*y + x^32*z0 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 - x^28*z0^2 + x^29 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 - x^26*y*z0 + x^27 - x^26*y + x^9*y*z0, + x^54*z0 + x^53*z0^2 - x^54 - x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y - x^50*z0^2 - x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 + x^49*y - x^48*y*z0 - x^47*y*z0^2 + x^47*y*z0 + x^46*y*z0^2 + x^48 - x^46*z0^2 + x^47 - x^45*y*z0 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^37*y + x^37*z0 + x^35*y*z0^2 - x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^32*y*z0 + x^33 + x^32*y + x^32*z0 + x^31*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 + x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*y - x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y + x^26*z0 + x^9*y*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^32 + x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^10, + x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41*z0 - x^41 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*y + x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*z0 + x^32*z0^2 - x^32*z0 + x^31*y*z0 + x^32 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 - x^27*z0^2 + x^26*y*z0^2 + x^26*y*z0 - x^26*z0 + x^10*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*z0 - x^45*z0^2 - x^46 - x^44*y*z0 + x^45 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y - x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*y - x^41*z0 + x^41 - x^40 - x^39*z0 - x^38*z0^2 - x^37*y*z0^2 + x^38*z0 + x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 - x^36*y*z0 - x^37 - x^36*y + x^36*z0 + x^35*z0^2 + x^36 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 - x^35 + x^33*y*z0 - x^33*z0^2 + x^33*y + x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 + x^32*y + x^32*z0 - x^32 + x^31 + x^30*z0 + x^29*z0^2 + x^28*y*z0^2 - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^29 + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 + x^28 + x^27*y - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^10*z0^2, + -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^49*y*z0 - x^48*y*z0^2 + x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*y + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^42 + x^41*y - x^41 - x^39*z0^2 + x^39*z0 - x^38*z0^2 + x^39 + x^38*y - x^38*z0 + x^38 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^36 - x^35*y + x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 + x^34 + x^33*y + x^33*z0 + x^33 - x^32*y + x^31*z0^2 + x^32 - x^30*z0^2 - x^30*z0 + x^29*z0^2 - x^30 - x^29*y + x^29*z0 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*y - x^26*z0 + x^10*y*z0^2, + x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*y + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27 - x^26*y - x^26*z0 + x^11, + x^55 - x^53*z0^2 - x^53*y + x^53*z0 + x^51*y*z0^2 - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 - x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 + x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y - x^32*z0 - x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^26*y*z0 - x^26*y + x^11*z0, + x^55 - x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^51 - x^49*y*z0 - x^49*z0^2 + x^50 - x^49*y + x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^47 - x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y + x^41*z0 + x^40*z0 + x^39*z0^2 - x^38*y*z0^2 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 + x^37*y + x^36*y*z0 - x^36*z0^2 + x^37 + x^36*y + x^35*z0^2 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^34 - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^31*z0 - x^30*z0^2 + x^29*y*z0^2 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^26*y - x^26*z0 + x^11*z0^2, + -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*y + x^11*y, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^26*z0 + x^11*y*z0, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*z0^2 - x^50*y*z0^2 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 + x^47*y*z0^2 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^46 - x^45*y + x^45*z0 + x^43*y*z0^2 + x^44*y + x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 - x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*z0^2 + x^42 - x^41*y - x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^38*y*z0 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*z0 - x^35*y*z0 + x^35*z0^2 - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^33*y*z0^2 + x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 - x^33*y - x^33*z0 - x^33 + x^32*y - x^31*z0^2 - x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*z0^2 + x^29 - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^11*y*z0^2, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27 - x^26*y + x^26*z0 + x^12, + x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 - x^41 + x^40*z0 - x^39*y*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*z0^2 - x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*y*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^27*z0 - x^27 - x^26*y - x^26*z0 + x^12*z0, + -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 + x^52*y - x^51*y*z0 + x^52 + x^51*y + x^51*z0 + x^50*z0^2 + x^51 + x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 - x^44*y*z0 - x^44*z0^2 - x^45 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^39*y*z0^2 + x^41 - x^39*z0^2 + x^39*y - x^39*z0 + x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^30*y*z0^2 - x^32 + x^30*z0^2 - x^30*y + x^30*z0 - x^29*z0^2 - x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^28*y - x^28*z0 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^12*z0^2, + -x^55 + x^53*z0^2 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^41*y*z0^2 + x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^28*y*z0 - x^28*z0^2 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27 + x^26*z0 + x^12*y, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y - x^41 + x^40*z0 - x^39*z0^2 - x^40 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^26*y*z0 + x^27 + x^26*y + x^12*y*z0, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 + x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 - x^51 + x^50*y + x^49*y*z0 - x^49*z0^2 - x^50 + x^49 - x^48*y + x^48*z0 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*z0 - x^45*y*z0 + x^45*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^43*y*z0 + x^43*z0^2 - x^44 - x^43*z0 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 - x^38 - x^36*y*z0 + x^36*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^35*z0^2 - x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^34*z0 + x^33*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 - x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^27 - x^26*y + x^12*y*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 + x^41 - x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^32*y - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*z0^2 - x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^27 + x^26*y - x^26*z0 + x^13, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^45*y*z0^2 - x^46*y + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^39 + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*z0^2 - x^36*y + x^35*y*z0 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 - x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*z0 + x^13*z0^2, + x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 + x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^26*z0 + x^13*y, + -x^54*z0 - x^53*z0^2 + x^54 + x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*y - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^42*y*z0 + x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^41 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*y - x^38*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^33*y - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 + x^32*y - x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y + x^28*z0^2 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^26*y + x^26*z0 + x^13*y*z0, + x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*z0^2 + x^51*y*z0^2 + x^52*y - x^52*z0 + x^51*y*z0 - x^50*y*z0^2 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^51 - x^50*y + x^49*y*z0 + x^49*z0^2 - x^49*y - x^49*z0 + x^48*y*z0 - x^47*y*z0^2 + x^48*y + x^47*z0^2 - x^46*y*z0^2 + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^45*z0^2 + x^46 - x^45*y - x^45*z0 + x^44*y*z0 + x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^44 + x^43*y - x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 - x^40*z0^2 + x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 + x^37*y*z0 + x^36*y*z0^2 + x^38 - x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^35*z0^2 - x^36 - x^35*y + x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^35 - x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 - x^32*y*z0^2 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^31*z0^2 - x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^27*y*z0^2 - x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 + x^26*z0 + x^13*y*z0^2, + x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y - x^46*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^27 + x^14, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y - x^49*y*z0 - x^49*z0^2 + x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 + x^47*z0^2 - x^46*y*z0^2 + x^48 - x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^44*y*z0^2 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*z0 - x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^38*y*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 + x^37*y*z0^2 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 + x^37 - x^36*y + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*y*z0 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*z0 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^29*y*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0 + x^14*z0^2, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^51*y*z0 - x^51*z0^2 - x^51*y - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^47*y*z0 - x^46*y*z0^2 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^28*y - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 - x^26*y + x^26*z0 + x^14*y, + -x^55 + x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*z0 + x^46*y*z0^2 + x^48 - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y - x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^37*z0^2 - x^37*y + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^29 + x^28*y + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^26*y*z0 - x^26*z0 + x^14*y*z0, + x^55 + x^54*z0 - x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^50*y*z0 - x^49*y*z0^2 + x^50*y - x^49*y*z0 - x^49*y - x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*z0 + x^46*z0^2 + x^46*y + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^43*y*z0 + x^44 + x^43*y + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 + x^41*y - x^41*z0 + x^40*z0^2 + x^41 - x^40*z0 - x^38*y*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^37*y*z0 + x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^37 - x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 - x^34*y - x^34*z0 - x^33*z0^2 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 - x^32*z0^2 - x^32*y + x^32*z0 - x^31*z0^2 - x^32 + x^31*z0 - x^30*z0^2 + x^29*y*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^28*y*z0 - x^28*z0^2 - x^29 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^26*y + x^14*y*z0^2, + -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^41 - x^40*y - x^40*z0 - x^39*z0^2 - x^40 - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^32 - x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27 + x^26*z0 + x^15, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*z0^2 + x^46*y*z0^2 + x^47*z0 - x^45*y*z0^2 + x^47 - x^46*z0 - x^45*y*z0 + x^46 + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^45 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^43*z0 - x^42*z0^2 - x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 + x^41*y + x^41*z0 + x^39*y*z0^2 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*z0 + x^38*y*z0 + x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 - x^38 - x^36*y*z0 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 - x^35*y*z0 - x^36 - x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*z0 + x^33*z0^2 + x^32*y*z0^2 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^31*y*z0^2 - x^32*y - x^32*z0 - x^30*y*z0^2 + x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*z0 - x^29*y*z0 + x^28*y*z0^2 + x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 + x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 - x^26*z0^2 + x^27 + x^26*y + x^15*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*z0 + x^51*z0^2 + x^52 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y - x^44*y*z0^2 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*y - x^43*z0 - x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^40*z0 - x^39*y*z0 - x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*z0 + x^30*y*z0 + x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 + x^26*y*z0 - x^27 - x^26*z0 + x^15*y*z0, + -x^55 - x^54*z0 + x^54 + x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*y + x^48*y*z0 - x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^45*y*z0^2 + x^46*y + x^45*y*z0 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^42*z0^2 - x^41*y*z0^2 - x^42*y - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*z0 + x^40*z0^2 - x^39*y*z0^2 - x^41 - x^40*z0 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 + x^33*y + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*z0 + x^31*z0^2 + x^30*y*z0^2 + x^32 + x^31*z0 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 - x^26*z0 + x^15*y*z0^2, + x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27 + x^26*y - x^26*z0 + x^16, + x^55 - x^53*z0^2 + x^54 - x^53*y + x^52*z0^2 + x^51*y*z0^2 - x^52*y + x^52*z0 - x^50*y*z0^2 - x^52 - x^50*y*z0 + x^50*z0^2 - x^51 - x^50*z0 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^48 - x^47*z0 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*z0^2 + x^45 - x^44*y - x^43*z0^2 + x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^40*y*z0^2 + x^42 - x^41*y - x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 - x^38*y*z0^2 + x^38*y*z0 - x^39 - x^38*y + x^38*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 + x^37*y - x^37*z0 + x^36*y*z0 + x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 + x^35*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*z0^2 - x^35 - x^34*y + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^31*y*z0^2 - x^33 + x^32*y + x^31*z0^2 - x^32 - x^31*z0 + x^30*z0^2 - x^29*y*z0 + x^28*y*z0^2 + x^30 + x^29*y - x^29*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^26*y - x^26*z0 + x^16*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 + x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^40*y*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 - x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*z0 + x^31*y*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 + x^26*y*z0 + x^27 + x^16*y*z0, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^52*z0^2 - x^51*y*z0^2 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^50*y*z0^2 + x^51*z0 - x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^50*y - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*z0 - x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 + x^49 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 + x^46 + x^45*z0 - x^44*y*z0 + x^43*y*z0^2 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 - x^40*y*z0^2 + x^42 + x^41*y + x^41*z0 + x^40*z0^2 - x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*y + x^36*y*z0 + x^36*z0^2 + x^37 - x^34*y*z0^2 - x^36 - x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 - x^33 - x^32*y - x^32*z0 - x^31*z0^2 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^26*y - x^26*z0 + x^16*y*z0^2, + x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 + x^32*y*z0 - x^32*z0^2 + x^33 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^26*y - x^26*z0 + x^17, + x^55 - x^53*z0^2 - x^53*y + x^51*y*z0^2 + x^53 + x^52 - x^51*y - x^51 + x^50*y + x^48*y*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^47 + x^46 - x^45 + x^42*y*z0^2 + x^42*y + x^41*y - x^39*y*z0^2 - x^41 + x^38*y*z0^2 + x^40 + x^36*y*z0^2 - x^38 + x^35*y*z0^2 + x^37 + x^36*y - x^36 + x^35 - x^33*y - x^32*y + x^32 - x^31 + x^29 - x^28 - x^27*y + x^26*z0^2 + x^27 + x^26*y + x^17*z0^2, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^28*y*z0 - x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y - x^27 - x^26*y + x^26*z0 + x^17*y, + x^54*z0 + x^53*z0^2 - x^54 - x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*y - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^49*y*z0 - x^49*z0^2 + x^50 + x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 + x^45*z0^2 + x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^43*y*z0 + x^43*z0^2 - x^44 + x^43*z0 - x^42*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*y*z0 - x^42 + x^41*y - x^41*z0 - x^40*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 + x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^34*z0 - x^34 + x^33*y - x^33*z0 - x^32*y*z0 + x^33 - x^32*y + x^32*z0 + x^31*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 + x^29*y*z0 - x^28*y*z0^2 - x^29*y - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 - x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^26*y + x^17*y*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^40*y*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^37*z0^2 + x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 + x^26*z0 + x^18*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 - x^52*y + x^52*z0 + x^51*y*z0 + x^50*y*z0^2 - x^50*y*z0 - x^50*z0^2 - x^51 + x^50*y - x^49*y*z0 - x^48*y*z0^2 + x^49*y + x^48*z0^2 - x^47*y*z0^2 - x^48*y - x^48*z0 + x^47*z0^2 - x^47*z0 - x^46*z0^2 + x^46*y + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*z0^2 + x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 + x^42 - x^41*z0 + x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y + x^37*y*z0 - x^37*z0^2 - x^38 + x^36*y*z0 + x^36*z0^2 + x^36*y - x^36*z0 + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*y*z0 + x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*z0^2 - x^32*y*z0^2 + x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y - x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 - x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^18*z0^2, + -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 + x^27 + x^26*y + x^18*y, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^52*y*z0 + x^51*y*z0^2 - x^52*z0 - x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y - x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^18*y*z0, + x^54 - x^53*z0 - x^52*z0^2 + x^53 - x^52*y + x^51*y*z0 + x^50*y*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 - x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^48 - x^47*y - x^46*y*z0 - x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 + x^44*y*z0 - x^45 + x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y + x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y - x^41*z0 + x^40*z0^2 + x^41 + x^39*z0^2 - x^40 + x^39*z0 + x^38*z0^2 - x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 + x^36 + x^34*y*z0 - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y + x^32*z0 - x^32 + x^31 - x^30*z0 + x^29*y + x^29*z0 - x^28*y*z0 + x^27*y*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 - x^26*y + x^18*y*z0^2, + -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 + x^41 + x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 - x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^28*y*z0 - x^28*z0^2 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y + x^26*y + x^26*z0 + x^19, + -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 + x^52 - x^51*y - x^50*y*z0 - x^50*z0^2 + x^51 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^45*y*z0 + x^45*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^43*y*z0 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*z0^2 - x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 + x^40*y*z0^2 - x^42 - x^41*y - x^41*z0 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^39 + x^38*y + x^37*y*z0 + x^38 - x^37*y + x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^36 + x^35*y + x^35*z0 - x^34*y*z0 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*z0^2 + x^34 - x^33*z0 - x^32*y*z0 + x^33 + x^32*y + x^32*z0 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^30*y + x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*y - x^28*y*z0 + x^29 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y + x^19*z0^2, + x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^52*y + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^46*z0 - x^44*y*z0^2 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*y + x^19*y, + x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^47*y*z0 - x^46*y*z0^2 - x^48 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41 + x^40*z0 + x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 - x^37*z0^2 + x^37*y - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^32 - x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 - x^28*y + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 + x^26*y*z0 + x^19*y*z0, + x^55 - x^53*z0^2 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^48*y - x^48 - x^47*y - x^47*z0 + x^46*y*z0 - x^45*y*z0^2 + x^47 - x^46*y - x^46 - x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 + x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 + x^40*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y + x^36*y*z0 + x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 - x^34 + x^33*y - x^33*z0 + x^32*y*z0 + x^32*y - x^32*z0 - x^32 - x^31*z0 - x^31 + x^30*z0 - x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*z0 + x^28*y*z0 - x^29 - x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*y - x^26*z0 + x^19*y*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^41*y*z0^2 + x^43 - x^42*y - x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 + x^31*z0 + x^30*y*z0 - x^30*z0^2 - x^31 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^27*y + x^26*y*z0 - x^27 + x^26*y + x^20*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y + x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 - x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y - x^51*z0 + x^49*y*z0^2 + x^51 - x^50*y - x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 - x^46 + x^45*y + x^45*z0 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 + x^43*z0^2 + x^44 - x^42*y*z0 - x^41*y*z0^2 + x^42*y - x^41*y*z0 - x^41*z0^2 + x^41*y + x^41*z0 + x^40*z0 + x^39*z0^2 + x^38*y*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 - x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 - x^32*y*z0^2 - x^33*y + x^32*y*z0 + x^32*z0^2 - x^32*y - x^32*z0 + x^30*y*z0^2 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 + x^28*z0 - x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*z0^2 - x^27 + x^26*y + x^26*z0 + x^20*z0^2, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*y + x^48*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*y - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^32*y*z0 + x^32*z0^2 + x^32*z0 - x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^26*z0 + x^20*y*z0, + -x^55 + x^53*z0^2 + x^53*y - x^53*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^52 - x^51*y - x^51*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 + x^42*y + x^41*y*z0 - x^41*z0^2 + x^41*y - x^41*z0 - x^40*z0^2 - x^39*z0^2 - x^40 + x^39*y + x^39*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*z0 + x^37*y*z0 + x^38 - x^37*z0 - x^36*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*y + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*y - x^32*y*z0 - x^32*z0^2 - x^32*y + x^32*z0 - x^31*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*z0 - x^28*y*z0 + x^28*z0 + x^28 - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^27 + x^26*y + x^20*y*z0^2, + x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*y*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^37*z0^2 - x^38 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^32*y*z0^2 - x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 - x^32*y + x^32*z0 + x^31*y*z0 - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*z0 + x^26*y - x^26*z0 + x^21*z0, + -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^52 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^51 - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*z0 - x^45*z0^2 + x^44*y*z0^2 + x^46 + x^45*y - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^39*y*z0^2 + x^39*z0^2 - x^39*y - x^39*z0 - x^38*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 + x^33 + x^32*y + x^32*z0 - x^30*z0^2 + x^30*y + x^30*z0 + x^29*z0^2 - x^30 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 + x^29 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^26*y - x^26*z0 + x^21*z0^2, + x^54*z0 + x^53*z0^2 + x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 - x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 + x^46 - x^43*y*z0^2 - x^45 + x^44*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^39*z0^2 - x^40 - x^39*y + x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 - x^36*y*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^36*y - x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^33 + x^32*y - x^32*z0 - x^31*z0^2 - x^30*z0^2 + x^31 + x^30*y - x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^28*y*z0 + x^27*y*z0^2 - x^29 - x^28*y - x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^27 - x^26*y - x^26*z0 + x^21*y*z0^2, + -x^55 + x^53*z0^2 + x^54 + x^53*y - x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*z0^2 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*z0 + x^41*z0^2 + x^42 + x^41*y + x^40*y*z0 - x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*y + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y + x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*z0 - x^26*y*z0 + x^26*y - x^26*z0 + x^22*z0, + -x^55 + x^53*z0^2 + x^53*y + x^53*z0 + x^52*z0^2 - x^51*y*z0^2 - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^48*y*z0^2 - x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^41*y*z0^2 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^40*y*z0^2 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 - x^37*y*z0 + x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^32*y*z0^2 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^28*y*z0 + x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27 + x^26*z0 + x^22*z0^2, + -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 + x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 + x^26*y + x^22*y, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 + x^44*y*z0^2 + x^46 + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 + x^39*z0^2 + x^40 - x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*y + x^26*z0 + x^22*y*z0, + x^54*z0 + x^53*z0^2 + x^54 - x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*y + x^51*z0^2 + x^50*y*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^50 + x^49*z0 - x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*y - x^46*z0 - x^45*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^43*z0 + x^42*z0^2 - x^41*y*z0^2 - x^43 - x^42*y + x^41*z0^2 + x^42 + x^40*z0^2 - x^41 + x^40*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 - x^38*y - x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^34*z0 + x^32*y*z0^2 + x^34 + x^33*y + x^32*z0^2 - x^33 + x^32 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*y + x^27*y*z0^2 + x^28*y - x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 + x^26*z0 + x^22*y*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 + x^52 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y - x^26*z0 + x^23, + x^55 - x^53*z0^2 - x^53*y + x^51*y*z0^2 - x^53 - x^51*z0^2 + x^52 + x^51*y - x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*y - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^42*y - x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^39*y*z0 + x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*z0 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 + x^30*y*z0 - x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^23*z0, + -x^55 - x^54*z0 + x^53*y + x^52*y*z0 - x^52*z0 - x^51*z0^2 - x^52 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^47*y*z0^2 + x^49 - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 - x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^41*y - x^39*y*z0^2 - x^41 + x^40*z0 + x^39*z0^2 - x^38*y*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*z0 - x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 - x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^34*y - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 + x^32*z0^2 + x^32*y + x^30*y*z0^2 + x^32 - x^31*z0 - x^30*z0^2 + x^29*y*z0^2 + x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*z0 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27 - x^26*y + x^23*z0^2, + x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*z0 - x^46*y*z0^2 - x^48 + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41 - x^40*z0 + x^39*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^37*z0^2 + x^37*y - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^26*y*z0 + x^26*z0 + x^23*y*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^52 - x^51*y - x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^49*y - x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^48*z0 + x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^43*y*z0^2 + x^45 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*z0^2 - x^43 - x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*y - x^41*z0 - x^40*z0^2 - x^40*z0 + x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y + x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^34 + x^33*y - x^33*z0 - x^32*y*z0 + x^32*y + x^32*z0 + x^31*z0^2 + x^31*z0 - x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^28*y*z0 - x^28*z0^2 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y + x^23*y*z0^2, + -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 - x^52*y + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y - x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 + x^42 - x^41*z0 - x^40*y*z0 + x^41 + x^40*z0 - x^39*y*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 - x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*z0 + x^31*y*z0 - x^32 - x^31*z0 + x^30*y*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*z0 + x^24*z0, + x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 + x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^50*z0 + x^48*y*z0^2 + x^50 - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 + x^44*y*z0^2 + x^45*y - x^43*y*z0^2 - x^44*y + x^44*z0 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*z0^2 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 - x^41*y + x^41*z0 - x^39*y*z0^2 - x^41 + x^39*y - x^38*z0^2 - x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*z0^2 + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 + x^32*y - x^32*z0 + x^30*y*z0^2 + x^32 - x^30*y + x^29*z0^2 + x^28*y*z0^2 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*z0 + x^27*y*z0 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y - x^26*z0 + x^24*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^24*y, + x^54*z0 + x^53*z0^2 + x^54 - x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*z0^2 + x^52 - x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^44*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*z0 + x^26*y + x^26*z0 + x^24*y*z0, + -x^54 - x^53*z0 + x^52*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y + x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 + x^48*y*z0 + x^47*y*z0^2 + x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 - x^46*y*z0 + x^45*z0^2 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 - x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^42 - x^41*z0 + x^40*z0^2 + x^39*y*z0^2 - x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^33 + x^32*z0 - x^31*z0^2 - x^30*y*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 + x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 + x^26*z0 + x^24*y*z0^2, + x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^41 - x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y + x^32*z0 - x^32 + x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27 - x^26*z0 + x^25, + x^55 + x^54*z0 + x^54 - x^53*y - x^53*z0 - x^52*y*z0 + x^52*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 + x^48*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^46*z0 + x^45*z0^2 - x^44*y*z0^2 + x^45*y - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 - x^42*y*z0 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 + x^42 - x^41*y - x^41*z0 + x^40*z0^2 - x^41 - x^39*z0^2 + x^39*y - x^39*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^36*y*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 - x^35*z0^2 - x^34*y*z0^2 + x^35*y - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 - x^33 + x^32*y + x^32*z0 - x^31*z0^2 + x^32 + x^30*z0^2 - x^30*y + x^30*z0 + x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^27*y*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^27 - x^26*y - x^26*z0 + x^25*z0^2, + -x^55 - x^54*z0 + x^54 + x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^50*y*z0^2 - x^51*y - x^50*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*y - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^47*y - x^45*y*z0^2 - x^47 + x^46*y + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^43*z0 - x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^41*y*z0 + x^40*y*z0^2 + x^42 + x^41*y + x^41*z0 - x^40*z0^2 - x^40*z0 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^36*y + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*z0 + x^34*y*z0 + x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 + x^33*y*z0 - x^33*z0^2 - x^32*y*z0^2 + x^32*y*z0 - x^31*y*z0^2 - x^33 - x^32*y - x^32*z0 + x^31*z0^2 + x^31*z0 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 + x^27*z0^2 - x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^25*y*z0^2 - x^27 + x^26*y - x^26*z0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element() +[?7h[?12l[?25h[?2004l[?7h[] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx, + (1/y) * dx, + (z0/y) * dx, + ((-x^2 + z0^2)/y) * dx, + (x/y) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS. + AS.a_number AS.branch_points AS.de_rham_basis   + AS.at_most_poles AS.cartier_matrix AS.dx   + AS.at_most_poles_forms AS.characteristic AS.dx_series > + AS.base_ring AS.cohomology_of_structure_sheaf_basis AS.exponent_of_different   + [?7h[?12l[?25h[?25l[?7la_number + AS.a_number  + + + + [?7h[?12l[?25h[?25l[?7lt_most_poles + AS.a_number  + AS.at_most_poles [?7h[?12l[?25h[?25l[?7lcartiermatrix + + AS.at_most_poles  AS.cartier_matrix [?7h[?12l[?25h[?25l[?7ldx + + AS.cartier_matrix  AS.dx [?7h[?12l[?25h[?25l[?7lfct_field + branch_pointsde_rham_basiexponent_of_different_prim + cartiermatrixdx fct_field +<characeristic dx_seris function + cohomoloy_of_structure_sheaf_basisexpnent_of_different genus [?7h[?12l[?25h[?25l[?7lheight +de_rham_basiexponent_of_different_primgroup  +dx fct_fieldheight  +dx_seris functionholomorphic_differentials_basis +expnent_of_different genus ith_ramification_gp[?7h[?12l[?25h[?25l[?7llift_o_de_rham +exponent_of_different_primgroup jumps +fct_fieldheight lift_o_de_rham +functionholomorphic_differentials_basismagical_element  +genus ith_ramification_gpnb_of_pts_at_nfty [?7h[?12l[?25h[?25l[?7lprec +group jumpsone  +height lift_o_de_rhamprec  +holomorphic_differentials_basismagical_element pseudo_magical_element +ith_ramification_gpnb_of_pts_at_nfty quotien [?7h[?12l[?25h[?25l[?7luniformizer +jumpsone ramification_jumps +lift_o_de_rhamprec uniformizer +magical_element pseudo_magical_elementx  +nb_of_pts_at_nfty quotien x_series[?7h[?12l[?25h[?25l[?7ly_series +one ramification_jumpsy   +prec uniformizery_series   +pseudo_magical_elementx z  +quotien x_seriesz  [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7luniformizer + + AS.uniformizer  AS.y_series [?7h[?12l[?25h[?25l[?7lprec + + AS.prec  AS.uniformizer [?7h[?12l[?25h[?25l[?7llift_to_de_rham +jumpsone ramification_jumps  +lift_to_de_rhamprec uniformizer  +magical_element pseudo_magical_elementx> +nb_of_ps_at_inftyquotientx  [?7h[?12l[?25h[?25l[?7lheigh +groupjumpsone  +heigh lift_to_de_rhamprec  +holomorphic_differentials_basismagical_element pseudo_magical_element +ith_ramificaton_gpnb_of_ps_at_inftyquotient[?7h[?12l[?25h[?25l[?7lfct_field +exponent_of_different_primgroupjumps +fct_fieldheigh lift_to_de_rham +functions holomorphic_differentials_basismagical_element  +genus ith_ramificaton_gpnb_of_ps_at_infty[?7h[?12l[?25h[?25l[?7ldx +de_rham_basis exponent_of_different_primgroup +dx fct_fieldheigh  +dx_seriefunctions holomorphic_differentials_basis +exponent_of_differentgenus ith_ramificaton_gp[?7h[?12l[?25h[?25l[?7lcartier_matrix +branch_pointde_rham_basis exponent_of_different_prim +cartier_matrixdx fct_field +charactristicdx_seriefunctions  +cohmology_of_structure_sheaf_basisexponent_of_differentgenus [?7h[?12l[?25h[?25l[?7lat_mostpoles + a_number branch_pointde_rham_basis  + at_mostpoles cartier_matrixdx  + at_mos_poles_formscharactristicdx_serie + base_rin cohmology_of_structure_sheaf_basisexponent_of_different[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_forms + + AS.at_most_poles  + AS.at_most_poles_forms [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.at_most_poles_forms(1) +[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx, + ((x^3 + x*z0^2 + y*z0)/y) * dx, + (1/y) * dx, + (z0/y) * dx, + ((-x^2 + z0^2)/y) * dx, + (x/y) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + x + 1 over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + x + 1 over Finite Field of size 3 with the equation: + z^3 - z = x*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lholomorphicdifferentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1/y) dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = crys[0].regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om = AS.at_most_poles_forms(1)[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.cycle_type()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^3 - x[?7h[?12l[?25h[?25l[?7lorn in range(n0 + 1, 30):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li(m-1)/2, M - (m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for i in range(3): +....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrang[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.trace() +[?7h[?12l[?25h[?2004l[?7h((-x)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^3 - x[?7h[?12l[?25h[?25l[?7lorn in range(n0 + 1, 30):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....: [?7h[?12l[?25h[?25l[?7lprint(n, psp(n-n0, 3)> jprime(2*n, 2)^2)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(b))[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(omega.trace()) +....: [?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....:  print(omega.trace()) +....:  +[?7h[?12l[?25h[?2004l0 dx +((-x)/y) dx +0 dx +0 dx +((-1)/y) dx +0 dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1) + macaulay2 magma %man map %%markdown  + macaulay2_console magma_console mandelbrot_plot map_threaded math  + %macro magma_free manifolds maple mathematica > + %magic magmathis manual maple_console mathematica_console  + [?7h[?12l[?25h[?25l[?7lt + + + +[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l + matrix  + matrix_plot + matroids [?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.cycle_type()[?7h[?12l[?25h[?25l[?7lroup_acion_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lup + group_action_matrices group_action_matrices_log  + group_action_matrices_dR group_action_matrices_old  + group_action_matrices_holo groups [?7h[?12l[?25h[?25l[?7l_action_matrices + group_action_matrices  + + + [?7h[?12l[?25h[?25l[?7l_log + group_action_matrices  group_action_matrices_log [?7h[?12l[?25h[?25l[?7l( + + + +[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices_log(AS) +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Cell In [110], line 1 +----> 1 group_action_matrices_log(AS) + +File :62, in group_action_matrices_log(C_AS) + +File :241, in at_most_poles_forms(self, pole_order, threshold) + +File :277, in holomorphic_combinations_forms(S, pole_order) + +File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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 :78, in __rmul__(self, constant) + +File :3, in __init__(self, C, g) + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l,group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lBgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l=group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_log(AS) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [111], line 1 +----> 1 A, B = group_action_matrices_log(AS) + +File :79, in group_action_matrices_log(C_AS) + +File :96, in coordinates(self, basis) + +File :96, in (.0) + +File /ext/sage/9.8/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.8/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.8/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  variable_names = 'x, y' +....:  for j in range(n): +....:  variable_names += ', z' + str(j) +....:  Rxyz = PolynomialRing(F, n+2, variable_names) +....:  x, y = Rxyz.gens()[:2] +....:  z = Rxyz.gens()[2:] +....:  holo_forms = [Rxyz(omega*denom) for omega in holo_forms] +....:  A = [[] for i in range(n)] +....:  for omega in holo: +....:  for i in range(n): +....:  ei = n*[0] +....:  ei[i] = 1 +....:  omega1 = omega.group_action(ei) +....:  omega1 = denom * omega1 +....:  v1 = omega1.coordinates(holo_forms) +....:  A[i] += [v1] +....:  for i in range(n): +....:  A[i] = matrix(F, A[i]) +....:  A[i] = A[i].transpose() +....:  return A[?7h[?12l[?25h[?25l[?7lfor j in range(n): + variable_names += ', z' + str(j) +Rxyz = PolynomialRing(F, n+2,variable_names) +x, yRxyz.gens()[:2] +z = Rxyz.gens()[2:] +holo_forms = [Rxyz(omega*denom) for omega in holo_forms] +A = [[] for i in range(n)] +foromega in holo: + for irange(n): + ei =n*[0] +[i] = 1 +omega1 = omega.group_action(ei) +denom * meg1 +v1 = omega1.coordinates(holo_forms) +A[i]+= [v] +foriin range(n): + A[i]= matrix(F, A[i]) +A[i].transpose() +return A +[?7h[?12l[?25h[?25l[?7l....:  for j in range(n): +....:  variable_names += ', z' + str(j) +....:  Rxyz = PolynomialRing(F, n+2, variable_names) +....:  x, y = Rxyz.gens()[:2] +....:  z = Rxyz.gens()[2:] +....:  holo_forms = [Rxyz(omega*denom) for omega in holo_forms] +....:  A = [[] for i in range(n)] +....:  for omega in holo: +....:  for i in range(n): +....:  ei = n*[0] +....:  ei[i] = 1 +....:  omega1 = omega.group_action(ei) +....:  omega1 = denom * omega1 +....:  v1 = omega1.coordinates(holo_forms) +....:  A[i] += [v1] +....:  for i in range(n): +....:  A[i] = matrix(F, A[i]) +....:  A[i] = A[i].transpose() +....:  return A +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l B = group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_log(AS) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [113], line 1 +----> 1 A, B = group_action_matrices_log(AS) + +Cell In [112], line 6, in group_action_matrices_log(C_AS) + 4 holo = C_AS.at_most_poles_forms(Integer(1)) + 5 holo_forms = [omega for omega in holo] +----> 6 denom = LCM([denominator(omega) for omega in holo_forms]) + 7 variable_names = 'x, y' + 8 for j in range(n): + +Cell In [112], line 6, in (.0) + 4 holo = C_AS.at_most_poles_forms(Integer(1)) + 5 holo_forms = [omega for omega in holo] +----> 6 denom = LCM([denominator(omega) for omega in holo_forms]) + 7 variable_names = 'x, y' + 8 for j in range(n): + +File /ext/sage/9.8/src/sage/misc/functional.py:251, in denominator(x) + 249 if isinstance(x, int): + 250 return 1 +--> 251 return x.denominator() + +AttributeError: 'as_form' object has no attribute 'denominator' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def group_action_matrices_log(AS): +....:  n = AS.height +....:  generators = [] +....:  for i in range(n): +....:  ei = n*[0] +....:  ei[i] = 1 +....:  generators += [ei] +....:  return group_action_matrices(AS.at_most_poles_forms(1), generators, basis = AS.holomorphic_differentials_basis ( +....: ))[?7h[?12l[?25h[?25l[?7l( +....: )) +....: [?7h[?12l[?25h[?25l[?7lsage: def group_action_matrices_log(AS): +....:  n = AS.height +....:  generators = [] +....:  for i in range(n): +....:  ei = n*[0] +....:  ei[i] = 1 +....:  generators += [ei] +....:  return group_action_matrices(AS.at_most_poles_forms(1), generators, basis = AS.holomorphic_differentials_basis ( +....: )) +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7lS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l,group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lBgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l=group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_log(AS) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Cell In [115], line 1 +----> 1 A, B = group_action_matrices_log(AS) + +Cell In [114], line 8, in group_action_matrices_log(AS) + 6 ei[i] = Integer(1) + 7 generators += [ei] +----> 8 return group_action_matrices(AS.at_most_poles_forms(Integer(1)), generators, basis = AS.holomorphic_differentials_basis()) + +File :10, in group_action_matrices(space, list_of_group_elements, basis) + +File /ext/sage/9.8/src/sage/matrix/matrix0.pyx:1520, in sage.matrix.matrix0.Matrix.__setitem__() + 1518 raise IndexError("value does not have the right number of columns") + 1519 elif single_col and row_list_len != len(value_list): +-> 1520 raise IndexError("value does not have the right number of rows") + 1521 else: + 1522 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[?7lsage: def group_action_matrices_log(AS): +....:  n = AS.height +....:  generators = [] +....:  for i in range(n): +....:  ei = n*[0] +....:  ei[i] = 1 +....:  generators += [ei] +....:  return group_action_matrices(AS.at_most_poles_forms(1), generators, basis = AS.at_most_poles_forms(1))[?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +[?2004l ┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Using Python 3.11.1. Type "help()" for help. │ +│ Enhanced for CoCalc. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [2], line 1 +----> 1 AS + +NameError: name 'AS' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x*C.y], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lat_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lsage: AS.at_most_poles_forms(1) +[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx, + ((x^3 + x*z0^2 + y*z0)/y) * dx, + (1/y) * dx, + (z0/y) * dx, + ((-x^2 + z0^2)/y) * dx, + (x/y) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l_(1)[?7h[?12l[?25h[?25l[?7lf(1)[?7h[?12l[?25h[?25l[?7lo(1)[?7h[?12l[?25h[?25l[?7lr(1)[?7h[?12l[?25h[?25l[?7lm(1)[?7h[?12l[?25h[?25l[?7ls(1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC1)[?7h[?12l[?25h[?25l[?7l,1)[?7h[?12l[?25h[?25l[?7l 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_forms(C, 1)[?7h[?12l[?25h[?25l[?7lat_most_poles_forms(C, 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_forms(C, 1) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [5], line 1 +----> 1 at_most_poles_forms(C, Integer(1)) + +NameError: name 'at_most_poles_forms' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_forms(C, 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C, 1)[?7h[?12l[?25h[?25l[?7l(C, 1)[?7h[?12l[?25h[?25l[?7l(C, 1)[?7h[?12l[?25h[?25l[?7l(C, 1)[?7h[?12l[?25h[?25l[?7l(C, 1)[?7h[?12l[?25h[?25l[?7ls(C, 1)[?7h[?12l[?25h[?25l[?7lu(C, 1)[?7h[?12l[?25h[?25l[?7lp(C, 1)[?7h[?12l[?25h[?25l[?7le(C, 1)[?7h[?12l[?25h[?25l[?7lr(C, 1)[?7h[?12l[?25h[?25l[?7le(C, 1)[?7h[?12l[?25h[?25l[?7ll(C, 1)[?7h[?12l[?25h[?25l[?7ll(C, 1)[?7h[?12l[?25h[?25l[?7li(C, 1)[?7h[?12l[?25h[?25l[?7lp(C, 1)[?7h[?12l[?25h[?25l[?7lt(C, 1)[?7h[?12l[?25h[?25l[?7li(C, 1)[?7h[?12l[?25h[?25l[?7lc(C, 1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C, 1) +[?7h[?12l[?25h[?2004l[?7h[1, x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lat_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lsage: AS.at_most_poles_forms(1) +[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx, + ((x^3 + x*z0^2 + y*z0)/y) * dx, + (1/y) * dx, + (z0/y) * dx, + ((-x^2 + z0^2)/y) * dx, + (x/y) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lblock_matrix([[A1, A2]])[?7h[?12l[?25h[?25l[?7lase_ring(parent(x))[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx, + (1/y) * dx, + (z0/y) * dx, + ((-x^2 + z0^2)/y) * dx, + (x/y) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor omega in AS.at_most_poles_forms(1):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega in AS.at_most_poles_forms(1):[?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....: [?7h[?12l[?25h[?25l[?7lprint(omega.trace())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(omega, omega.trace()) +....: [?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....:  print(omega, omega.trace()) +....:  +[?7h[?12l[?25h[?2004l((-x*z0 + y)/y) * dx 0 dx +((x^3 + x*z0^2 + y*z0)/y) * dx ((-x)/y) dx +(1/y) * dx 0 dx +(z0/y) * dx 0 dx +((-x^2 + z0^2)/y) * dx ((-1)/y) dx +(x/y) * dx 0 dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....:  print(omega, omega.trace())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(omega, omega.trace(), omega - omega.group_action([1])) +....: [?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....:  print(omega, omega.trace(), omega - omega.group_action([1])) +....:  +[?7h[?12l[?25h[?2004l((-x*z0 + y)/y) * dx 0 dx (x/y) * dx +((x^3 + x*z0^2 + y*z0)/y) * dx ((-x)/y) dx ((x*z0 - x - y)/y) * dx +(1/y) * dx 0 dx (0) * dx +(z0/y) * dx 0 dx ((-1)/y) * dx +((-x^2 + z0^2)/y) * dx ((-1)/y) dx ((z0 - 1)/y) * dx +(x/y) * dx 0 dx (0) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....:  print(omega, omega.trace(), omega - omega.group_action([1]))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l +....:  +....:  print(omega, omega.trace(), omega - omega.group_action([1]))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l print(omega, omega.trace(), omega - omega.group_action([1])[?7h[?12l[?25h[?25l[?7l print(omega, omega.trace(), omega - omega.group_action([1])[?7h[?12l[?25h[?25l[?7l print(omega, omega.trace(), omega - omega.group_action([1])[?7h[?12l[?25h[?25l[?7l print(omega, omega.trace(), omega - omega.group_action([1])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l....:  print(omega, omega.trace(), omega - omega.group_action([1])) +....: [?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....:  if omega.valuation() < 0: +....:  print(omega, omega.trace(), omega - omega.group_action([1])) +....:  +[?7h[?12l[?25h[?2004l((x^3 + x*z0^2 + y*z0)/y) * dx ((-x)/y) dx ((x*z0 - x - y)/y) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.trace()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = C1.x^2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: omega = AS.at_most_poles + AS.at_most_poles  + AS.at_most_poles_forms + + + [?7h[?12l[?25h[?25l[?7l + AS.at_most_poles  + + [?7h[?12l[?25h[?25l[?7l_forms + AS.at_most_poles  + AS.at_most_poles_forms[?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: omega = AS.at_most_poles_forms(1)[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lomega = AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega +[?7h[?12l[?25h[?2004l[?7h((x^3 + x*z0^2 + y*z0)/y) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega.valuation() +[?7h[?12l[?25h[?2004l[?7h-1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + x + 1 over Finite Field of size 3 with the equation: + z^3 - z = x*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lpseud_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7leudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 30) +[?7h[?12l[?25h[?2004l[?7h[-x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + z0^2, + -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + y, + x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 + y*z0, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^47 + x^45*y*z0 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^42*y*z0 - x^42*z0 + x^41*z0^2 + x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^33*y*z0 + x^33*z0 - x^32*z0^2 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*y + x^27 + y*z0^2, + -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + x*z0, + -x^55 + x^53*z0^2 - x^54 + x^53*y - x^53*z0 + x^52*z0^2 - x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^49*y*z0^2 - x^51 + x^50*z0 + x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y + x^48*z0 + x^47*y*z0 - x^47*z0^2 + x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*y - x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^42*z0^2 - x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^42 - x^41*z0 + x^40*z0^2 + x^40*z0 - x^39*z0^2 + x^38*y*z0^2 + x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^37*y*z0 + x^36*y*z0^2 - x^38 + x^37*y + x^37*z0 + x^36*y*z0 + x^36*y + x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^33*z0^2 + x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^33 + x^32*z0 - x^31*z0^2 - x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^30*z0 - x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y - x^26*z0^2 + x^27 - x^26*z0 + x*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 + x^41 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 - x^32 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x*y, + x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^51*y - x^51*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^47*y - x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 - x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 + x^45*y + x^44*y*z0 - x^44*y + x^44*z0 - x^43*y*z0 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y + x^41*y*z0 - x^41*z0^2 + x^40*y*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 - x^39*z0^2 - x^40 + x^39*z0 + x^38*z0^2 - x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*z0 - x^36*z0^2 - x^36*z0 - x^35*y*z0 - x^36 + x^35*y + x^34*y*z0 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 - x^31*y*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*z0 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 + x^26*y + x*y*z0^2, + -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + x^2, + x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 + x^2*z0, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^47 + x^45*y*z0 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^42*y*z0 - x^42*z0 + x^41*z0^2 + x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^33*y*z0 + x^33*z0 - x^32*z0^2 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*y + x^27 + x^2*z0^2, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*y + x^26*z0 + x^2*y, + x^54*z0 + x^53*z0^2 + x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y + x^46*z0 - x^44*y*z0^2 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^42*y*z0 - x^41*y*z0^2 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^38*z0 + x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^35*y*z0 - x^34*y*z0^2 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^34*y - x^33*y*z0 + x^32*y*z0^2 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y + x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^26*y*z0 - x^26*y + x^26*z0 + x^2*y*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y + x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 + x^51 - x^50*y + x^50*z0 + x^48*y*z0^2 - x^49*z0 + x^47*y*z0^2 - x^49 + x^48*y + x^47*y*z0 + x^47*z0 - x^46*y*z0 - x^46*z0^2 - x^47 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^44*z0^2 + x^45 + x^44*z0 - x^42*y*z0^2 + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*y + x^41*z0 - x^40*z0^2 + x^41 - x^39*z0^2 - x^40 + x^38*z0^2 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^35*y*z0 + x^36 + x^33*y*z0^2 - x^35 - x^34*z0 - x^33*z0^2 - x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 + x^32*y - x^32*z0 - x^31*z0^2 - x^32 + x^30*z0^2 + x^29*y*z0^2 + x^31 - x^29*z0^2 + x^28*y*z0 + x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^2*y*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 + x^41 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 - x^32 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^3, + -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^47*y - x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*y + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 - x^45 - x^44*z0 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*z0^2 + x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^40*y*z0^2 + x^42 - x^41*y - x^41*z0 - x^41 - x^39*z0^2 - x^40 + x^39*y + x^38*z0^2 + x^39 - x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*z0 + x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 - x^33*z0^2 - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^31*y*z0^2 - x^33 + x^32*y + x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*y - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y - x^28*y*z0 + x^28*z0^2 + x^28*z0 - x^27*y*z0 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^26*z0^2 - x^26*y + x^26*z0 + x^3*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 - x^27 - x^26*z0 + x^3*y, + x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 - x^41*y*z0^2 - x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y + x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^37*y*z0 + x^37*z0^2 - x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^35*y*z0 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^32*y*z0^2 + x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^32 - x^31*z0 + x^30*y*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 + x^26*y*z0 + x^26*y - x^26*z0 + x^3*y*z0, + x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*y*z0 + x^50*y*z0^2 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 - x^44*y*z0 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 - x^44 + x^43*y - x^42*z0^2 + x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^40*z0^2 + x^41 - x^40*z0 - x^40 + x^39*y - x^39*z0 - x^38*y*z0 - x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^36*y - x^36*z0 - x^35*y*z0 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^35 - x^34*y + x^33*z0^2 - x^32*y*z0^2 - x^33*y + x^33*z0 + x^32*y*z0 + x^33 - x^32*z0 + x^31*z0^2 + x^30*y*z0^2 - x^32 + x^31*z0 + x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^30 - x^29*y + x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^28 - x^27*y - x^26*z0^2 + x^27 + x^26*z0 + x^3*y*z0^2, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*y + x^26*z0 + x^4, + -x^55 + x^53*z0^2 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^46*y*z0^2 - x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^28*y*z0 - x^28*z0^2 + x^29 + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27*z0 - x^27 - x^26*z0 + x^4*z0, + x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 + x^52*z0^2 + x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^50*y*z0^2 - x^52 - x^51*y - x^51*z0 + x^50*y*z0 - x^50*z0^2 - x^51 + x^49*y*z0 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 + x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*z0^2 - x^48 - x^47*y + x^47*z0 - x^46*y*z0 - x^45*y*z0^2 - x^47 + x^45*z0^2 + x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^45 + x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y - x^43*z0 - x^42*y*z0 - x^42*z0^2 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 + x^42 - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^38*y*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^39 - x^38*y + x^38*z0 + x^37*y*z0 + x^37*z0^2 - x^38 + x^37*y - x^36*y*z0 + x^36*z0^2 + x^37 - x^35*z0^2 + x^36 + x^35*z0 + x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 - x^33 + x^32*z0 + x^31*z0^2 + x^32 + x^31*z0 + x^30*z0^2 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^30 + x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^26*z0 + x^4*z0^2, + -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y + x^27 + x^26*z0 + x^4*y, + x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*z0^2 - x^52 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y + x^31*y*z0 - x^32 + x^31*z0 + x^30*z0^2 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y - x^27*z0 - x^27 + x^26*y + x^26*z0 + x^4*y*z0, + x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 - x^52*z0^2 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^50*y*z0^2 - x^52 + x^51*y - x^51*z0 - x^50*y*z0 - x^51 + x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^47 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^43*y*z0^2 + x^45 + x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^39 - x^38*y + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 - x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 - x^35*z0^2 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^33*z0^2 - x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 - x^33 - x^32*y + x^32*z0 - x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^30 + x^29*y - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 - x^28*y - x^27*y*z0 - x^26*y*z0^2 + x^28 - x^26*z0^2 + x^26*y - x^26*z0 + x^4*y*z0^2, + -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*z0^2 + x^52 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 + x^45*y + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^39*y*z0 + x^39*z0^2 - x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y - x^32*z0 - x^30*z0^2 + x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^26*y*z0 - x^26*y + x^5*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 - x^52*y + x^52*z0 + x^51*z0^2 + x^51*z0 - x^50*y*z0 - x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 + x^48*z0^2 - x^48*y + x^47*y*z0 + x^46*y*z0^2 - x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^45*y*z0 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 - x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^44 - x^43*y - x^42*y*z0 - x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*z0^2 + x^42 + x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^38*y*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 - x^35 + x^34*y + x^33*y*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 - x^33 + x^32 + x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 - x^28*z0^2 + x^27*y*z0^2 + x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^28 + x^27*y + x^26*z0^2 - x^27 + x^5*z0^2, + x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*y - x^26*z0 + x^5*y, + -x^55 + x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^44*z0^2 + x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*z0^2 + x^42 + x^40*z0 - x^39*z0^2 + x^40 + x^39*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^31*z0 + x^30*z0^2 - x^31 + x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 - x^26*z0 + x^5*y*z0, + -x^55 + x^53*z0^2 + x^53*y + x^52*z0^2 - x^51*y*z0^2 - x^52*z0 - x^50*y*z0^2 - x^52 + x^50*y*z0 - x^50*z0^2 - x^50*y + x^50*z0 - x^49*z0^2 + x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*z0 + x^47*y*z0 - x^47*z0^2 - x^48 + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 - x^45*z0 + x^44*z0^2 + x^45 + x^43*z0^2 - x^44 - x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^41*y - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 - x^40 + x^39*y - x^38*y*z0 + x^38*z0^2 + x^39 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^35*z0 + x^34*y - x^34*z0 - x^33*y*z0 - x^34 + x^33*y + x^33*z0 + x^32*z0^2 + x^32*y - x^31*z0^2 + x^32 + x^31*z0 + x^29*y*z0^2 + x^31 - x^30*y + x^29*y*z0 - x^29*z0^2 - x^30 + x^29*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 - x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^26*z0 + x^5*y*z0^2, + x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*z0 - x^44*y*z0^2 + x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y + x^41*z0 + x^41 + x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^27 + x^26*y + x^6, + x^55 + x^54*z0 - x^54 - x^53*y - x^52*y*z0 + x^52*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*z0^2 - x^50*y*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^49*y*z0^2 + x^51 - x^50*y + x^49*y*z0 - x^49*z0^2 + x^50 - x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^48*y - x^48*z0 - x^47*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^47 - x^46*y + x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^42*z0 + x^40*y*z0^2 - x^42 - x^41*y + x^39*y*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*z0^2 - x^39 + x^38*y - x^38*z0 + x^36*y*z0^2 + x^38 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^33*z0 + x^33 + x^32*y - x^30*y*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^29 + x^27*y*z0 + x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y - x^26*z0 + x^6*z0^2, + x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0 + x^6*y, + -x^54*z0 - x^53*z0^2 - x^54 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 - x^51*z0^2 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 - x^41 - x^40*z0 - x^39*y*z0 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32 + x^30*y*z0 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 + x^28*y - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27 - x^26*z0 + x^6*y*z0, + -x^55 - x^54*z0 + x^53*y + x^52*y*z0 + x^52*z0^2 - x^50*y*z0^2 - x^52 - x^51*z0 + x^50*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^48*y*z0^2 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*z0 + x^47*y*z0 - x^48 - x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 - x^46*y + x^46*z0 + x^45*z0^2 - x^45*z0 - x^44*y*z0 + x^45 + x^44*z0 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^41*z0^2 - x^41*y - x^40*z0^2 - x^39*y*z0^2 - x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^39 + x^37*y + x^37*z0 + x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^34*y + x^34*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^32*y + x^30*y*z0^2 + x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 - x^28*z0^2 + x^29 - x^28*y + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y - x^26*z0 + x^6*y*z0^2, + x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^52 + x^51*y + x^50*y*z0 - x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 + x^50 + x^48*y*z0 + x^47*y*z0^2 - x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^48 + x^47*y + x^47*z0 + x^47 - x^46*y - x^46*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^42*y*z0 - x^42*z0^2 + x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 + x^41*y*z0 + x^40*y*z0^2 + x^42 - x^41*z0 - x^40*z0^2 - x^41 + x^39*z0^2 - x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 + x^33*z0^2 + x^34 + x^33*y + x^33*z0 - x^32*y*z0 - x^31*y*z0^2 - x^33 + x^32*z0 + x^31*z0^2 + x^32 - x^30*z0^2 - x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 + x^26*z0^2 + x^27 - x^26*z0 + x^7*z0^2, + x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^46*y - x^46*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41*z0 - x^40*y - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^27*y + x^27*z0 - x^26*y*z0 + x^27 + x^26*y + x^7*y, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 + x^51*y + x^51*z0 - x^49*y*z0^2 - x^50*y - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 - x^48*y*z0 - x^49 + x^48*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 - x^47*y + x^46*y*z0 + x^46*z0^2 + x^46*y - x^46*z0 - x^45*y*z0 - x^46 + x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^44*z0 + x^42*y*z0^2 + x^42*y*z0 - x^42*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 - x^42 + x^41*y - x^41*z0 + x^40*z0^2 - x^40*z0 - x^39*z0^2 - x^40 + x^39*y - x^38*y*z0 + x^38*y - x^38*z0 + x^37*y*z0 + x^36*y*z0^2 + x^37*y - x^37 - x^36*y + x^36*z0 - x^35*y*z0 + x^35*z0^2 + x^36 + x^35*y + x^35*z0 - x^33*y*z0^2 + x^35 - x^33*y*z0 - x^34 + x^33*y - x^32*y*z0 + x^31*y*z0^2 + x^33 - x^32*y + x^32*z0 - x^31*z0^2 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^29*y*z0 - x^29*z0^2 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*z0^2 - x^28 - x^27*y + x^26*y - x^26*z0 + x^7*y*z0^2, + -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^27 + x^26*y + x^8, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^47*y*z0 + x^46*y*z0^2 - x^48 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 - x^26*y*z0 + x^26*z0 + x^8*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^52 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^49*y*z0 + x^49*z0^2 - x^50 + x^48*z0^2 - x^49 + x^48*y - x^48*z0 + x^46*y*z0^2 - x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^41*y*z0^2 + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 + x^38 + x^36*y*z0 + x^36*z0^2 - x^37 - x^36*z0 + x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*z0 + x^32*y*z0^2 - x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^32*z0 - x^30*y*z0^2 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^8*z0^2, + x^54*z0 + x^53*z0^2 - x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*z0 + x^51*z0^2 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^48*z0^2 + x^47*y*z0^2 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^44*y*z0^2 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*z0 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^36*z0 - x^34*y*z0^2 + x^35*y - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^32*y*z0^2 + x^33*y + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^29 + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y - x^26*y + x^8*y*z0, + x^55 - x^53*z0^2 - x^53*y + x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^50 + x^49*y + x^49*z0 - x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 - x^43*y + x^43 - x^42*z0 - x^41*y*z0 + x^41*z0 - x^40*z0^2 - x^41 - x^40*z0 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 - x^37*y*z0^2 + x^39 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^34*y - x^33*z0^2 - x^34 + x^33*z0 + x^32*y*z0 - x^32*z0 - x^31*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^26*z0^2 + x^26*z0 + x^8*y*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^52*y + x^51*y*z0 - x^51*z0^2 - x^52 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^40*y*z0 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 - x^37*z0^2 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^31*y*z0 - x^31*z0 + x^30*y*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^26*y*z0 + x^27 + x^26*y + x^26*z0 + x^9*z0, + -x^54 + x^52*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 - x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 - x^45*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^43*z0^2 - x^42*y*z0^2 + x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^42*y - x^42*z0 - x^40*y*z0^2 - x^42 + x^41*y + x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y - x^38*z0 - x^38 + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*z0 + x^35*y*z0 + x^35*z0 - x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 + x^33*y + x^33*z0 - x^31*y*z0^2 + x^33 - x^32*y + x^30*y*z0^2 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 + x^26*y + x^26*z0 + x^9*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 + x^51*z0^2 + x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^37*z0^2 + x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y + x^36*z0 - x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^33*y*z0 + x^32*y*z0^2 + x^32*y*z0 - x^32*z0^2 + x^33 + x^32*y + x^32*z0 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 - x^28*z0^2 + x^29 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 - x^26*y*z0 + x^27 - x^26*y + x^9*y*z0, + x^54*z0 + x^53*z0^2 - x^54 - x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y - x^50*z0^2 - x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 + x^49*y - x^48*y*z0 - x^47*y*z0^2 + x^47*y*z0 + x^46*y*z0^2 + x^48 - x^46*z0^2 + x^47 - x^45*y*z0 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^37*y + x^37*z0 + x^35*y*z0^2 - x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^32*y*z0 + x^33 + x^32*y + x^32*z0 + x^31*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 + x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*y - x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y + x^26*z0 + x^9*y*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^32 + x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^10, + x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41*z0 - x^41 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*y + x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*z0 + x^32*z0^2 - x^32*z0 + x^31*y*z0 + x^32 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 - x^27*z0^2 + x^26*y*z0^2 + x^26*y*z0 - x^26*z0 + x^10*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*z0 - x^45*z0^2 - x^46 - x^44*y*z0 + x^45 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y - x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*y - x^41*z0 + x^41 - x^40 - x^39*z0 - x^38*z0^2 - x^37*y*z0^2 + x^38*z0 + x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 - x^36*y*z0 - x^37 - x^36*y + x^36*z0 + x^35*z0^2 + x^36 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 - x^35 + x^33*y*z0 - x^33*z0^2 + x^33*y + x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 + x^32*y + x^32*z0 - x^32 + x^31 + x^30*z0 + x^29*z0^2 + x^28*y*z0^2 - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^29 + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 + x^28 + x^27*y - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^10*z0^2, + -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^49*y*z0 - x^48*y*z0^2 + x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*y + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^42 + x^41*y - x^41 - x^39*z0^2 + x^39*z0 - x^38*z0^2 + x^39 + x^38*y - x^38*z0 + x^38 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^36 - x^35*y + x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 + x^34 + x^33*y + x^33*z0 + x^33 - x^32*y + x^31*z0^2 + x^32 - x^30*z0^2 - x^30*z0 + x^29*z0^2 - x^30 - x^29*y + x^29*z0 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*y - x^26*z0 + x^10*y*z0^2, + x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*y + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27 - x^26*y - x^26*z0 + x^11, + x^55 - x^53*z0^2 - x^53*y + x^53*z0 + x^51*y*z0^2 - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 - x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 + x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y - x^32*z0 - x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^26*y*z0 - x^26*y + x^11*z0, + x^55 - x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^51 - x^49*y*z0 - x^49*z0^2 + x^50 - x^49*y + x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^47 - x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y + x^41*z0 + x^40*z0 + x^39*z0^2 - x^38*y*z0^2 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 + x^37*y + x^36*y*z0 - x^36*z0^2 + x^37 + x^36*y + x^35*z0^2 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^34 - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^31*z0 - x^30*z0^2 + x^29*y*z0^2 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^26*y - x^26*z0 + x^11*z0^2, + -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*y + x^11*y, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^26*z0 + x^11*y*z0, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*z0^2 - x^50*y*z0^2 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 + x^47*y*z0^2 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^46 - x^45*y + x^45*z0 + x^43*y*z0^2 + x^44*y + x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 - x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*z0^2 + x^42 - x^41*y - x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^38*y*z0 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*z0 - x^35*y*z0 + x^35*z0^2 - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^33*y*z0^2 + x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 - x^33*y - x^33*z0 - x^33 + x^32*y - x^31*z0^2 - x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*z0^2 + x^29 - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^11*y*z0^2, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27 - x^26*y + x^26*z0 + x^12, + x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 - x^41 + x^40*z0 - x^39*y*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*z0^2 - x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*y*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^27*z0 - x^27 - x^26*y - x^26*z0 + x^12*z0, + -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 + x^52*y - x^51*y*z0 + x^52 + x^51*y + x^51*z0 + x^50*z0^2 + x^51 + x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 - x^44*y*z0 - x^44*z0^2 - x^45 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^39*y*z0^2 + x^41 - x^39*z0^2 + x^39*y - x^39*z0 + x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^30*y*z0^2 - x^32 + x^30*z0^2 - x^30*y + x^30*z0 - x^29*z0^2 - x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^28*y - x^28*z0 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^12*z0^2, + -x^55 + x^53*z0^2 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^41*y*z0^2 + x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^28*y*z0 - x^28*z0^2 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27 + x^26*z0 + x^12*y, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y - x^41 + x^40*z0 - x^39*z0^2 - x^40 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^26*y*z0 + x^27 + x^26*y + x^12*y*z0, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 + x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 - x^51 + x^50*y + x^49*y*z0 - x^49*z0^2 - x^50 + x^49 - x^48*y + x^48*z0 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*z0 - x^45*y*z0 + x^45*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^43*y*z0 + x^43*z0^2 - x^44 - x^43*z0 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 - x^38 - x^36*y*z0 + x^36*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^35*z0^2 - x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^34*z0 + x^33*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 - x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^27 - x^26*y + x^12*y*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 + x^41 - x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^32*y - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*z0^2 - x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^27 + x^26*y - x^26*z0 + x^13, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^45*y*z0^2 - x^46*y + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^39 + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*z0^2 - x^36*y + x^35*y*z0 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 - x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*z0 + x^13*z0^2, + x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 + x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^26*z0 + x^13*y, + -x^54*z0 - x^53*z0^2 + x^54 + x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*y - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^42*y*z0 + x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^41 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*y - x^38*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^33*y - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 + x^32*y - x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y + x^28*z0^2 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^26*y + x^26*z0 + x^13*y*z0, + x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*z0^2 + x^51*y*z0^2 + x^52*y - x^52*z0 + x^51*y*z0 - x^50*y*z0^2 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^51 - x^50*y + x^49*y*z0 + x^49*z0^2 - x^49*y - x^49*z0 + x^48*y*z0 - x^47*y*z0^2 + x^48*y + x^47*z0^2 - x^46*y*z0^2 + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^45*z0^2 + x^46 - x^45*y - x^45*z0 + x^44*y*z0 + x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^44 + x^43*y - x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 - x^40*z0^2 + x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 + x^37*y*z0 + x^36*y*z0^2 + x^38 - x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^35*z0^2 - x^36 - x^35*y + x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^35 - x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 - x^32*y*z0^2 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^31*z0^2 - x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^27*y*z0^2 - x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 + x^26*z0 + x^13*y*z0^2, + x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y - x^46*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^27 + x^14, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y - x^49*y*z0 - x^49*z0^2 + x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 + x^47*z0^2 - x^46*y*z0^2 + x^48 - x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^44*y*z0^2 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*z0 - x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^38*y*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 + x^37*y*z0^2 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 + x^37 - x^36*y + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*y*z0 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*z0 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^29*y*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0 + x^14*z0^2, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^51*y*z0 - x^51*z0^2 - x^51*y - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^47*y*z0 - x^46*y*z0^2 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^28*y - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 - x^26*y + x^26*z0 + x^14*y, + -x^55 + x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*z0 + x^46*y*z0^2 + x^48 - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y - x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^37*z0^2 - x^37*y + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^29 + x^28*y + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^26*y*z0 - x^26*z0 + x^14*y*z0, + x^55 + x^54*z0 - x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^50*y*z0 - x^49*y*z0^2 + x^50*y - x^49*y*z0 - x^49*y - x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*z0 + x^46*z0^2 + x^46*y + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^43*y*z0 + x^44 + x^43*y + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 + x^41*y - x^41*z0 + x^40*z0^2 + x^41 - x^40*z0 - x^38*y*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^37*y*z0 + x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^37 - x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 - x^34*y - x^34*z0 - x^33*z0^2 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 - x^32*z0^2 - x^32*y + x^32*z0 - x^31*z0^2 - x^32 + x^31*z0 - x^30*z0^2 + x^29*y*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^28*y*z0 - x^28*z0^2 - x^29 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^26*y + x^14*y*z0^2, + -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^41 - x^40*y - x^40*z0 - x^39*z0^2 - x^40 - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^32 - x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27 + x^26*z0 + x^15, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*z0^2 + x^46*y*z0^2 + x^47*z0 - x^45*y*z0^2 + x^47 - x^46*z0 - x^45*y*z0 + x^46 + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^45 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^43*z0 - x^42*z0^2 - x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 + x^41*y + x^41*z0 + x^39*y*z0^2 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*z0 + x^38*y*z0 + x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 - x^38 - x^36*y*z0 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 - x^35*y*z0 - x^36 - x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*z0 + x^33*z0^2 + x^32*y*z0^2 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^31*y*z0^2 - x^32*y - x^32*z0 - x^30*y*z0^2 + x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*z0 - x^29*y*z0 + x^28*y*z0^2 + x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 + x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 - x^26*z0^2 + x^27 + x^26*y + x^15*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*z0 + x^51*z0^2 + x^52 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y - x^44*y*z0^2 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*y - x^43*z0 - x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^40*z0 - x^39*y*z0 - x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*z0 + x^30*y*z0 + x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 + x^26*y*z0 - x^27 - x^26*z0 + x^15*y*z0, + -x^55 - x^54*z0 + x^54 + x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*y + x^48*y*z0 - x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^45*y*z0^2 + x^46*y + x^45*y*z0 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^42*z0^2 - x^41*y*z0^2 - x^42*y - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*z0 + x^40*z0^2 - x^39*y*z0^2 - x^41 - x^40*z0 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 + x^33*y + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*z0 + x^31*z0^2 + x^30*y*z0^2 + x^32 + x^31*z0 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 - x^26*z0 + x^15*y*z0^2, + x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27 + x^26*y - x^26*z0 + x^16, + x^55 - x^53*z0^2 + x^54 - x^53*y + x^52*z0^2 + x^51*y*z0^2 - x^52*y + x^52*z0 - x^50*y*z0^2 - x^52 - x^50*y*z0 + x^50*z0^2 - x^51 - x^50*z0 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^48 - x^47*z0 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*z0^2 + x^45 - x^44*y - x^43*z0^2 + x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^40*y*z0^2 + x^42 - x^41*y - x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 - x^38*y*z0^2 + x^38*y*z0 - x^39 - x^38*y + x^38*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 + x^37*y - x^37*z0 + x^36*y*z0 + x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 + x^35*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*z0^2 - x^35 - x^34*y + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^31*y*z0^2 - x^33 + x^32*y + x^31*z0^2 - x^32 - x^31*z0 + x^30*z0^2 - x^29*y*z0 + x^28*y*z0^2 + x^30 + x^29*y - x^29*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^26*y - x^26*z0 + x^16*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 + x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^40*y*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 - x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*z0 + x^31*y*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 + x^26*y*z0 + x^27 + x^16*y*z0, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^52*z0^2 - x^51*y*z0^2 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^50*y*z0^2 + x^51*z0 - x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^50*y - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*z0 - x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 + x^49 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 + x^46 + x^45*z0 - x^44*y*z0 + x^43*y*z0^2 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 - x^40*y*z0^2 + x^42 + x^41*y + x^41*z0 + x^40*z0^2 - x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*y + x^36*y*z0 + x^36*z0^2 + x^37 - x^34*y*z0^2 - x^36 - x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 - x^33 - x^32*y - x^32*z0 - x^31*z0^2 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^26*y - x^26*z0 + x^16*y*z0^2, + x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 + x^32*y*z0 - x^32*z0^2 + x^33 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^26*y - x^26*z0 + x^17, + x^55 - x^53*z0^2 - x^53*y + x^51*y*z0^2 + x^53 + x^52 - x^51*y - x^51 + x^50*y + x^48*y*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^47 + x^46 - x^45 + x^42*y*z0^2 + x^42*y + x^41*y - x^39*y*z0^2 - x^41 + x^38*y*z0^2 + x^40 + x^36*y*z0^2 - x^38 + x^35*y*z0^2 + x^37 + x^36*y - x^36 + x^35 - x^33*y - x^32*y + x^32 - x^31 + x^29 - x^28 - x^27*y + x^26*z0^2 + x^27 + x^26*y + x^17*z0^2, + -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^28*y*z0 - x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y - x^27 - x^26*y + x^26*z0 + x^17*y, + x^54*z0 + x^53*z0^2 - x^54 - x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*y - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^49*y*z0 - x^49*z0^2 + x^50 + x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 + x^45*z0^2 + x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^43*y*z0 + x^43*z0^2 - x^44 + x^43*z0 - x^42*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*y*z0 - x^42 + x^41*y - x^41*z0 - x^40*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 + x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^34*z0 - x^34 + x^33*y - x^33*z0 - x^32*y*z0 + x^33 - x^32*y + x^32*z0 + x^31*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 + x^29*y*z0 - x^28*y*z0^2 - x^29*y - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 - x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^26*y + x^17*y*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^40*y*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^37*z0^2 + x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 + x^26*z0 + x^18*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 - x^52*y + x^52*z0 + x^51*y*z0 + x^50*y*z0^2 - x^50*y*z0 - x^50*z0^2 - x^51 + x^50*y - x^49*y*z0 - x^48*y*z0^2 + x^49*y + x^48*z0^2 - x^47*y*z0^2 - x^48*y - x^48*z0 + x^47*z0^2 - x^47*z0 - x^46*z0^2 + x^46*y + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*z0^2 + x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 + x^42 - x^41*z0 + x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y + x^37*y*z0 - x^37*z0^2 - x^38 + x^36*y*z0 + x^36*z0^2 + x^36*y - x^36*z0 + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*y*z0 + x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*z0^2 - x^32*y*z0^2 + x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y - x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 - x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^18*z0^2, + -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 + x^27 + x^26*y + x^18*y, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^52*y*z0 + x^51*y*z0^2 - x^52*z0 - x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y - x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^18*y*z0, + x^54 - x^53*z0 - x^52*z0^2 + x^53 - x^52*y + x^51*y*z0 + x^50*y*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 - x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^48 - x^47*y - x^46*y*z0 - x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 + x^44*y*z0 - x^45 + x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y + x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y - x^41*z0 + x^40*z0^2 + x^41 + x^39*z0^2 - x^40 + x^39*z0 + x^38*z0^2 - x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 + x^36 + x^34*y*z0 - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y + x^32*z0 - x^32 + x^31 - x^30*z0 + x^29*y + x^29*z0 - x^28*y*z0 + x^27*y*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 - x^26*y + x^18*y*z0^2, + -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 + x^41 + x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 - x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^28*y*z0 - x^28*z0^2 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y + x^26*y + x^26*z0 + x^19, + -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 + x^52 - x^51*y - x^50*y*z0 - x^50*z0^2 + x^51 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^45*y*z0 + x^45*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^43*y*z0 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*z0^2 - x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 + x^40*y*z0^2 - x^42 - x^41*y - x^41*z0 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^39 + x^38*y + x^37*y*z0 + x^38 - x^37*y + x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^36 + x^35*y + x^35*z0 - x^34*y*z0 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*z0^2 + x^34 - x^33*z0 - x^32*y*z0 + x^33 + x^32*y + x^32*z0 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^30*y + x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*y - x^28*y*z0 + x^29 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y + x^19*z0^2, + x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^52*y + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^46*z0 - x^44*y*z0^2 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*y + x^19*y, + x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^47*y*z0 - x^46*y*z0^2 - x^48 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41 + x^40*z0 + x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 - x^37*z0^2 + x^37*y - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^32 - x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 - x^28*y + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 + x^26*y*z0 + x^19*y*z0, + x^55 - x^53*z0^2 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^48*y - x^48 - x^47*y - x^47*z0 + x^46*y*z0 - x^45*y*z0^2 + x^47 - x^46*y - x^46 - x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 + x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 + x^40*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y + x^36*y*z0 + x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 - x^34 + x^33*y - x^33*z0 + x^32*y*z0 + x^32*y - x^32*z0 - x^32 - x^31*z0 - x^31 + x^30*z0 - x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*z0 + x^28*y*z0 - x^29 - x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*y - x^26*z0 + x^19*y*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^41*y*z0^2 + x^43 - x^42*y - x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 + x^31*z0 + x^30*y*z0 - x^30*z0^2 - x^31 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^27*y + x^26*y*z0 - x^27 + x^26*y + x^20*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y + x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 - x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y - x^51*z0 + x^49*y*z0^2 + x^51 - x^50*y - x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 - x^46 + x^45*y + x^45*z0 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 + x^43*z0^2 + x^44 - x^42*y*z0 - x^41*y*z0^2 + x^42*y - x^41*y*z0 - x^41*z0^2 + x^41*y + x^41*z0 + x^40*z0 + x^39*z0^2 + x^38*y*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 - x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 - x^32*y*z0^2 - x^33*y + x^32*y*z0 + x^32*z0^2 - x^32*y - x^32*z0 + x^30*y*z0^2 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 + x^28*z0 - x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*z0^2 - x^27 + x^26*y + x^26*z0 + x^20*z0^2, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*y + x^48*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*y - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^32*y*z0 + x^32*z0^2 + x^32*z0 - x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^26*z0 + x^20*y*z0, + -x^55 + x^53*z0^2 + x^53*y - x^53*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^52 - x^51*y - x^51*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 + x^42*y + x^41*y*z0 - x^41*z0^2 + x^41*y - x^41*z0 - x^40*z0^2 - x^39*z0^2 - x^40 + x^39*y + x^39*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*z0 + x^37*y*z0 + x^38 - x^37*z0 - x^36*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*y + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*y - x^32*y*z0 - x^32*z0^2 - x^32*y + x^32*z0 - x^31*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*z0 - x^28*y*z0 + x^28*z0 + x^28 - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^27 + x^26*y + x^20*y*z0^2, + x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*y*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^37*z0^2 - x^38 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^32*y*z0^2 - x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 - x^32*y + x^32*z0 + x^31*y*z0 - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*z0 + x^26*y - x^26*z0 + x^21*z0, + -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^52 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^51 - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*z0 - x^45*z0^2 + x^44*y*z0^2 + x^46 + x^45*y - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^39*y*z0^2 + x^39*z0^2 - x^39*y - x^39*z0 - x^38*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 + x^33 + x^32*y + x^32*z0 - x^30*z0^2 + x^30*y + x^30*z0 + x^29*z0^2 - x^30 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 + x^29 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^26*y - x^26*z0 + x^21*z0^2, + x^54*z0 + x^53*z0^2 + x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 - x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 + x^46 - x^43*y*z0^2 - x^45 + x^44*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^39*z0^2 - x^40 - x^39*y + x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 - x^36*y*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^36*y - x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^33 + x^32*y - x^32*z0 - x^31*z0^2 - x^30*z0^2 + x^31 + x^30*y - x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^28*y*z0 + x^27*y*z0^2 - x^29 - x^28*y - x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^27 - x^26*y - x^26*z0 + x^21*y*z0^2, + -x^55 + x^53*z0^2 + x^54 + x^53*y - x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*z0^2 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*z0 + x^41*z0^2 + x^42 + x^41*y + x^40*y*z0 - x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*y + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y + x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*z0 - x^26*y*z0 + x^26*y - x^26*z0 + x^22*z0, + -x^55 + x^53*z0^2 + x^53*y + x^53*z0 + x^52*z0^2 - x^51*y*z0^2 - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^48*y*z0^2 - x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^41*y*z0^2 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^40*y*z0^2 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 - x^37*y*z0 + x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^32*y*z0^2 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^28*y*z0 + x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27 + x^26*z0 + x^22*z0^2, + -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 + x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 + x^26*y + x^22*y, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 + x^44*y*z0^2 + x^46 + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 + x^39*z0^2 + x^40 - x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*y + x^26*z0 + x^22*y*z0, + x^54*z0 + x^53*z0^2 + x^54 - x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*y + x^51*z0^2 + x^50*y*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^50 + x^49*z0 - x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*y - x^46*z0 - x^45*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^43*z0 + x^42*z0^2 - x^41*y*z0^2 - x^43 - x^42*y + x^41*z0^2 + x^42 + x^40*z0^2 - x^41 + x^40*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 - x^38*y - x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^34*z0 + x^32*y*z0^2 + x^34 + x^33*y + x^32*z0^2 - x^33 + x^32 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*y + x^27*y*z0^2 + x^28*y - x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 + x^26*z0 + x^22*y*z0^2, + x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 + x^52 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y - x^26*z0 + x^23, + x^55 - x^53*z0^2 - x^53*y + x^51*y*z0^2 - x^53 - x^51*z0^2 + x^52 + x^51*y - x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*y - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^42*y - x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^39*y*z0 + x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*z0 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 + x^30*y*z0 - x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^23*z0, + -x^55 - x^54*z0 + x^53*y + x^52*y*z0 - x^52*z0 - x^51*z0^2 - x^52 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^47*y*z0^2 + x^49 - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 - x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^41*y - x^39*y*z0^2 - x^41 + x^40*z0 + x^39*z0^2 - x^38*y*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*z0 - x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 - x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^34*y - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 + x^32*z0^2 + x^32*y + x^30*y*z0^2 + x^32 - x^31*z0 - x^30*z0^2 + x^29*y*z0^2 + x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*z0 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27 - x^26*y + x^23*z0^2, + x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*z0 - x^46*y*z0^2 - x^48 + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41 - x^40*z0 + x^39*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^37*z0^2 + x^37*y - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^26*y*z0 + x^26*z0 + x^23*y*z0, + -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^52 - x^51*y - x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^49*y - x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^48*z0 + x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^43*y*z0^2 + x^45 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*z0^2 - x^43 - x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*y - x^41*z0 - x^40*z0^2 - x^40*z0 + x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y + x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^34 + x^33*y - x^33*z0 - x^32*y*z0 + x^32*y + x^32*z0 + x^31*z0^2 + x^31*z0 - x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^28*y*z0 - x^28*z0^2 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y + x^23*y*z0^2, + -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 - x^52*y + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y - x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 + x^42 - x^41*z0 - x^40*y*z0 + x^41 + x^40*z0 - x^39*y*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 - x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*z0 + x^31*y*z0 - x^32 - x^31*z0 + x^30*y*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*z0 + x^24*z0, + x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 + x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^50*z0 + x^48*y*z0^2 + x^50 - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 + x^44*y*z0^2 + x^45*y - x^43*y*z0^2 - x^44*y + x^44*z0 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*z0^2 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 - x^41*y + x^41*z0 - x^39*y*z0^2 - x^41 + x^39*y - x^38*z0^2 - x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*z0^2 + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 + x^32*y - x^32*z0 + x^30*y*z0^2 + x^32 - x^30*y + x^29*z0^2 + x^28*y*z0^2 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*z0 + x^27*y*z0 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y - x^26*z0 + x^24*z0^2, + -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^24*y, + x^54*z0 + x^53*z0^2 + x^54 - x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*z0^2 + x^52 - x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^44*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*z0 + x^26*y + x^26*z0 + x^24*y*z0, + -x^54 - x^53*z0 + x^52*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y + x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 + x^48*y*z0 + x^47*y*z0^2 + x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 - x^46*y*z0 + x^45*z0^2 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 - x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^42 - x^41*z0 + x^40*z0^2 + x^39*y*z0^2 - x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^33 + x^32*z0 - x^31*z0^2 - x^30*y*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 + x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 + x^26*z0 + x^24*y*z0^2, + x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^41 - x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y + x^32*z0 - x^32 + x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27 - x^26*z0 + x^25, + x^55 + x^54*z0 + x^54 - x^53*y - x^53*z0 - x^52*y*z0 + x^52*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 + x^48*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^46*z0 + x^45*z0^2 - x^44*y*z0^2 + x^45*y - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 - x^42*y*z0 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 + x^42 - x^41*y - x^41*z0 + x^40*z0^2 - x^41 - x^39*z0^2 + x^39*y - x^39*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^36*y*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 - x^35*z0^2 - x^34*y*z0^2 + x^35*y - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 - x^33 + x^32*y + x^32*z0 - x^31*z0^2 + x^32 + x^30*z0^2 - x^30*y + x^30*z0 + x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^27*y*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^27 - x^26*y - x^26*z0 + x^25*z0^2, + -x^55 - x^54*z0 + x^54 + x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^50*y*z0^2 - x^51*y - x^50*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*y - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^47*y - x^45*y*z0^2 - x^47 + x^46*y + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^43*z0 - x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^41*y*z0 + x^40*y*z0^2 + x^42 + x^41*y + x^41*z0 - x^40*z0^2 - x^40*z0 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^36*y + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*z0 + x^34*y*z0 + x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 + x^33*y*z0 - x^33*z0^2 - x^32*y*z0^2 + x^32*y*z0 - x^31*y*z0^2 - x^33 - x^32*y - x^32*z0 + x^31*z0^2 + x^31*z0 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 + x^27*z0^2 - x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^25*y*z0^2 - x^27 + x^26*y - x^26*z0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1/y) dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.expansionat_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y +[?7h[?12l[?25h[?2004l[?7hy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-3 + 2*t^2 + 2*t^3 + t^8 + t^9 + 2*t^14 + 2*t^15 + t^17 + 2*t^18 + 2*t^20 + 2*t^24 + 2*t^26 + t^27 + 2*t^29 + t^35 + 2*t^42 + t^47 + 2*t^48 + 2*t^51 + 2*t^53 + t^54 + 2*t^56 + 2*t^60 + 2*t^62 + t^68 + 2*t^74 + t^78 + t^81 + 2*t^83 + 2*t^87 + t^89 + 2*t^93 + O(t^97) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7las_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7l.y], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 30) +[?7h[?12l[?25h[?2004l[?7h[-x^115 + x^113*z0^2 + x^112*z0^2 - x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 + x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^105*y*z0^2 + x^107 - x^106*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*z0^2 + x^100*y*z0^2 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^97*y*z0 + x^98 - x^97*y - x^97*z0 + x^96*z0^2 + x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 + x^96 + x^95*y + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^92*y*z0 - x^92*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 + x^90 + x^89*y - x^87*y*z0^2 - x^89 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^84*y*z0^2 + x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^78*y*z0 - x^77*y*z0^2 - x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^76*y + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 + x^75 - x^74*y - x^72*y*z0^2 + x^73*y + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^70 - x^69*z0 - x^67*y*z0^2 + x^68*y - x^67*y*z0 + x^67*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y + x^57*y*z0^2 - x^57*y*z0 + x^56*y*z0^2 + x^57*y - x^56*y*z0 + x^56*z0^2 - x^57 - x^55*y*z0 - x^56 + z0^2, + -x^115 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^102 - x^100*y*z0 - x^101 + x^100*y + x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y + x^98*y*z0 + x^97*y*z0^2 - x^99 - x^97*z0^2 + x^96*y*z0^2 + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^93*y*z0^2 - x^95 - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*z0^2 + x^92 - x^91*y + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 + x^86 - x^84*y*z0 + x^84*z0^2 - x^84*z0 - x^82*y*z0^2 - x^83*y - x^82*y*z0 + x^81*y*z0 - x^81*z0^2 - x^82 - x^81*y + x^79*y*z0^2 + x^81 + x^79*y*z0 + x^79*z0^2 + x^80 - x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^72 + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y + x^61*y*z0^2 + x^63 + x^62*y + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^61 - x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56*z0 + x^55*y*z0 - x^56 - x^55*y + y, + -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*z0 - x^108*y*z0 + x^109 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y + x^104*y*z0 - x^103*y*z0^2 + x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^102 - x^101*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^99*y*z0 + x^99*z0^2 - x^100 - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*z0 - x^92*y*z0 + x^92*y + x^92*z0 + x^90*y*z0^2 + x^92 + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^91 + x^89*y*z0 - x^89*z0^2 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*y + x^86*z0 + x^85*y*z0 - x^86 - x^85*z0 - x^84*y*z0 - x^83*y*z0^2 - x^84*y + x^84*z0 - x^82*y*z0^2 + x^84 - x^83*z0 - x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 - x^77*y*z0^2 - x^79 - x^77*y*z0 - x^76*y*z0^2 + x^78 - x^77*y - x^76*y*z0 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^73*y*z0 - x^72*y*z0^2 - x^74 + x^72*y + x^72*z0 + x^71*y*z0 + x^72 - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^66*y*z0^2 - x^67*z0 - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^66 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^61 - x^59*z0^2 - x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + y*z0, + x^115 + x^114*z0 - x^113*z0 + x^112*z0^2 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^112 + x^110*y*z0 - x^109*y*z0^2 - x^111 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*z0^2 - x^109 + x^108*y + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y - x^104*z0^2 + x^103*y*z0^2 + x^104*z0 + x^103*y*z0 + x^104 + x^103*y - x^103*z0 - x^102*z0^2 - x^102*y - x^102*z0 + x^101*y - x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*z0 - x^98*y + x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^94*y*z0^2 - x^94*z0^2 - x^95 + x^94*z0 + x^93*y*z0 - x^94 - x^93*y + x^93*z0 - x^92*z0^2 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^91*z0 - x^90*z0^2 + x^91 + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^88*y*z0 - x^88*z0^2 + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^87 + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^84*y*z0 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*y + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^74*y*z0 + x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^71*y*z0^2 - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*y + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^65 + x^63*z0^2 - x^62*y*z0^2 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*z0 + x^61*z0^2 + x^61*y - x^59*y*z0^2 - x^61 - x^60*y + x^59*z0^2 + x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^58 - x^57*z0 + x^56*z0^2 - x^56*y + x^56*z0 - x^55*y*z0 + x^55*y + y*z0^2, + -x^115 + x^113*z0^2 + x^112*z0^2 - x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 + x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^105*y*z0^2 + x^107 - x^106*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*z0^2 + x^100*y*z0^2 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^97*y*z0 + x^98 - x^97*y - x^97*z0 + x^96*z0^2 + x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 + x^96 + x^95*y + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^92*y*z0 - x^92*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 + x^90 + x^89*y - x^87*y*z0^2 - x^89 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^84*y*z0^2 + x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^78*y*z0 - x^77*y*z0^2 - x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^76*y + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 + x^75 - x^74*y - x^72*y*z0^2 + x^73*y + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^70 - x^69*z0 - x^67*y*z0^2 + x^68*y - x^67*y*z0 + x^67*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y + x^57*y*z0^2 - x^57*y*z0 + x^56*y*z0^2 + x^57*y - x^56*y*z0 + x^56*z0^2 - x^57 - x^55*y*z0 - x^56 + x*z0, + x^115 - x^113*z0^2 - x^112*z0^2 + x^113 - x^112*y + x^110*y*z0^2 - x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y + x^110 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 + x^107*y - x^107*z0 + x^106*z0^2 + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^105 - x^104*y + x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^102*y + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*z0^2 + x^100*y + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*y - x^96*y*z0^2 - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^93*y*z0 + x^93*z0^2 - x^94 - x^93*y - x^92*z0^2 - x^91*y*z0^2 + x^92*y + x^92*z0 + x^91*y*z0 + x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 - x^89*y*z0^2 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^89*y + x^88*y*z0 - x^89 - x^88*y - x^86*y*z0^2 - x^87*y + x^87*z0 - x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^82*y*z0^2 - x^84 - x^83*y + x^82*y*z0 + x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*z0^2 - x^81 + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y + x^75*y*z0 - x^74*y*z0^2 + x^75*y - x^75*z0 + x^73*y*z0^2 + x^75 + x^74*z0 + x^73*y*z0 - x^72*y*z0^2 - x^73*y + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*z0 + x^70*y*z0^2 + x^72 - x^71*y - x^70*z0^2 - x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 - x^70 + x^68*z0^2 + x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 + x^67 + x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^64*y*z0 + x^64*z0^2 - x^65 - x^64*y - x^64*z0 - x^62*y*z0^2 - x^63*y + x^61*y*z0^2 + x^63 - x^61*z0^2 - x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 + x^60*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*z0 - x^57*y*z0 + x^57*y - x^56*y*z0 + x^55*y*z0^2 - x^56*y + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x*z0^2, + x^115 - x^114*z0 + x^113*z0^2 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*z0 + x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*z0 - x^106*y*z0^2 - x^108 - x^106*y*z0 - x^106*z0^2 - x^107 + x^106*z0 + x^104*y*z0^2 - x^106 - x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*y - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*y + x^102*y*z0 + x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 + x^101*z0^2 - x^102 + x^101*z0 + x^99*y*z0^2 - x^99*y*z0 - x^99*z0^2 + x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*z0 + x^96*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*z0^2 + x^96 + x^94*z0^2 + x^95 - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 + x^90*z0^2 + x^90*y + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^89*z0 + x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*z0 - x^85*y*z0^2 - x^87 + x^86*z0 + x^85*y*z0 - x^84*y*z0^2 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^84 + x^83*y + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^81*y*z0 + x^80*y*z0^2 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y - x^79*z0^2 - x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*z0^2 - x^76 + x^75*y + x^74*z0^2 + x^73*y*z0^2 + x^73*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 - x^69*y*z0^2 + x^71 - x^70*y - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y + x^66*z0^2 - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^64*y*z0 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*y*z0 + x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*y - x^62*z0 + x^61*y*z0 + x^62 - x^61*y - x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^58*z0^2 + x^59 + x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^57*y + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y + x^55*y*z0 - x^56 + x*y, + -x^114 - x^113 + x^112*z0 + x^111*z0^2 + x^112 + x^111*y - x^110*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^102*z0 - x^101*y*z0 - x^102 - x^101*y - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 + x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^93*y*z0^2 - x^94*y - x^93*y*z0 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^89*y - x^88*y*z0 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^88 - x^87*y + x^86*y*z0 - x^85*y*z0^2 + x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 - x^82*y*z0 - x^82*y - x^81*y*z0 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*z0 + x^79*z0^2 - x^80 + x^79*y - x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^76 + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*z0^2 + x^73 - x^72*y + x^71*z0^2 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^70 - x^69*z0 - x^68*y*z0 + x^67*y*z0^2 - x^69 - x^68*y - x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^64*y - x^64*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 - x^59*y*z0 - x^58*y*z0^2 + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x*y*z0, + x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^113 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 - x^110*z0^2 - x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^110 + x^109*y + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^107*y*z0 - x^107*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^105*y*z0 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*z0^2 - x^101*y - x^101*z0 + x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*y*z0 + x^99 + x^98*y + x^98*z0 + x^97*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*z0 - x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^92*y*z0^2 + x^94 - x^93*y + x^92*y*z0 + x^91*y*z0^2 + x^93 + x^91*y*z0 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^89*y*z0 - x^89*z0^2 - x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*y*z0 - x^88 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^86*z0 + x^85*y*z0 - x^84*y*z0^2 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*z0 - x^81*z0^2 + x^82 - x^81*y + x^80*y*z0 - x^79*y*z0^2 + x^78*y*z0^2 + x^80 - x^79*y + x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^65*y*z0 + x^66 - x^65*y + x^65*z0 + x^64*z0^2 + x^65 - x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 + x^56 + x^55*y + x*y*z0^2, + -x^115 + x^113*z0^2 + x^112*z0^2 - x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 + x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^105*y*z0^2 + x^107 - x^106*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*z0^2 + x^100*y*z0^2 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^97*y*z0 + x^98 - x^97*y - x^97*z0 + x^96*z0^2 + x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 + x^96 + x^95*y + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^92*y*z0 - x^92*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 + x^90 + x^89*y - x^87*y*z0^2 - x^89 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^84*y*z0^2 + x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^78*y*z0 - x^77*y*z0^2 - x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^76*y + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 + x^75 - x^74*y - x^72*y*z0^2 + x^73*y + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^70 - x^69*z0 - x^67*y*z0^2 + x^68*y - x^67*y*z0 + x^67*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y + x^57*y*z0^2 - x^57*y*z0 + x^56*y*z0^2 + x^57*y - x^56*y*z0 + x^56*z0^2 - x^57 - x^55*y*z0 - x^56 + x^2, + x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^113 - x^112*y + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 + x^110*z0^2 + x^111 - x^110*y + x^110*z0 + x^110 + x^109*y - x^109*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^107*y - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*z0 - x^104*y*z0 - x^103*y*z0^2 - x^104*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^102 - x^101*y + x^100*z0^2 + x^101 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y + x^98*z0^2 - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 + x^94*y*z0 - x^95 + x^93*y*z0 - x^92*y*z0^2 + x^93*y - x^93*z0 + x^92*y*z0 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y + x^90*y*z0 + x^90*z0^2 + x^90*z0 + x^89*z0^2 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 - x^88*y - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^86*y*z0 - x^86*z0^2 - x^87 + x^85*y*z0 - x^84*y*z0^2 - x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^85 + x^84*y + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*z0 - x^81*z0^2 - x^82 + x^81*y + x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*y*z0 + x^80 - x^78*y*z0 - x^77*y*z0^2 - x^79 - x^78*z0 + x^78 - x^77*y - x^77*z0 - x^77 - x^76*y + x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*y + x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^73*y - x^72*y*z0 + x^72*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^72 + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^70*y + x^68*y*z0^2 + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^69 - x^68*y - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 + x^64*y - x^64*z0 + x^63*y*z0 + x^62*y*z0^2 + x^64 + x^63*z0 + x^61*y*z0^2 - x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^58*y*z0 + x^59 + x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 + x^55*y*z0 + x^2*z0, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^110 - x^109*y + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^107*y*z0 - x^106*y*z0^2 - x^108 - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*z0 - x^103*z0^2 + x^104 + x^103*y - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*y + x^101*z0^2 + x^100*y*z0^2 + x^100*z0^2 + x^99*y*z0^2 + x^100*y - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^100 - x^99*y + x^98*y*z0 - x^96*y*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 - x^96*y - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*z0 - x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^93*y + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 + x^91*y*z0 - x^92 - x^91*y - x^90*y*z0 - x^90*z0^2 - x^91 + x^90*y + x^89*y + x^88*z0^2 + x^87*y*z0^2 + x^89 + x^88*y + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y + x^83 + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y + x^77*y*z0 - x^77*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^75*y*z0 + x^75*z0^2 + x^76 + x^74*y*z0 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^73*z0 + x^73 - x^72*y + x^72*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 - x^66*y*z0^2 + x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*y + x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*z0^2 - x^64 + x^63*y - x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 + x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^58 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^2*z0^2, + x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*z0 - x^108*y*z0^2 - x^110 - x^109*y + x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^108 - x^106*z0^2 + x^105*y*z0^2 + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*z0^2 - x^101 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^95*y*z0^2 - x^97 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*z0^2 + x^94 + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^90 - x^88*z0^2 - x^87*y*z0^2 + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^86*y - x^86*z0 - x^85*y*z0 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^85 - x^83*z0^2 - x^82*y*z0^2 - x^82*z0^2 + x^81*y*z0^2 - x^82*y + x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y + x^80*y*z0 + x^80*z0^2 + x^81 + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y + x^76*y*z0 + x^75*y*z0^2 + x^77 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^74*y - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*z0^2 + x^70 + x^69*y - x^69*z0 - x^67*y*z0^2 + x^69 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^65*y*z0^2 - x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*z0 + x^64 + x^63*y - x^63*z0 + x^61*y*z0^2 + x^62*y - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^60*y*z0 - x^61 - x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^55*y*z0 + x^56 + x^2*y, + -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 + x^110*y*z0 - x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y + x^105*y*z0^2 + x^106*y - x^105*z0^2 - x^105*y + x^105*z0 - x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^103*y + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y + x^96*y*z0 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^94*z0^2 - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^92*y*z0 + x^91*y*z0^2 + x^91*y*z0 + x^90*y*z0^2 - x^91*y - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^89*y*z0 - x^88*y*z0^2 - x^89*y - x^88*z0^2 + x^88*y - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*y + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 - x^77*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^74 - x^73*y - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^71*y + x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^69*y - x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y + x^61*y*z0 + x^61*z0^2 - x^62 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*z0^2 + x^60 + x^59*y - x^58*y*z0 + x^58*z0^2 - x^59 - x^58*y - x^57*y*z0 - x^58 + x^57*y + x^57*z0 - x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 + x^2*y*z0, + x^115 + x^114*z0 + x^114 - x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^112 - x^111*y - x^110*z0^2 + x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^103*y*z0^2 + x^105 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^101*z0 + x^100*z0^2 - x^101 + x^100*y + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^99 + x^96*y*z0^2 - x^98 - x^97*y - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*z0 - x^95*z0^2 - x^95*y - x^94*y*z0 - x^93*y*z0^2 + x^95 - x^94*y + x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*z0 - x^89*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^89 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*z0 - x^83*y*z0 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^81*z0^2 + x^82 - x^81*y + x^81*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*z0^2 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*z0 - x^75*z0^2 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^72*y - x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y + x^70*z0 + x^69*z0^2 - x^70 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*z0 + x^67*y + x^65*y*z0^2 - x^67 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*y + x^62*z0 + x^61*y*z0 - x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^60*z0 - x^59*y - x^59*z0 - x^58*z0^2 + x^58*y + x^58*z0 - x^57*y*z0 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^55*y + x^2*y*z0^2, + -x^115 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^102 - x^100*y*z0 - x^101 + x^100*y + x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y + x^98*y*z0 + x^97*y*z0^2 - x^99 - x^97*z0^2 + x^96*y*z0^2 + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^93*y*z0^2 - x^95 - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*z0^2 + x^92 - x^91*y + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 + x^86 - x^84*y*z0 + x^84*z0^2 - x^84*z0 - x^82*y*z0^2 - x^83*y - x^82*y*z0 + x^81*y*z0 - x^81*z0^2 - x^82 - x^81*y + x^79*y*z0^2 + x^81 + x^79*y*z0 + x^79*z0^2 + x^80 - x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^72 + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y + x^61*y*z0^2 + x^63 + x^62*y + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^61 - x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^3, + -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*z0 - x^108*y*z0 + x^109 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y + x^104*y*z0 - x^103*y*z0^2 + x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^102 - x^101*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^99*y*z0 + x^99*z0^2 - x^100 - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*z0 - x^92*y*z0 + x^92*y + x^92*z0 + x^90*y*z0^2 + x^92 + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^91 + x^89*y*z0 - x^89*z0^2 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*y + x^86*z0 + x^85*y*z0 - x^86 - x^85*z0 - x^84*y*z0 - x^83*y*z0^2 - x^84*y + x^84*z0 - x^82*y*z0^2 + x^84 - x^83*z0 - x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 - x^77*y*z0^2 - x^79 - x^77*y*z0 - x^76*y*z0^2 + x^78 - x^77*y - x^76*y*z0 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^73*y*z0 - x^72*y*z0^2 - x^74 + x^72*y + x^72*z0 + x^71*y*z0 + x^72 - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^66*y*z0^2 - x^67*z0 - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^66 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^61 - x^59*z0^2 - x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^3*z0, + x^115 + x^114*z0 - x^113*z0 + x^112*z0^2 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^112 + x^110*y*z0 - x^109*y*z0^2 - x^111 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*z0^2 - x^109 + x^108*y + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y - x^104*z0^2 + x^103*y*z0^2 + x^104*z0 + x^103*y*z0 + x^104 + x^103*y - x^103*z0 - x^102*z0^2 - x^102*y - x^102*z0 + x^101*y - x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*z0 - x^98*y + x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^94*y*z0^2 - x^94*z0^2 - x^95 + x^94*z0 + x^93*y*z0 - x^94 - x^93*y + x^93*z0 - x^92*z0^2 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^91*z0 - x^90*z0^2 + x^91 + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^88*y*z0 - x^88*z0^2 + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^87 + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^84*y*z0 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*y + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^74*y*z0 + x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^71*y*z0^2 - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*y + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^65 + x^63*z0^2 - x^62*y*z0^2 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*z0 + x^61*z0^2 + x^61*y - x^59*y*z0^2 - x^61 - x^60*y + x^59*z0^2 + x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^58 - x^57*z0 + x^56*z0^2 - x^56*y + x^56*z0 - x^55*y*z0 + x^55*y + x^3*z0^2, + x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^111*y - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^111 - x^109*y*z0 - x^108*y*z0^2 + x^108*y*z0 + x^109 + x^108*y - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y + x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 - x^102*y*z0^2 + x^104 + x^103*z0 - x^103 - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*z0^2 + x^97*y*z0^2 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^93 - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*z0 - x^90*z0^2 - x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^88 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^86*y - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^83 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*z0^2 + x^81 + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^77*y - x^75*y*z0^2 - x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*z0^2 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 - x^69*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y + x^67*z0^2 - x^66*y*z0^2 - x^67*y - x^65*y*z0^2 - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^64*y*z0 + x^64*y - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^63 + x^62*y - x^62*z0 - x^61*y*z0 + x^60*y*z0^2 - x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*z0 - x^58*z0^2 - x^59 - x^58*y - x^58*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^55*y*z0^2 + x^56*y + x^3*y, + -x^115 - x^114*z0 - x^114 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^109*y - x^108*y*z0 - x^107*y*z0^2 + x^109 - x^108*y + x^106*y*z0^2 + x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 + x^106*y + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y + x^104*y*z0 + x^103*y*z0^2 + x^105 - x^104*z0 + x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*y + x^97*y*z0 - x^97*z0^2 + x^98 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^95*z0^2 - x^96 - x^95*z0 - x^94*y*z0 - x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*z0^2 - x^87*y*z0^2 - x^88*y - x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y - x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^78*z0 - x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^76*y + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^75 - x^73*y*z0 + x^73*z0^2 + x^73*y - x^73*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y + x^67*y*z0^2 - x^69 - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*z0 - x^65*y*z0 - x^64*y*z0^2 + x^65*y + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^63*y + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^60*y*z0 + x^60*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y - x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^56 + x^55*y + x^3*y*z0, + x^115 - x^113*z0^2 - x^113*z0 - x^112*y + x^110*y*z0^2 - x^112 - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^111 - x^110*z0 + x^110 + x^109*y + x^108*y*z0 - x^107*y*z0^2 - x^108*y + x^107*y*z0 + x^108 + x^107*y + x^107*z0 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 + x^105*y*z0 + x^104*y*z0^2 - x^105*y + x^105*z0 - x^104*z0^2 + x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 + x^102*y*z0 + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*y*z0 + x^101 - x^100*y + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 - x^98*y*z0 + x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^96 + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 + x^91*y*z0 - x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*y - x^90*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*y + x^89*z0 - x^88*y*z0 + x^87*y*z0^2 - x^89 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y + x^86*y*z0 + x^85*y*z0^2 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*y*z0 + x^84 - x^83*y + x^83*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 + x^81*y*z0 + x^81*y - x^81*z0 + x^80*y*z0 + x^81 + x^80*y - x^79*y*z0 + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^76*y + x^75*y*z0 - x^74*y*z0^2 + x^76 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 + x^73 - x^72*y - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*z0 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y + x^69*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 - x^65 - x^64*y - x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y + x^61*z0^2 + x^62 - x^61*y + x^60*y*z0 + x^60*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 - x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^59 + x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 - x^55*y + x^3*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*z0 + x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*z0 - x^106*y*z0^2 - x^108 - x^106*y*z0 - x^106*z0^2 - x^107 + x^106*z0 + x^104*y*z0^2 - x^106 - x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*y - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*y + x^102*y*z0 + x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 + x^101*z0^2 - x^102 + x^101*z0 + x^99*y*z0^2 - x^99*y*z0 - x^99*z0^2 + x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*z0 + x^96*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*z0^2 + x^96 + x^94*z0^2 + x^95 - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 + x^90*z0^2 + x^90*y + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^89*z0 + x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*z0 - x^85*y*z0^2 - x^87 + x^86*z0 + x^85*y*z0 - x^84*y*z0^2 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^84 + x^83*y + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^81*y*z0 + x^80*y*z0^2 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y - x^79*z0^2 - x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*z0^2 - x^76 + x^75*y + x^74*z0^2 + x^73*y*z0^2 + x^73*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 - x^69*y*z0^2 + x^71 - x^70*y - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y + x^66*z0^2 - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^64*y*z0 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*y*z0 + x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*y - x^62*z0 + x^61*y*z0 + x^62 - x^61*y - x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^58*z0^2 + x^59 + x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^57*y + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y + x^55*y*z0 - x^56 + x^4, + -x^114 - x^113 + x^112*z0 + x^111*z0^2 + x^112 + x^111*y - x^110*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^102*z0 - x^101*y*z0 - x^102 - x^101*y - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 + x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^93*y*z0^2 - x^94*y - x^93*y*z0 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^89*y - x^88*y*z0 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^88 - x^87*y + x^86*y*z0 - x^85*y*z0^2 + x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 - x^82*y*z0 - x^82*y - x^81*y*z0 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*z0 + x^79*z0^2 - x^80 + x^79*y - x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^76 + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*z0^2 + x^73 - x^72*y + x^71*z0^2 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^70 - x^69*z0 - x^68*y*z0 + x^67*y*z0^2 - x^69 - x^68*y - x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^64*y - x^64*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 - x^59*y*z0 - x^58*y*z0^2 + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x^4*z0, + x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^113 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 - x^110*z0^2 - x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^110 + x^109*y + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^107*y*z0 - x^107*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^105*y*z0 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*z0^2 - x^101*y - x^101*z0 + x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*y*z0 + x^99 + x^98*y + x^98*z0 + x^97*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*z0 - x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^92*y*z0^2 + x^94 - x^93*y + x^92*y*z0 + x^91*y*z0^2 + x^93 + x^91*y*z0 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^89*y*z0 - x^89*z0^2 - x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*y*z0 - x^88 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^86*z0 + x^85*y*z0 - x^84*y*z0^2 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*z0 - x^81*z0^2 + x^82 - x^81*y + x^80*y*z0 - x^79*y*z0^2 + x^78*y*z0^2 + x^80 - x^79*y + x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^65*y*z0 + x^66 - x^65*y + x^65*z0 + x^64*z0^2 + x^65 - x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 + x^56 + x^55*y + x^4*z0^2, + x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^105*z0 + x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*z0 + x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^100*y*z0 - x^99*y*z0^2 - x^101 + x^100*y - x^99*y*z0 - x^99*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*y + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 - x^92*z0^2 - x^93 + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^90*z0^2 - x^89*y*z0^2 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y + x^88*y*z0 + x^88*z0^2 - x^89 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^86 + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^82*z0 - x^81*z0^2 + x^82 - x^81*y - x^81*z0 + x^81 + x^79*y*z0 - x^79*z0^2 + x^80 - x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y - x^77*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 - x^76 - x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^73 + x^72*z0 - x^71*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*z0^2 + x^70*y - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^68*z0^2 + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y + x^65*y*z0 - x^64*y*z0^2 - x^66 - x^64*y*z0 - x^64*z0^2 + x^63*y*z0 + x^63*z0^2 - x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^63 - x^62*y - x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y - x^58*y*z0^2 - x^60 + x^59*y - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*y*z0 + x^56*y*z0^2 + x^57*y - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y + x^55*y*z0 + x^55*y + x^4*y, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^112*y - x^111*y*z0 + x^110*y*z0^2 + x^112 + x^111*y - x^110*z0^2 - x^111 - x^109*z0^2 + x^110 - x^109*y + x^109*z0 + x^107*y*z0^2 - x^109 + x^108*y + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^105*y*z0 - x^105*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y - x^101*y*z0 + x^101*z0^2 + x^101*y + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^100 + x^99*z0 + x^98*y*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*y*z0 - x^95*y - x^95*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^93 - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^91*y - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^86 - x^85*y + x^85*z0 + x^84*z0^2 - x^84*z0 + x^83*y*z0 - x^82*y*z0^2 - x^84 - x^83*y + x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 + x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 + x^80 - x^79*y + x^78*y*z0 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 + x^77*z0 + x^76*y*z0 + x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 + x^73*y*z0^2 - x^75 - x^73*z0^2 - x^74 + x^72*y*z0 + x^73 - x^72*y - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0 - x^64*z0^2 - x^65 + x^64*y - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*z0^2 + x^62*y + x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^61*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y - x^57*z0^2 + x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x^4*y*z0, + -x^115 + x^114*z0 - x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 + x^104*y*z0^2 - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y + x^102*y*z0 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*y + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^98*y*z0 - x^98*z0^2 + x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^98 + x^97*y - x^96*y*z0 - x^96*z0^2 - x^97 + x^96*z0 - x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*z0 - x^94*y*z0 - x^95 + x^94*z0 + x^92*y*z0^2 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*z0^2 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*z0^2 - x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*z0 - x^86*y*z0 + x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 - x^85 + x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^83 + x^82*y + x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y + x^80*y*z0 + x^80*z0^2 - x^81 + x^79*y*z0 + x^80 - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^77*y*z0 - x^76*y*z0^2 - x^77*y - x^77*z0 + x^76*y*z0 + x^75*y*z0^2 - x^77 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^74 + x^73*y + x^72*y*z0 + x^72*z0^2 + x^73 - x^72*z0 - x^70*y*z0^2 + x^70*y*z0 - x^70*z0^2 + x^71 + x^70*z0 - x^69*z0^2 - x^70 + x^69*y - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^66*z0 + x^65*z0^2 - x^66 + x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 - x^62*y*z0^2 + x^64 - x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^62*y + x^62*z0 + x^60*y*z0^2 - x^61*y + x^60*y*z0 - x^60*z0^2 - x^61 + x^60*z0 + x^59*z0^2 - x^60 - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*y + x^57*y*z0 + x^58 - x^57*y - x^57*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*z0 + x^56 + x^55*y + x^4*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*z0 - x^108*y*z0^2 - x^110 - x^109*y + x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^108 - x^106*z0^2 + x^105*y*z0^2 + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*z0^2 - x^101 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^95*y*z0^2 - x^97 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*z0^2 + x^94 + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^90 - x^88*z0^2 - x^87*y*z0^2 + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^86*y - x^86*z0 - x^85*y*z0 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^85 - x^83*z0^2 - x^82*y*z0^2 - x^82*z0^2 + x^81*y*z0^2 - x^82*y + x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y + x^80*y*z0 + x^80*z0^2 + x^81 + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y + x^76*y*z0 + x^75*y*z0^2 + x^77 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^74*y - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*z0^2 + x^70 + x^69*y - x^69*z0 - x^67*y*z0^2 + x^69 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^65*y*z0^2 - x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*z0 + x^64 + x^63*y - x^63*z0 + x^61*y*z0^2 + x^62*y - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^60*y*z0 - x^61 - x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^55*y*z0 + x^56 + x^5, + -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 + x^110*y*z0 - x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y + x^105*y*z0^2 + x^106*y - x^105*z0^2 - x^105*y + x^105*z0 - x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^103*y + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y + x^96*y*z0 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^94*z0^2 - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^92*y*z0 + x^91*y*z0^2 + x^91*y*z0 + x^90*y*z0^2 - x^91*y - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^89*y*z0 - x^88*y*z0^2 - x^89*y - x^88*z0^2 + x^88*y - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*y + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 - x^77*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^74 - x^73*y - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^71*y + x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^69*y - x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y + x^61*y*z0 + x^61*z0^2 - x^62 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*z0^2 + x^60 + x^59*y - x^58*y*z0 + x^58*z0^2 - x^59 - x^58*y - x^57*y*z0 - x^58 + x^57*y + x^57*z0 - x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 + x^5*z0, + -x^115 - x^114*z0 - x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^111*y*z0 + x^111*z0^2 + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^108*y - x^107*y*z0 + x^106*y*z0^2 - x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*y - x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^102 + x^100*y*z0 + x^101 - x^99*y*z0 - x^99*z0^2 + x^100 - x^99*y + x^98*y*z0 + x^97*y*z0^2 + x^99 - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 + x^97*y + x^96*y*z0 + x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y - x^94*y*z0 + x^94*z0^2 + x^95 + x^94*y - x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*z0 - x^93 + x^92*y + x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*z0 + x^89*y*z0^2 - x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^89*z0 - x^88*z0^2 - x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^86*y*z0 + x^86*z0^2 + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*z0 + x^81*y*z0 - x^82 + x^81*y + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^78*y - x^77*y*z0 - x^77*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 + x^76 + x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*y - x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^59*z0 - x^58*z0^2 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56 - x^55*y + x^5*z0^2, + -x^115 - x^114*z0 + x^114 + x^112*z0^2 + x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*y + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y - x^109*y*z0 - x^109*z0^2 + x^110 + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^106*z0^2 - x^106*y - x^105*y*z0 + x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y + x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*z0^2 - x^103 - x^102*y - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^96*y - x^94*y*z0^2 + x^96 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y - x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^90 + x^88*z0^2 - x^89 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^86*y*z0 + x^85*y*z0^2 + x^85*y - x^85*z0 - x^84*y*z0 + x^85 - x^84*z0 - x^83*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^82 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^76*z0 - x^75*y*z0 - x^74*y*z0^2 - x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*y*z0 + x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^72 - x^70*z0^2 + x^71 + x^70*z0 - x^69*y*z0 - x^68*y*z0^2 + x^70 + x^69*y - x^68*y*z0 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y - x^64*z0^2 + x^65 - x^64*y + x^64*z0 + x^64 + x^63*y + x^63*z0 + x^63 - x^62*z0 + x^62 - x^61*y + x^60*z0^2 + x^61 + x^60*z0 + x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 + x^58*y*z0 + x^57*y*z0^2 + x^59 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^56*y - x^56*z0 + x^56 + x^5*y, + -x^115 + x^113*z0^2 - x^114 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^107 + x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 - x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 - x^103*y + x^102*y*z0 + x^102*z0^2 + x^103 + x^101*y*z0 + x^101*z0^2 + x^102 - x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^100*y + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^98*y*z0 - x^97*y*z0^2 - x^98*z0 + x^97*y*z0 + x^98 + x^97*y - x^97*z0 + x^96*y*z0 - x^97 - x^96*y + x^96*z0 - x^95*y*z0 + x^96 - x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 - x^91 - x^90*y - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*y - x^87*y*z0 - x^87*z0^2 - x^88 + x^87*y + x^87*z0 - x^86*y*z0 + x^85*y*z0^2 - x^87 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y - x^83*y*z0 - x^83*z0^2 - x^84 - x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*y + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^80*z0^2 - x^79*y*z0^2 + x^81 - x^80*y - x^79*z0^2 + x^80 + x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*z0^2 + x^76*y - x^75*z0^2 + x^76 + x^75*y + x^75*z0 + x^74*z0^2 + x^75 + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^74 - x^72*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 - x^68*y*z0 + x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^68 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y - x^63*z0^2 - x^62*y*z0^2 - x^64 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^60*y*z0^2 + x^62 + x^61*y - x^60*y*z0 + x^59*y*z0^2 + x^60*y - x^59*y*z0 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 - x^56*z0^2 - x^57 - x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^5*y*z0, + x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 + x^111 - x^110*z0 + x^109*y*z0 + x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*y*z0 + x^109 - x^108*y - x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^107*y + x^107*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^103*y + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*z0^2 - x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 + x^100 - x^99*y - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 - x^98*y - x^98*z0 - x^97*z0^2 - x^98 + x^97*y + x^96*y*z0 - x^95*y*z0^2 - x^97 - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^93*y*z0 - x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^91*z0 + x^90*y*z0 + x^89*y*z0^2 - x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^90 - x^89*y - x^89*z0 + x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 + x^85*y*z0^2 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^84*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^80*y*z0^2 - x^82 - x^81*y - x^81 + x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^80 + x^79*y - x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^76*z0^2 - x^75*y*z0^2 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 + x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^73 + x^72*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 - x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y - x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^56*y*z0 - x^56*z0^2 + x^57 - x^56*z0 + x^55*y + x^5*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^111*y - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^111 - x^109*y*z0 - x^108*y*z0^2 + x^108*y*z0 + x^109 + x^108*y - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y + x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 - x^102*y*z0^2 + x^104 + x^103*z0 - x^103 - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*z0^2 + x^97*y*z0^2 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^93 - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*z0 - x^90*z0^2 - x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^88 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^86*y - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^83 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*z0^2 + x^81 + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^77*y - x^75*y*z0^2 - x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*z0^2 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 - x^69*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y + x^67*z0^2 - x^66*y*z0^2 - x^67*y - x^65*y*z0^2 - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^64*y*z0 + x^64*y - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^63 + x^62*y - x^62*z0 - x^61*y*z0 + x^60*y*z0^2 - x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*z0 - x^58*z0^2 - x^59 - x^58*y - x^58*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^55*y*z0^2 + x^56*y + x^6, + -x^115 + x^113*z0^2 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 - x^108*y*z0^2 + x^109*y - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 + x^107*y + x^107*z0 - x^106*z0^2 + x^107 + x^106*z0 + x^105*y*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y - x^101*y*z0^2 + x^103 - x^102*z0 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 + x^96*y*z0 - x^95*y*z0^2 - x^97 + x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 + x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 - x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^88 - x^87*y - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 + x^84*y*z0 - x^84*z0^2 + x^84*y + x^83*z0^2 + x^82*y*z0^2 + x^84 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 + x^81*y*z0 - x^81*z0^2 + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^78 + x^77*z0 - x^76*y*z0 + x^77 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^73*y*z0 + x^73*z0^2 + x^73*y - x^72*z0^2 - x^73 - x^72*y - x^71*y*z0 - x^72 - x^71*y + x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^70*y + x^69*y*z0 - x^69*z0^2 + x^69*y + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^66*z0^2 + x^65*y*z0^2 + x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^64 + x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*y + x^58*z0 - x^57*y + x^56*y*z0 - x^56*z0^2 + x^57 + x^56*y - x^56*z0 + x^56 + x^6*z0, + -x^114*z0 - x^113*z0^2 + x^114 + x^113 + x^111*y*z0 + x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*z0^2 - x^111 - x^110*y - x^110*z0 + x^110 + x^108*y*z0 + x^107*y*z0^2 + x^108*y - x^108*z0 + x^107*y*z0 - x^108 - x^107*y - x^107*z0 + x^106*y*z0 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y + x^104*y*z0 - x^104*z0^2 - x^103*y*z0 + x^103*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^101*y + x^101*z0 - x^100*z0^2 - x^100*y + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 + x^98*y*z0 - x^98*y + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^94*y*z0 + x^95 + x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*z0^2 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^91 + x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*y + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y + x^85*z0 + x^84*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*z0 + x^82*y*z0 - x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 + x^81*z0^2 + x^82 - x^81*y + x^80*z0^2 - x^79*y*z0^2 + x^80*y - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^79 - x^78*y - x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*z0 + x^76*y*z0 - x^76*y + x^75*y*z0 + x^74*y*z0^2 + x^75*y + x^75*z0 + x^74*z0^2 + x^75 + x^73*y*z0 + x^72*y*z0^2 - x^74 - x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^73 - x^72*z0 + x^71*y*z0 - x^72 - x^71*y - x^70*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^70 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 - x^67*y*z0 - x^66*y*z0^2 - x^67*y + x^67*z0 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*y - x^65*z0 - x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^60 - x^59*y - x^59*z0 + x^58*y*z0 - x^58*y - x^58*z0 + x^57*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^6*z0^2, + -x^115 + x^113*z0^2 - x^114 - x^113 + x^112*y + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 - x^110*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 + x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^106*y*z0 - x^105*y*z0^2 + x^105*y*z0 - x^106 + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0 - x^102*y*z0 - x^101*y*z0^2 + x^103 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^97*y*z0 + x^97*z0^2 + x^98 - x^97*y + x^96*y*z0 - x^96*z0^2 + x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^94 - x^93*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*y - x^92*z0 - x^90*y*z0^2 + x^92 + x^91*y + x^90*y*z0 + x^90*z0^2 - x^91 - x^90*y + x^90*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 + x^88*z0^2 + x^89 + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y + x^82*y*z0 - x^82*z0 - x^80*y*z0^2 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 + x^79*z0^2 - x^80 - x^78*z0^2 - x^79 + x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^77*z0 + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 - x^75*z0^2 + x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^75 + x^74*z0 - x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^70 - x^69*y + x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*z0 + x^65*z0^2 + x^66 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*z0 + x^63*z0^2 + x^63*y + x^63*z0 + x^61*y*z0^2 + x^62*y - x^62*z0 + x^61*y*z0 - x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^60 + x^59*y - x^59*z0 + x^58*z0^2 + x^59 - x^58*y + x^58*z0 - x^58 - x^57*y - x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^6*y, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y - x^111*z0 - x^110*z0^2 - x^111 - x^110*y + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^106*y*z0 + x^106*z0^2 - x^106*y - x^106*z0 - x^105*y*z0 - x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^104 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y - x^101*z0^2 - x^102 - x^101*y - x^100*y*z0 - x^99*y*z0^2 + x^100*z0 + x^98*y*z0^2 - x^99*y + x^99*z0 + x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^97*y - x^97*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^94 - x^93*y - x^93*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^90*y - x^90*z0 - x^89*z0^2 + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^86*y - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y - x^83 - x^82*y + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^79*y*z0 + x^80 + x^79*y + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*z0 + x^76 - x^75*y + x^75*z0 + x^74*z0^2 - x^73*y*z0^2 + x^73*y*z0 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^70*y*z0^2 - x^71*y + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*z0 - x^68*y*z0 - x^67*y*z0^2 + x^69 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^64*y - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y + x^61*y*z0 + x^60*y*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^59 - x^57*y*z0 + x^58 - x^57*y - x^56*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^6*y*z0, + x^115 + x^114*z0 - x^114 - x^113*z0 - x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^112 + x^111*y + x^110*y*z0 + x^110*z0^2 - x^111 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 + x^101*y - x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*y + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^95*z0^2 - x^96 - x^95*y + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^91*z0 - x^91 + x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 - x^87*y*z0^2 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^84*z0 - x^83*y*z0 - x^84 + x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^80*y*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*y + x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^79*y + x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*y - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*z0 - x^74*y*z0 - x^75 - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*y - x^72*y*z0 + x^72*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*y - x^69*y*z0 + x^69*z0^2 + x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*z0 - x^67*z0^2 - x^67*y - x^66*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y - x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*z0 - x^60*y*z0^2 + x^62 - x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y - x^60*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 - x^57*z0^2 - x^57*y + x^56*y*z0 + x^56*z0^2 - x^57 + x^56*y + x^56*z0 + x^56 - x^55*y + x^6*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 + x^112*z0^2 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*z0 - x^110*y*z0 - x^109*y*z0^2 + x^111 + x^110*z0 - x^109*y*z0 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^108 + x^107*z0 + x^106*z0^2 - x^107 - x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^106 - x^105*y + x^105*z0 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^102 + x^101*y - x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^98*y*z0^2 + x^99*y - x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 - x^94*y*z0^2 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*z0 + x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 + x^90*y*z0 + x^89*y*z0^2 + x^91 - x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y - x^87*y*z0^2 + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^85*y + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*y + x^84*z0 + x^83*y*z0 - x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*y*z0 - x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^75 - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 + x^71*y - x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 + x^70 - x^69*y - x^68*y*z0 + x^68*z0^2 - x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^68 - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 - x^65*y + x^64*y*z0 - x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 - x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*z0^2 - x^63 - x^62*y + x^61*y*z0 - x^62 - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^7, + -x^115 - x^114*z0 - x^113*z0 + x^113 + x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^111 - x^110*y - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^108*y*z0 + x^107*y*z0^2 + x^108*y - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^106*y*z0 - x^107 + x^106*y + x^106*z0 - x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 - x^103*y*z0^2 + x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^104 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^101 + x^100*y + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^99*y + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^91*y*z0^2 - x^93 - x^92*z0 - x^91*y*z0 - x^90*y*z0^2 + x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y - x^89*z0 + x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*z0^2 + x^83 - x^82*y + x^82*z0 + x^81*y*z0 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y + x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y + x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^74*y*z0 - x^74*z0^2 + x^72*y*z0^2 - x^74 + x^73*y + x^72*y*z0 + x^72*z0^2 + x^73 - x^72*y - x^71*y*z0 - x^70*y*z0^2 + x^71*y + x^71*z0 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 + x^69*y + x^68*z0^2 + x^68*y - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y - x^65*y*z0^2 + x^66*y - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 + x^64*y*z0 - x^63*y*z0^2 - x^64*z0 - x^63*z0^2 + x^64 + x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*y + x^61*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^58*y*z0 + x^59 + x^58*y - x^58*z0 - x^56*y*z0^2 + x^57*y - x^56*y*z0 + x^55*y*z0^2 + x^57 - x^56*z0 + x^56 + x^55*y + x^7*z0, + -x^115 - x^114*z0 - x^114 + x^113 + x^112*y + x^111*y*z0 + x^111*y - x^111*z0 + x^110*z0^2 - x^110*y - x^109*z0^2 + x^110 + x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y - x^105*y*z0 - x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 + x^101*y - x^101*z0 + x^100*y*z0 + x^99*y*z0^2 + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^95*y*z0^2 - x^97 + x^96*y - x^95*z0^2 - x^96 + x^95*y + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*y*z0 - x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^91*y - x^91*z0 - x^90*y*z0 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^90 + x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^87*y + x^87*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*y - x^85*z0^2 - x^86 + x^85*z0 + x^84*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*y - x^83*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^81*z0^2 - x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^79*y*z0 + x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*z0 + x^77*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^76*y + x^75*y*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^70*y - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y + x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*z0 - x^64*z0^2 + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^63*z0 + x^62*y*z0 + x^63 + x^62*y - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y + x^60*y*z0 + x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 + x^60 + x^59*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*y - x^57*y*z0 + x^57*z0^2 + x^57*y + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^56*z0 + x^56 + x^55*y + x^7*z0^2, + -x^113*z0 + x^112*z0^2 - x^112*z0 + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 - x^108*y + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^106*z0 + x^105*y*z0 + x^106 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 - x^102*z0^2 - x^102*y + x^102*z0 - x^100*y*z0^2 - x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^99*y*z0 + x^98*y*z0 + x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 - x^97*y + x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 - x^95*y - x^94*y*z0 + x^94*z0^2 + x^95 - x^94*y + x^94*z0 + x^92*y*z0^2 - x^94 + x^93*y - x^92*z0^2 + x^91*y*z0^2 - x^92*y - x^91*y*z0 - x^90*y*z0 - x^90*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^85*y*z0 + x^85*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*z0 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 + x^80*y*z0^2 - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^81 - x^80*y + x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^78*y + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*z0 - x^76*z0^2 - x^75*y*z0^2 - x^76*y + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 - x^75*z0 + x^74*y*z0 - x^73*y*z0^2 + x^75 - x^74*y + x^73*y*z0 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^69*y*z0 - x^69*z0^2 - x^70 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*z0 - x^63*y*z0^2 + x^65 - x^64*y - x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^63 - x^62*z0 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 + x^58*y - x^57*y*z0 + x^56*y*z0^2 - x^58 - x^56*y*z0 + x^56*z0^2 - x^56*z0 + x^55*y*z0 + x^56 + x^55*y + x^7*y, + -x^114*z0 - x^113*z0^2 + x^114 + x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y + x^107*y*z0^2 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 + x^105*y*z0 + x^104*y*z0^2 - x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*z0 - x^102*y*z0^2 - x^104 - x^102*z0^2 + x^101*y*z0^2 - x^102*y - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^101*y - x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^100*y + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^97 + x^96*y - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^93*y - x^93*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 - x^92 + x^91*z0 + x^90*z0^2 + x^89*y*z0^2 - x^89*z0^2 + x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*z0^2 - x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^85 + x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 - x^80 + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^77*z0^2 + x^76*y*z0^2 + x^77*z0 + x^76*z0^2 - x^75*y*z0^2 - x^76*y + x^76*z0 - x^75*y*z0 - x^74*y*z0^2 - x^76 + x^75*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^73*z0 - x^71*y*z0^2 + x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^72 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 + x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 - x^67 + x^66*y + x^66*z0 - x^65*y*z0 + x^66 + x^65*y - x^65*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 - x^61 + x^60*y - x^59*z0^2 - x^58*y*z0^2 + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^59 - x^57*y*z0 - x^56*y*z0^2 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y + x^55*y*z0 + x^56 + x^55*y + x^7*y*z0, + x^114*z0 + x^113*z0^2 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 + x^112 + x^111*z0 - x^110*z0^2 + x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^105*z0 - x^103*y*z0^2 + x^105 + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^103*y - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 + x^99*z0^2 - x^100 - x^99*y + x^98*y*z0 - x^97*y*z0^2 - x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*z0 + x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^90*z0 - x^89*z0^2 + x^88*y*z0^2 + x^89*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 + x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 + x^85*y*z0^2 + x^86*z0 - x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^85 - x^84*z0 - x^83*z0^2 - x^82*y*z0^2 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^78 - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y - x^74*y*z0 - x^74*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^72*y - x^70*y*z0^2 - x^71*y - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^68*y*z0 - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 + x^67*y*z0 + x^66*y*z0^2 - x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*y - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 + x^64*z0^2 - x^65 + x^64*y - x^64*z0 - x^63*y*z0 + x^62*y*z0^2 + x^64 + x^63*y - x^62*y*z0 - x^61*y*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^60*z0^2 - x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*z0^2 - x^60 + x^59*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^58 + x^57*y - x^57*z0 + x^56*z0 - x^56 + x^7*y*z0^2, + x^115 - x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 - x^112*y - x^112*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*y - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*z0 + x^109*y*z0 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^109 + x^108*y - x^107*y*z0 - x^107*z0^2 - x^108 + x^107*y - x^106*y*z0 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^106 - x^105*y - x^105*z0 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y + x^103*z0 - x^102*z0^2 + x^102*z0 + x^100*y*z0^2 + x^102 - x^101*y + x^100*y*z0 - x^99*y*z0^2 + x^101 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y + x^98*y*z0 - x^98*z0^2 - x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^94*y*z0 - x^95 - x^94*y - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^92*y*z0 - x^91*y*z0^2 - x^93 - x^92*z0 + x^91*z0^2 - x^92 + x^91*y - x^91*z0 - x^89*y*z0^2 - x^91 + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 + x^87*y*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^88 + x^87*y + x^87*z0 - x^86*z0^2 - x^85*y*z0^2 + x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^84*z0 + x^83*y*z0 - x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 - x^79*y - x^79 - x^78*y - x^76*y*z0^2 - x^78 + x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 - x^74*y*z0 - x^74*z0^2 + x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*z0^2 - x^66*y*z0^2 - x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*z0 + x^63*z0^2 + x^62*y*z0^2 - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 - x^60*y*z0 - x^60*y + x^60*z0 - x^59*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^56*y*z0^2 + x^58 + x^57*z0 + x^56*y + x^55*y*z0 - x^55*y + x^8, + x^114*z0 + x^113*z0^2 - x^113 - x^111*y*z0 - x^110*y*z0^2 + x^112 + x^111*z0 + x^110*z0^2 - x^111 + x^110*y - x^109*z0^2 + x^110 - x^109*y + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 + x^108*y - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*z0 + x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*z0 + x^101*y*z0^2 + x^103 + x^102*y + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*z0 + x^99*y*z0 + x^100 + x^99*y + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^95*y - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^94 - x^93*y + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^91*y*z0 + x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^88*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*z0^2 - x^88 - x^87*y + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^84 + x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0 - x^80*y*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 + x^81 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y + x^75*z0 - x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*z0^2 + x^74 - x^73*y - x^72*y*z0 + x^73 + x^72*y + x^72*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^71 - x^69*z0^2 + x^70 + x^69*y - x^68*y*z0 - x^68*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*z0^2 + x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^67 - x^66*y - x^66 + x^65*y + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^59*y*z0^2 - x^60*y + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0 - x^57*z0^2 + x^58 - x^57*y + x^57*z0 + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x^8*z0, + -x^115 - x^114*z0 + x^113*z0 - x^112*z0^2 + x^112*y + x^111*y*z0 - x^111*z0^2 + x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^110*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 - x^106*y + x^106*z0 - x^105*z0 + x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^104 + x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^103 - x^102*y - x^101*y*z0 - x^101*z0^2 - x^102 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^100 - x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^98*y + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*y + x^96*y*z0 + x^95*y*z0^2 - x^97 - x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y + x^92*z0^2 - x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^89*y*z0^2 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^88*y + x^87*z0^2 + x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*z0^2 - x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^82*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 - x^82 - x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 + x^77*y - x^76*z0^2 - x^75*y*z0^2 + x^76*y + x^75*z0^2 + x^74*y*z0^2 - x^74*y*z0 - x^74*z0^2 - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 - x^73 + x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 + x^70*z0 + x^70 - x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^66 - x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*y - x^62*y*z0 - x^62*z0^2 - x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^61*y - x^61*z0 - x^61 + x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^55*y*z0 - x^55*y + x^8*z0^2, + -x^114*z0 - x^113*z0^2 + x^114 - x^112*z0^2 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 - x^107 - x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^104*z0 + x^102*y*z0^2 + x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^99*z0^2 - x^99*y - x^98*y*z0 - x^99 - x^98*y - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 + x^98 - x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y - x^92*z0 - x^91*y*z0 - x^92 + x^91*y + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*y + x^86*z0^2 - x^87 + x^86*y + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 - x^84*y*z0 - x^83*y*z0^2 + x^85 + x^84*y + x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 + x^83 - x^82*y - x^82*z0 + x^80*y*z0^2 - x^82 + x^81*y - x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*y - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*y - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*z0 - x^74*y*z0^2 - x^76 - x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*y - x^74*z0 - x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 + x^73 + x^71*z0^2 - x^70*y*z0^2 + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^69*y - x^68*y*z0 - x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^68 + x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^62*y*z0 - x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^61*y - x^61*z0 - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^60 - x^59*y - x^59*z0 + x^58*y + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 + x^57*z0 - x^56*z0^2 - x^55*y*z0^2 - x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^8*y, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 + x^107*y*z0^2 + x^109 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^102*y - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^100*z0^2 + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^99*y - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 + x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^92*y*z0 + x^91*y*z0^2 - x^93 - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^89*z0 - x^87*y*z0^2 + x^88*y - x^88*z0 - x^87*z0^2 + x^87*y + x^87*z0 + x^86*z0^2 + x^87 + x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^84*z0 - x^83*y*z0 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*z0 + x^79*y*z0^2 - x^80*y - x^80*z0 + x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*y + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^74*y - x^74*z0 - x^73*z0^2 + x^74 + x^73*y + x^72*y*z0 + x^72*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^69*z0 - x^68*y*z0 + x^67*y*z0^2 + x^69 - x^68*y + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^65*y*z0 + x^65*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^64*y + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 + x^64 - x^63*y + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 + x^61*y*z0 - x^62 - x^61*y - x^61*z0 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 - x^60 + x^59*y + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^8*y*z0, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 - x^112 - x^111*y + x^110*y*z0 - x^110*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y + x^109*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 - x^105*y*z0^2 + x^106*y - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^104 + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 - x^98*y*z0 + x^98*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 - x^93*y*z0 - x^93*z0^2 - x^94 - x^93*z0 - x^91*y*z0^2 - x^93 + x^92*z0 + x^91*z0^2 + x^91*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^88*y*z0 + x^89 + x^88*y + x^88*z0 + x^86*y*z0^2 - x^87*y + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 + x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y + x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^77*y*z0^2 + x^79 - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 + x^78 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^74*y*z0 - x^75 + x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^72*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 + x^69*y*z0 + x^70 - x^69*y - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y - x^68*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 - x^64*y*z0 + x^63*y*z0^2 - x^65 + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 + x^64 + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^61*y*z0 + x^61*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 + x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*z0 - x^56*y*z0^2 - x^58 + x^57*y - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 + x^56 + x^8*y*z0^2, + -x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^110*y + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^109*y - x^108*y*z0 - x^107*y*z0^2 - x^109 + x^108*z0 - x^107*y*z0 + x^108 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*z0 + x^105 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*y - x^99*z0 + x^98*y*z0 + x^97*y*z0^2 + x^98*y + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^96 - x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 + x^92*y*z0^2 + x^93*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^91*y - x^90*y*z0 - x^90*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^87*y*z0 + x^87*z0^2 - x^87*y - x^86*y*z0 + x^86*y + x^86*z0 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^82*z0 - x^80*y*z0^2 - x^82 - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 - x^78*y - x^77*y*z0 - x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y + x^75*y*z0 - x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^71 - x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*z0 + x^66*z0^2 + x^66*y - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^64*z0 - x^63*z0^2 - x^64 + x^63*y - x^62*y*z0 - x^61*y*z0^2 + x^62*y + x^61*y*z0 - x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^9, + -x^114*z0 - x^113*z0^2 - x^114 + x^112*z0^2 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^101 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*z0 + x^96*z0^2 - x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 + x^95*y + x^95*z0 + x^94*y*z0 + x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y - x^91*z0 - x^89*y*z0^2 - x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 + x^87*y*z0 - x^87*z0^2 - x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^86*y - x^86 + x^84*z0^2 + x^85 + x^83*y*z0 - x^83*z0^2 - x^84 - x^83*y + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^80*y - x^80*z0 - x^79*z0^2 - x^80 + x^79*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*z0 + x^74*z0^2 - x^74*y - x^72*y*z0^2 + x^73*z0 - x^72*y*z0 + x^71*y*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 - x^67*z0^2 - x^66*y*z0^2 - x^67*y + x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*z0 + x^65*z0^2 + x^66 + x^65*z0 - x^64*y*z0 + x^65 - x^64*y + x^64*z0 - x^63*z0^2 + x^62*y*z0^2 - x^63*y - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^61*y*z0 + x^61*z0^2 - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^60*y + x^60*z0 + x^58*y*z0^2 - x^59*y + x^58*z0^2 + x^57*y*z0^2 - x^59 + x^57*y*z0 - x^57*z0^2 + x^58 - x^57*y - x^57*z0 - x^56*z0^2 + x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^9*z0, + x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^111 - x^110*z0 + x^108*y*z0^2 - x^110 + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^108*y + x^107*y*z0 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y + x^104*y*z0 + x^104*z0^2 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 + x^101*y*z0^2 - x^103 - x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 + x^99*y*z0 + x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 - x^92 - x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^89*z0 + x^88*z0^2 + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^78*y*z0^2 + x^79*y + x^79*z0 - x^79 - x^78*y + x^78*z0 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^76*y - x^76*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 + x^75 - x^74*y - x^73*y*z0 - x^72*y*z0^2 - x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y - x^71*y*z0 - x^71*z0^2 + x^72 - x^71*y - x^70*y*z0 - x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 + x^69*y*z0 + x^68*y*z0^2 + x^70 - x^69*y - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^67*y*z0 + x^67*z0^2 + x^68 + x^67*y + x^66*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^66 + x^65*y - x^64*z0^2 + x^65 + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^63 + x^62*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^60*z0 + x^59*y*z0 + x^59*y - x^58*y*z0 + x^57*y*z0^2 - x^59 - x^57*y*z0 - x^58 - x^57*y + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^9*z0^2, + x^115 - x^113*z0^2 - x^113*z0 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^107 - x^106*y + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*y*z0 - x^98*y*z0^2 - x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*y + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y + x^91*y*z0 + x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 + x^91 - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*z0 + x^87*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*z0^2 - x^87 + x^86*y - x^85*y*z0 + x^86 - x^85*y - x^84*y*z0 - x^84*z0^2 - x^85 + x^83*y*z0 + x^83*z0^2 - x^84 - x^83*y + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*z0 - x^81*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y + x^78 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^75*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^73 - x^72*y + x^71*y*z0 - x^70*y*z0^2 - x^72 - x^71*z0 - x^70*z0^2 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*y + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*z0 + x^65*z0^2 + x^66 + x^64*y*z0 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^60*y*z0^2 - x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y - x^58*y*z0 - x^58*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^57*y + x^57*z0 + x^56*y*z0 + x^55*y*z0^2 + x^57 - x^55*y + x^9*y, + -x^115 + x^113*z0^2 - x^113*z0 + x^112*y - x^112*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*z0 + x^110*y*z0 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^106*y*z0 - x^106*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 + x^104*y*z0^2 + x^105*y - x^104*y*z0 + x^104*z0^2 + x^105 + x^104*y - x^103*z0^2 - x^102*y*z0^2 - x^103*z0 - x^102*z0^2 + x^103 + x^102*y - x^102 - x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^99*y*z0 + x^99*z0^2 + x^100 - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^98*y - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^97 - x^96*y + x^96*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y - x^93*y*z0^2 + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 + x^91*y*z0^2 + x^93 - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^87*y - x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^85*y - x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^83*y*z0 + x^84 + x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*z0 + x^78*y*z0^2 - x^80 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 - x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 - x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^74 + x^72*y*z0 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^72 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 + x^66*y + x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*z0 - x^65 - x^64*y - x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^62*z0^2 + x^63 - x^62*y + x^61*y*z0 + x^62 + x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 - x^60 - x^59*y + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 + x^57*y*z0 + x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 + x^9*y*z0, + -x^115 - x^114*z0 + x^114 - x^113*z0 - x^112*z0^2 + x^112*y + x^111*y*z0 - x^111*z0^2 + x^112 - x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*z0 + x^108*y*z0^2 - x^110 - x^109*y + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^108*y - x^107*y*z0 - x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^103*y*z0 - x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*z0^2 - x^103 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 + x^98*y - x^97*z0^2 + x^96*y*z0^2 + x^97*y - x^97 + x^96*y + x^96*z0 + x^95*z0^2 - x^94*y*z0 + x^93*y*z0^2 + x^94*y - x^94*z0 + x^92*y*z0^2 - x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 + x^93 + x^92*y + x^91*y*z0 - x^90*y*z0^2 - x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^90 - x^89*y - x^88*y*z0 + x^89 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^86*z0^2 + x^87 - x^86*y + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^85*y - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^83*y*z0 - x^83*z0^2 + x^84 + x^83*y + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 - x^81*y*z0 + x^80*y*z0^2 + x^81*y + x^80*z0^2 - x^80*y - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 - x^78*z0^2 + x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 + x^78 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*z0 - x^71*y*z0^2 + x^73 - x^72*y + x^72*z0 - x^70*y*z0^2 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y + x^67*y*z0 - x^67*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 + x^67 + x^66*y + x^66*z0 + x^64*y*z0^2 + x^66 + x^65*z0 + x^64*y*z0 - x^65 + x^64*y + x^64*z0 - x^63*z0^2 + x^63*y - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^61*z0 + x^61 + x^60*y - x^60*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*z0 + x^58*y*z0 - x^59 + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^56*y - x^55*y*z0 - x^56 + x^55*y + x^9*y*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y - x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 - x^109 + x^108*y - x^108*z0 + x^107*y*z0 - x^106*y*z0^2 + x^108 - x^107*z0 + x^105*y*z0^2 - x^107 + x^106*z0 + x^104*y*z0^2 + x^105*y + x^103*y*z0^2 + x^105 - x^104*y + x^104*z0 + x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 + x^102 - x^101*y + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^99*y - x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*z0 - x^95*y*z0 - x^96 + x^95*z0 - x^94*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*y*z0 - x^94 - x^93*y - x^92*y*z0 - x^92*z0^2 - x^92*y - x^91*y*z0 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 - x^89*y*z0^2 - x^89*y*z0 - x^89*z0^2 + x^90 - x^89*y + x^89*z0 - x^88*z0^2 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^87*y - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*z0 + x^84*y*z0^2 - x^85*y + x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y - x^82*y*z0 - x^82*z0^2 + x^83 + x^82*y + x^81*z0^2 - x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^80*y - x^79*y*z0 + x^78*y*z0^2 + x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^79 + x^78*y - x^78*z0 + x^76*y*z0^2 - x^76*y*z0 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 - x^75*z0^2 - x^75*y - x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^72*y*z0 + x^73 + x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^69*z0^2 - x^69*y - x^69*z0 + x^69 - x^68*y - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 + x^64 + x^63*y - x^63*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 + x^59*y*z0^2 + x^61 + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*z0 + x^58*y - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 + x^57 + x^56*y + x^55*y*z0 - x^56 - x^55*y + x^10, + x^115 - x^113*z0^2 + x^114 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^110*z0^2 - x^109*y*z0^2 - x^110*y + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^109*y - x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^108 - x^107*y + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 - x^103*z0^2 - x^104 - x^102*y*z0 + x^103 - x^102*y - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 - x^101 - x^100*y - x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 - x^98*z0^2 - x^99 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y - x^94*y*z0 - x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^93*y - x^93*z0 + x^92*y*z0 + x^93 + x^92*y + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 + x^90*y*z0 - x^90*z0^2 + x^91 - x^90*y + x^88*y*z0^2 - x^90 + x^89*y - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^87*y + x^86*z0^2 - x^85*y*z0^2 - x^85*y*z0 - x^84*y*z0^2 + x^86 + x^85*y + x^84*z0^2 + x^85 - x^84*y + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^81*y*z0 + x^82 + x^81*z0 - x^80*y*z0 + x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^78 + x^77*y - x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*y - x^75*y*z0 - x^74*y*z0^2 + x^76 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 - x^71*y - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 + x^70 + x^69*z0 + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^68 - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^65*y + x^64*y*z0 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^59 - x^58*y + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 + x^58 + x^57*y + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y + x^10*z0, + x^115 - x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^112*y - x^112*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*z0 - x^110*y*z0 + x^109*y*z0^2 + x^110*z0 + x^109*y*z0 - x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 + x^109 + x^108*z0 - x^107*y*z0 + x^107*z0 + x^106*z0^2 + x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102 - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*y - x^98*y*z0 - x^97*y*z0^2 - x^99 + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^96*z0^2 + x^97 - x^96*y - x^95*y*z0 - x^95*z0^2 - x^96 + x^95*y + x^94*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^92*z0^2 - x^91*y*z0^2 + x^92*y + x^92*z0 + x^91*y*z0 + x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^88*y + x^88*z0 - x^88 - x^87*y + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*z0 - x^85 - x^84*y + x^83*z0^2 + x^83*y + x^82*z0^2 + x^83 + x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*y + x^81*z0 - x^79*y*z0^2 + x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 + x^79*z0 + x^78*y*z0 - x^79 + x^77*z0^2 - x^76*y*z0^2 - x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y + x^74 + x^73*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 + x^70 - x^69*z0 - x^67*y*z0^2 + x^69 - x^68*y + x^67*z0^2 - x^66*y*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*z0^2 + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*z0 + x^61*y*z0^2 - x^63 + x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^61*y + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y - x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 + x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*z0 - x^55*y*z0 - x^55*y + x^10*z0^2, + -x^114*z0 - x^113*z0^2 - x^114 + x^112*z0^2 - x^113 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^104*y*z0 - x^103*y*z0^2 - x^104*y + x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^103*y - x^102*z0^2 + x^103 - x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^96 - x^95*y - x^94*y*z0 - x^94*z0^2 - x^95 + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^92*z0^2 - x^93 - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^90*y - x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 + x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 - x^88 - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^81*y*z0 + x^81*z0^2 + x^81*y - x^81*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 + x^79*y + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y + x^75*z0^2 + x^74*y*z0^2 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*y + x^72*y + x^72*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^67 - x^66*y - x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^60 - x^59*y + x^58*y*z0 - x^58*z0^2 - x^59 - x^58*y - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^10*y, + x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 + x^110*y*z0 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*y + x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^108 - x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 - x^106 - x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*z0 + x^101*y*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^99 + x^97*z0^2 - x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^97 + x^95*z0^2 + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^94 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 + x^91*y*z0 + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^87*y*z0 + x^87*z0^2 - x^87*y + x^86*y*z0 - x^86*z0^2 + x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*y - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^84*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*y*z0 - x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^76*y*z0^2 + x^78 + x^75*y*z0^2 - x^77 - x^76*y - x^75*y*z0 + x^75*y + x^75*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^74 + x^72*y*z0 + x^72*z0^2 + x^73 + x^72*y + x^72*z0 - x^71*z0^2 + x^72 - x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^71 - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*y + x^67 - x^66*y + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y - x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*z0 + x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^58*y*z0 + x^57*y*z0^2 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^58 + x^57*z0 - x^56*y*z0 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^10*y*z0, + -x^115 - x^114*z0 - x^113*z0 + x^112*z0^2 + x^112*y + x^111*y*z0 + x^111*z0^2 - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103 + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y - x^101*z0 + x^100*y*z0 + x^101 + x^100*y + x^100*z0 + x^99*y - x^99*z0 + x^98*y*z0 + x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^96*y*z0 + x^96*z0^2 + x^96*y + x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*y - x^94*y*z0 + x^94*z0^2 + x^95 + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^94 + x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^91*y - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 - x^89*z0^2 + x^90 - x^89*z0 - x^88*z0^2 - x^87*y*z0^2 + x^87*y*z0 + x^88 - x^87*y - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^84*z0^2 - x^83*y*z0^2 - x^84*y + x^83*z0^2 + x^84 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^81 - x^80*y - x^79*z0^2 + x^79*y + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^78*y + x^77*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*z0^2 - x^77 - x^76*y + x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 + x^73*y*z0^2 - x^75 + x^73*z0^2 + x^74 + x^72*y*z0 - x^72*z0^2 - x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^71 - x^70*y + x^69*y*z0 - x^68*y*z0^2 - x^69*y - x^69*z0 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^66*y*z0^2 - x^68 - x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^66 - x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^64 - x^62*z0^2 - x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^61 + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^60 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*z0 + x^56 - x^55*y + x^10*y*z0^2, + x^114 - x^112*z0^2 - x^113 - x^112 - x^111*y + x^111*z0 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*z0^2 + x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^106 + x^105*y + x^105*z0 + x^103*y*z0^2 + x^103*z0^2 - x^104 + x^103*y - x^102*y*z0 + x^101*y*z0^2 - x^103 - x^102*y - x^101*y*z0 + x^100*y*z0^2 + x^102 + x^100*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 + x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 - x^94*y*z0^2 - x^96 - x^95*y - x^94*y*z0 - x^94*z0^2 - x^95 - x^94*y - x^94*z0 - x^92*y*z0^2 - x^93*z0 - x^92*y*z0 + x^93 + x^91*y*z0 + x^90*y*z0^2 - x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*z0 - x^89*z0^2 + x^88*y*z0^2 + x^88*y*z0 - x^87*y*z0^2 - x^88*y + x^88*z0 + x^87*y*z0 - x^88 - x^87*y - x^87*z0 - x^86*z0^2 + x^86*y - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^85*y + x^85*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^82*y*z0 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^80*y*z0^2 + x^82 + x^81*y - x^80*y*z0 - x^81 - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 - x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 - x^67 + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y - x^64*y*z0 + x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 + x^64 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y - x^61*z0^2 - x^62 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^60*z0 - x^58*y*z0^2 + x^60 + x^59*z0 + x^59 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^56 + x^55*y + x^11, + x^115 + x^114*z0 - x^114 + x^113*z0 + x^112*z0^2 - x^112*y - x^111*y*z0 + x^111*z0^2 + x^112 + x^111*y - x^110*y*z0 - x^109*y*z0^2 + x^111 - x^110*z0 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^108 - x^107*y + x^106*y*z0 + x^107 + x^106*y + x^106*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^103*y*z0 + x^103*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*z0 - x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^99*y + x^99*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*z0^2 - x^98 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 - x^91*y*z0^2 - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y - x^90*z0 - x^89*z0^2 - x^88*y*z0^2 + x^89*y + x^89*z0 - x^88*y*z0 + x^88*y + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 - x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*z0^2 + x^84 + x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 - x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*y*z0 - x^80 + x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y - x^77*z0 + x^76*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*z0 - x^73*y*z0^2 + x^75 + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*z0^2 + x^72*y + x^72*z0 + x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^71 - x^70*y + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y + x^68*y*z0 + x^69 - x^68*z0 + x^67*y*z0 + x^67*y - x^67*z0 + x^66*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*z0 - x^64*y + x^64*z0 - x^63*y*z0 + x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^59*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 - x^58*y - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^57*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^11*z0, + x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 - x^103*y*z0 + x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 + x^101*y*z0^2 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^99*y*z0^2 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^99 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^97 + x^96*y - x^95*y*z0 + x^95*z0^2 + x^96 - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^93*z0 - x^92*z0^2 - x^91*y*z0^2 - x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^86*y - x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*y - x^80*z0 - x^79*y*z0 - x^79*y + x^78*y*z0 + x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 + x^76*y*z0^2 - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^76*y - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73 - x^72*y + x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*z0 + x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*y + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^60*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 - x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^11*z0^2, + x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^109*y*z0 + x^108*y*z0^2 + x^110 + x^109*y + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^107*z0^2 - x^108 - x^107*y - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 + x^104*y - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 + x^100*y*z0^2 + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*z0 - x^99*z0^2 + x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^97*y - x^97*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*y + x^96*z0 - x^95*y*z0 + x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 + x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 - x^92*y - x^91*y*z0 - x^91*y + x^91*z0 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^88*y*z0^2 - x^90 + x^89*z0 + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*z0^2 - x^87 + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y - x^84*y*z0 - x^84*y - x^84*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*z0 + x^81*z0^2 + x^80*y*z0^2 + x^81*y - x^80*z0^2 + x^81 + x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^78*y - x^77*y*z0 - x^77*z0^2 + x^78 + x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^76 + x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^74*z0 - x^72*y*z0^2 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^71*z0^2 + x^70*y*z0^2 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^70*y + x^70*z0 + x^69*z0^2 + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 - x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 + x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 + x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^55*y*z0 + x^56 + x^55*y + x^11*y, + -x^114 - x^113*z0 - x^112*z0 + x^111*z0^2 + x^112 + x^111*y + x^111*z0 + x^110*y*z0 + x^109*y*z0 - x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*z0^2 - x^108 + x^107*y - x^107*z0 + x^106*z0^2 - x^105*y*z0^2 + x^106*y - x^106*z0 + x^105*y*z0 + x^104*y*z0^2 - x^105*y + x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^103*y*z0 - x^102*y*z0^2 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y + x^98*z0^2 + x^99 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y + x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 - x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^87*y - x^86*y*z0 + x^86*z0^2 + x^86*y - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^85*y + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^82*y - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*z0^2 - x^79*y*z0^2 + x^80*y - x^79*z0^2 - x^80 - x^79*z0 - x^78*y*z0 + x^78*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*z0 - x^73*y*z0^2 + x^74*y - x^74*z0 - x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^70*y + x^69*z0^2 + x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^66 - x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^63 - x^62*y + x^60*y*z0^2 - x^61*y + x^61*z0 + x^60*z0^2 - x^59*y*z0^2 + x^60*y - x^60*z0 - x^59*y*z0 - x^59*y + x^58*y*z0 - x^58*z0^2 - x^59 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^56 - x^55*y + x^11*y*z0, + x^115 - x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^112*y + x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*z0 + x^109*z0^2 - x^110 + x^109*y + x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*y + x^105*y*z0 + x^104*y*z0^2 + x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*y*z0 + x^102*y - x^102*z0 + x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^98*y*z0^2 + x^100 - x^99*z0 + x^98*y*z0 + x^99 + x^97*y*z0 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 + x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^95 - x^94*y - x^94*z0 - x^94 + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^92*z0 - x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^88*z0 - x^87*y*z0 + x^88 + x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y - x^84*y*z0^2 + x^85*y + x^85*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^82*y*z0 + x^82*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*y - x^80*y*z0 + x^79*y*z0^2 - x^80*y - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*z0 + x^75*z0^2 + x^76 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y + x^72*z0^2 - x^73 - x^72*y - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 - x^68*y*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^67*y*z0 - x^68 - x^67*y + x^66*z0^2 + x^65*y*z0^2 - x^66*y + x^66*z0 + x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*y - x^64*y*z0 + x^64*z0^2 - x^65 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 + x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^60 + x^58*y*z0 + x^58*z0^2 + x^59 - x^57*y*z0 - x^58 + x^57*y - x^57*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^55*y*z0 + x^56 - x^55*y + x^11*y*z0^2, + -x^115 + x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y + x^112*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y + x^106*z0 - x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 + x^102*y*z0^2 - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^103 + x^102*y + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^101 - x^100*y - x^100*z0 + x^99*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*y - x^95*z0 - x^94*y*z0 - x^93*y*z0^2 - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^94 - x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y + x^91*y*z0 + x^90*y*z0^2 - x^90*y*z0 - x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y + x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 + x^87*y + x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^86*y + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*z0 - x^83*y*z0 - x^82*y*z0^2 + x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^82*y - x^81*y*z0 - x^80*y*z0^2 - x^80*y*z0 - x^80*z0^2 + x^80*y + x^80*z0 + x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 - x^77 + x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^75*y - x^74*y*z0 - x^74*z0^2 + x^74*y - x^74*z0 - x^74 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y - x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*z0^2 + x^69 + x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 + x^65*y + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^64 - x^63*y - x^63*z0 + x^61*y*z0^2 + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y + x^60 - x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*z0^2 + x^55*y*z0 + x^12, + x^115 - x^114*z0 + x^113*z0^2 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^106*y - x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 + x^105 - x^104*y - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y + x^101*y*z0^2 + x^103 + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 + x^101*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^98*y*z0 + x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^96*z0 - x^95*y*z0 + x^94*y*z0^2 + x^96 + x^95*y - x^94*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^91*y*z0 - x^90*y*z0^2 + x^90*y*z0 + x^90*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 + x^89*y + x^88*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^86*y*z0 + x^86*z0^2 + x^87 - x^86*y - x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*z0^2 + x^77 - x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 - x^73*y + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y - x^68*z0^2 + x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^68 + x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*z0 + x^66 - x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*y + x^62*y*z0 - x^61*y*z0^2 - x^63 + x^61*y*z0 + x^61*z0^2 + x^62 + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y - x^58*z0^2 - x^59 + x^58*y - x^57*z0^2 + x^56*y*z0^2 + x^57*z0 + x^56*z0^2 + x^56 + x^55*y + x^12*z0, + x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 - x^113 - x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^108*y*z0^2 - x^109*y - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y - x^107*y*z0 - x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 - x^107 - x^106*y + x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^104*y + x^104*z0 - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y + x^99*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y + x^97*z0^2 + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*y*z0 - x^97 + x^96*y - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 - x^87*y*z0^2 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^86*y - x^85*y*z0 - x^84*y*z0^2 + x^85*y - x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^82*y*z0^2 + x^84 - x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y - x^80*y*z0^2 - x^81*y - x^80*y*z0 - x^79*y*z0^2 - x^81 + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*y - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*y + x^77*z0 - x^76*z0^2 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^73*y + x^73 - x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^70*y - x^69*y*z0 + x^69*z0^2 + x^70 - x^69*y - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 + x^69 + x^68*y + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*y - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^64*y - x^64*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 - x^61*y*z0^2 - x^63 + x^62*z0 + x^61*y*z0 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 - x^59*z0^2 + x^58*y*z0^2 - x^58*y + x^56*y*z0^2 - x^58 + x^57*y - x^57*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^12*z0^2, + x^115 + x^114*z0 + x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^112 - x^111*y - x^110*y*z0 + x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 - x^109*y - x^109*z0 + x^109 + x^107*y*z0 - x^108 - x^107*y + x^106*z0^2 + x^107 + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^105 - x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^101 - x^99*y*z0 + x^99*z0^2 + x^100 - x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^98*y + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*z0 + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 - x^92*y*z0 - x^93 - x^92*y + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^91*z0 + x^91 - x^90*y - x^90*z0 - x^89*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*z0 + x^83*y*z0 + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 + x^83 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*y - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*y - x^78*y*z0 + x^77*y*z0^2 + x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*z0 - x^77 - x^76*y - x^76*z0 - x^75*y*z0 - x^75*y + x^75*z0 + x^73*y*z0 + x^73*z0^2 + x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^73 - x^72*y + x^71*y*z0 + x^71*z0^2 + x^71*y - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*y + x^70*z0 + x^69*z0^2 + x^70 - x^69*y + x^69*z0 + x^67*y*z0^2 + x^69 + x^68*z0 + x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*y + x^65*y*z0^2 - x^67 - x^65*y*z0 + x^64*y*z0^2 + x^66 + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 - x^64*y + x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^62*y*z0 - x^62*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^61*y - x^61*z0 + x^60*z0^2 - x^61 - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^58*y*z0 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*z0^2 - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^12*y, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*z0 - x^105*y*z0^2 - x^107 + x^106*y + x^106*z0 - x^105*y*z0 - x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 - x^104*z0^2 + x^104*z0 + x^103*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*z0 + x^101*z0^2 + x^102 + x^101*y - x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^100*y + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*y*z0 + x^97 - x^96*y + x^95*y*z0 - x^95*z0^2 + x^96 - x^95*y + x^95*z0 - x^94*y*z0 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y + x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^86*y - x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^83*y + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 - x^82*y + x^81*y - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*z0 - x^78*y*z0 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*z0^2 + x^78 - x^77*y - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^75*z0 + x^74*y*z0 - x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^71*y*z0^2 + x^73 - x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y + x^70*y*z0 - x^71 + x^70*y - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^61*y*z0 - x^60*y*z0^2 + x^62 - x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^61 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*z0^2 - x^59 - x^58*y + x^58*z0 + x^58 + x^56*y*z0 + x^55*y*z0^2 - x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^12*y*z0, + -x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 + x^109*y*z0 - x^108*y*z0^2 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^107*y*z0 + x^107*z0^2 + x^108 - x^106*y*z0 - x^106*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^104*y*z0 + x^103*y*z0^2 + x^104*y - x^103*z0^2 + x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y + x^102*z0 - x^101*y*z0 - x^102 - x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 + x^99*z0^2 + x^99*y - x^99*z0 - x^98*y + x^97*y*z0 + x^98 - x^97*y - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^93*y - x^92*y*z0 - x^92*z0^2 - x^92*y + x^92*z0 + x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^89*y - x^88*z0^2 + x^89 + x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 + x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*z0 + x^85*y*z0 - x^86 - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^84 + x^83*y + x^82*y*z0 - x^83 - x^82*z0 - x^81*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^78 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*z0 + x^74*z0^2 - x^73*y*z0^2 + x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^70*y - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*z0 + x^65*y*z0^2 + x^67 - x^66*y + x^65*z0^2 + x^64*y*z0^2 + x^65*y - x^65*z0 - x^64*y*z0 - x^63*y*z0^2 - x^65 - x^64*y - x^63*y*z0 + x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^63 - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^60*z0^2 + x^59*y*z0^2 - x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^58*y - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 + x^57*z0 - x^56*z0^2 + x^56*y - x^55*y*z0 - x^56 - x^55*y + x^12*y*z0^2, + -x^115 - x^114*z0 + x^114 - x^113*z0 + x^112*z0^2 + x^112*y + x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^109*z0 + x^108*z0^2 + x^107*y*z0^2 + x^106*y*z0^2 + x^107*y - x^106*z0^2 - x^105*y*z0^2 - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^101 + x^100*y - x^99*y*z0 + x^99*z0^2 - x^99*y - x^99*z0 - x^98*z0^2 - x^97*y*z0^2 - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^95*y*z0^2 + x^96*y - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^94 + x^93*y - x^92*y*z0 + x^91*y*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^91*y + x^91*z0 + x^90*y*z0 - x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^88 - x^87*z0 + x^86*y*z0 + x^85*y*z0^2 - x^87 - x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^84 + x^83*y + x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*z0 + x^80*y*z0 - x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 + x^79 - x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 + x^76*y*z0 + x^76*y + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^75*y - x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y + x^69*z0^2 + x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 - x^64*y*z0 + x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 - x^62*y*z0 - x^61*y*z0^2 + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^61 - x^60*y + x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 + x^59 - x^58*z0 - x^57*y*z0 + x^58 + x^57*y - x^56*y*z0 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^13, + x^115 + x^114*z0 - x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^110 - x^109*y - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 + x^107*y*z0 - x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^104 + x^103*z0 - x^102*y*z0 + x^103 - x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^99*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 + x^98*y - x^97*y*z0 + x^96*y*z0^2 + x^96*y*z0 - x^96*z0^2 - x^96*y - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^91 + x^90*y - x^89*y*z0 + x^89*z0^2 - x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 - x^88 + x^86*y*z0 + x^86*z0^2 - x^87 - x^86*z0 - x^85*z0^2 - x^86 - x^85*y + x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^79 + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^78 - x^76*y*z0 - x^76*z0^2 + x^77 + x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^75*z0 - x^74*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y + x^69*y*z0 - x^70 - x^68*y*z0 - x^68*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^67*y + x^67*z0 + x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*z0 - x^63*y*z0 + x^63*y - x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^62*y - x^62*z0 + x^62 + x^61*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^59*y + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 - x^55*y*z0 + x^13*z0, + x^115 - x^113*z0^2 - x^113*z0 - x^112*z0^2 - x^113 - x^112*y - x^111*z0^2 + x^110*y*z0^2 + x^112 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 + x^108*y*z0^2 - x^109*y - x^107*y*z0^2 - x^108*y + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^108 - x^107*y - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 + x^105*z0^2 - x^106 + x^104*y*z0 - x^104*z0^2 + x^104*y - x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 - x^103*y + x^102*y*z0 + x^102*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^102 - x^101*y - x^100*y*z0 - x^101 - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^97*y + x^97*z0 + x^96*z0^2 + x^97 + x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 + x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*z0^2 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y + x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^88*z0 - x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*z0 - x^85*z0^2 - x^84*y*z0^2 - x^85*y - x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^83 - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y - x^78 - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^76*y + x^76*z0 + x^74*y*z0^2 - x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^75 + x^74*y + x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^69*y*z0 - x^69*z0^2 - x^70 - x^69*y - x^68*y*z0 - x^67*y*z0^2 + x^69 - x^67*y*z0 - x^67*z0^2 + x^68 - x^67*y - x^65*y*z0^2 + x^67 + x^66*y + x^65*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^64*y + x^64*z0 + x^63*y - x^62*y*z0 + x^62*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 - x^59*y*z0 + x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*y - x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y + x^55*y*z0 + x^56 + x^55*y + x^13*z0^2, + x^114*z0 + x^113*z0^2 - x^114 - x^112*z0^2 + x^113 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 - x^110*y + x^110*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 - x^107*y*z0 - x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^105*y + x^105*z0 + x^104*y*z0 - x^105 + x^104*y + x^104*z0 - x^103*y + x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 + x^102 - x^101*y + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^99*y*z0 - x^99*z0^2 - x^100 + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 - x^97*z0^2 - x^97*y - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^89*y*z0 - x^89*z0^2 - x^90 - x^89*y + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 + x^86*y*z0^2 + x^88 + x^87*z0 - x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 + x^81*y + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^80*y + x^79*y*z0 - x^79*z0^2 + x^79*y + x^79*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^75*y - x^75 - x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*z0 + x^71*y*z0 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^71 - x^70*y + x^70*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^68*y - x^67*y*z0 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 + x^67 - x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 - x^65*y + x^64*y*z0 + x^64*z0^2 - x^65 + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^62*y - x^62*z0 - x^61*y*z0 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^56*y*z0 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^13*y, + x^115 - x^113*z0^2 + x^114 + x^112*z0^2 - x^113 - x^112*y + x^112*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^110*z0^2 - x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 + x^108*z0^2 - x^107*y*z0^2 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*z0 + x^106*y*z0 - x^107 + x^106*y - x^106*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 + x^103*z0^2 - x^102*y*z0^2 - x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*y + x^101*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*z0^2 - x^98*y*z0^2 - x^99*z0 - x^98*y*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y + x^96*z0 + x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*z0^2 + x^95 - x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^93*y + x^91*y*z0^2 - x^92*y - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 + x^92 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 + x^87 + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 + x^84*y - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^82*z0^2 - x^81*y*z0^2 + x^82*y - x^82*z0 - x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y + x^77*y*z0 - x^76*y*z0^2 + x^77*z0 + x^77 + x^76*y - x^76*z0 - x^74*y*z0^2 + x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*y - x^71*z0 + x^69*y*z0 + x^69*z0^2 + x^70 - x^69*y + x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^68*y - x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^65*y - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^62 + x^61*y - x^61*z0 + x^61 + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 + x^56*y*z0 - x^55*y*z0^2 + x^56*z0 + x^55*y*z0 - x^55*y + x^13*y*z0, + -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 + x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*z0 + x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^108*y*z0 + x^108*y - x^108*z0 - x^107*y*z0 - x^108 - x^107*y + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*z0^2 - x^105 - x^104*y - x^104*z0 - x^102*y*z0^2 - x^103*y - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*y*z0 - x^102 - x^101*y + x^100*y*z0 + x^101 + x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*y - x^95*z0 - x^94*y*z0 - x^95 + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y - x^92*y*z0 + x^92*z0^2 + x^93 - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*z0^2 + x^90 + x^89*z0 + x^88*z0^2 + x^88*y - x^87*y*z0 + x^88 - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*z0 - x^84*y*z0 - x^83*y*z0^2 + x^85 + x^84*z0 - x^84 - x^83*y + x^83*z0 - x^81*y*z0^2 + x^82*y - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^79 - x^78*y - x^77*y*z0 - x^77*z0^2 + x^78 + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*z0 - x^76 + x^75*y + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 - x^73*y*z0 + x^74 - x^73*y - x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 - x^72*y - x^72*z0 - x^70*y*z0^2 + x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70 + x^69*y - x^68*y*z0 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y + x^66*z0^2 + x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^63*y - x^62*y*z0 + x^62*z0^2 + x^63 - x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^60 - x^59*y + x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*z0 + x^56*z0^2 - x^56*y - x^55*y*z0 + x^56 + x^13*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 - x^112*y - x^112*z0 + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y + x^110*y*z0 + x^110*z0^2 + x^109*y*z0 + x^110 + x^109*y + x^109*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^107*z0^2 - x^108 + x^107*y - x^107*z0 + x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 + x^106 - x^105*y - x^105 + x^104*y + x^103*z0^2 - x^102*y*z0^2 + x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 - x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*z0 + x^97*z0^2 + x^98 + x^97*y - x^96*y*z0 + x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 - x^95*y + x^95*z0 + x^94*y*z0 + x^93*y*z0^2 + x^93*y*z0 + x^94 - x^93*y - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*z0^2 - x^89 - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*z0 - x^85*y*z0^2 + x^86*y + x^86*z0 - x^85*y*z0 - x^86 + x^85*y + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*y - x^80*z0 + x^79*z0^2 + x^80 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 + x^75*y*z0^2 + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 + x^72*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 - x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^67 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 - x^64*y*z0 - x^63*y*z0^2 + x^64*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^62*z0^2 + x^63 - x^62*y - x^61*y*z0 - x^60*y*z0^2 + x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 + x^60*y + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*z0 - x^57*z0^2 - x^58 - x^57*y - x^57*z0 - x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 - x^56 + x^55*y + x^14, + x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y - x^110*y*z0 - x^110*z0^2 - x^111 + x^110*z0 - x^108*y*z0^2 + x^110 + x^109*y + x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^108 + x^107*y + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^100*y*z0^2 + x^102 - x^101*y - x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*z0 + x^95*y*z0 - x^96 - x^95*y + x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^95 - x^93*y*z0 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^90*z0^2 - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*z0^2 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y - x^85*z0^2 - x^84*y*z0^2 + x^86 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y + x^82*y*z0 + x^82*z0^2 - x^82*z0 + x^81*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^79 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^74*y*z0^2 - x^75*z0 + x^74*y*z0 - x^74*z0 + x^73*y*z0 + x^74 - x^72*y*z0 - x^72*z0^2 - x^73 - x^72*y - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*z0^2 + x^67*z0 + x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^65*z0 + x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^63*y - x^63*z0 + x^62*y*z0 - x^63 + x^62*y - x^62*z0 + x^61*z0^2 - x^61*y + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*y - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y + x^58*y*z0 + x^59 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^58 + x^57*y - x^57*z0 + x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^55*y + x^14*z0, + x^114 - x^112*z0^2 + x^112*z0 + x^111*z0^2 - x^112 - x^111*y - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*z0 - x^109*y*z0 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 - x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 - x^105*y*z0 + x^104*y*z0^2 - x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^103*y*z0 + x^103*z0^2 - x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^102*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^101 - x^99*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^97*z0 + x^96*y*z0 + x^96*z0 - x^94*y*z0^2 + x^95*y + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*z0 + x^92*y*z0 - x^93 + x^92*z0 - x^91*y*z0 - x^90*y*z0^2 + x^92 - x^91*z0 - x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^86*y*z0 + x^85*y*z0^2 - x^87 + x^86*y - x^84*y*z0^2 - x^86 - x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^84*y + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 + x^83*z0 - x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 - x^81 - x^80*y - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^77*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^75 + x^74*y - x^74*z0 + x^73*y*z0 + x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^72 + x^71*z0 - x^71 + x^70*y + x^69*z0^2 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 - x^65*y + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^61*y + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^59 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y - x^55*y*z0 - x^56 - x^55*y + x^14*z0^2, + -x^115 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^112*y - x^112*z0 - x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^109*y*z0 - x^109*z0^2 + x^110 - x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^107*z0^2 + x^106*y*z0^2 + x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^102*y + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 - x^93*y*z0 + x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 - x^92*z0^2 + x^93 - x^92*y + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*z0 + x^89*z0^2 - x^89*y - x^89*z0 + x^88*z0^2 + x^89 + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^87*y - x^87*z0 - x^86*z0^2 + x^85*y*z0^2 + x^86*y - x^86*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^84*y - x^83*y*z0 + x^83*z0^2 - x^84 + x^83*y + x^83*z0 + x^82*z0^2 - x^82*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*y - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^77*y*z0 - x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^76*z0 + x^75*y - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y - x^74*z0 - x^73*y*z0 - x^74 + x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 - x^69*y*z0^2 + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*y + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y + x^62*z0^2 - x^62*z0 + x^61*y*z0 + x^60*y*z0^2 + x^62 + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y - x^57*y*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^55*y*z0 - x^56 + x^55*y + x^14*y, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^112*y - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^110*y*z0 - x^110*z0^2 - x^111 + x^110*z0 + x^108*y*z0^2 - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^107*y - x^106*z0^2 - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^103*y*z0 - x^104 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*y - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^99*y + x^99*z0 + x^98*z0^2 - x^99 + x^98*y - x^98*z0 - x^98 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 - x^93*y*z0^2 + x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^93*y - x^92*y*z0 - x^91*y*z0^2 + x^93 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^88*y*z0 + x^88*z0^2 + x^89 + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^82*y - x^81*y*z0 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^81 + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^77*y - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*z0^2 + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 - x^73*z0^2 - x^73*z0 - x^72*y*z0 + x^73 + x^72*y + x^72*z0 + x^71*z0^2 + x^72 + x^70*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*z0 - x^60*z0^2 - x^61 - x^60*y + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^14*y*z0, + x^115 + x^114*z0 - x^114 - x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^112 + x^111*y + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y + x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^106*y + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^106 - x^105*y + x^104*y*z0 + x^103*y*z0^2 + x^105 + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^102*y - x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^99*y + x^98*z0^2 - x^99 - x^98*y - x^98*z0 - x^97*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 - x^97 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^93*y*z0 - x^93*z0^2 + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y - x^92*z0 - x^91*y*z0 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^91 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^87*y*z0 + x^88 + x^87*y - x^86*y*z0 + x^85*y*z0^2 - x^86*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^84*z0^2 + x^85 - x^84*y + x^83*y*z0 - x^83*z0^2 + x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^81*y*z0 + x^80*y*z0^2 - x^81*y + x^81*z0 + x^80*y*z0 + x^79*y*z0^2 - x^80*z0 - x^79*z0^2 - x^80 + x^79*y + x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 - x^73*y*z0 + x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^72 + x^71*z0 - x^70*z0^2 + x^71 + x^70*y + x^69*y*z0 - x^69*z0^2 + x^69*z0 + x^68*y*z0 + x^69 + x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^66*z0^2 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 + x^65*y - x^64*y*z0 - x^63*y*z0^2 + x^64*y + x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^63 + x^62*y - x^62*z0 + x^61*y*z0 - x^62 + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 + x^58*y*z0^2 + x^60 - x^58*y*z0 - x^58*y + x^58 + x^57*z0 - x^56*z0^2 - x^55*y*z0^2 + x^55*y*z0 + x^56 - x^55*y + x^14*y*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 - x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*y + x^109*z0 + x^108*y*z0 + x^107*y*z0^2 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*y + x^106*z0 + x^105*z0^2 + x^106 + x^105*y + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*z0 - x^103*y*z0 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*z0 - x^101*y*z0 - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 - x^94*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 - x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^92*y + x^91*y*z0 + x^90*y*z0^2 + x^92 - x^91*y - x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 + x^90 - x^89*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y - x^86*y*z0 + x^85*y*z0^2 - x^87 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*z0 - x^82*z0^2 + x^81*y*z0^2 - x^82*y + x^82*z0 + x^81*z0^2 + x^82 - x^81*y + x^80*y*z0 + x^81 - x^79*z0^2 + x^80 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*z0 - x^77*z0^2 - x^77*y + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^74*z0^2 - x^74*y + x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 - x^72*z0^2 + x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^71 + x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 - x^67*y - x^66*z0^2 - x^66*y - x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^64*z0 + x^62*y*z0^2 - x^64 - x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*y + x^58*z0 - x^58 - x^56*y + x^56*z0 + x^56 - x^55*y + x^15, + x^115 + x^114*z0 + x^114 + x^113*z0 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 + x^111 + x^110*y - x^110*z0 - x^109*y*z0 - x^108*y*z0^2 - x^110 + x^109*y - x^108*y*z0 - x^109 - x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^107*z0 - x^106*y*z0 - x^106*y - x^106*z0 - x^105*y*z0 - x^104*y*z0^2 - x^106 - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^101*y + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^99*y*z0 + x^98*y*z0^2 + x^100 - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*y - x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 + x^94*y*z0 + x^93*y*z0^2 - x^95 + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 + x^90*y*z0^2 - x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y - x^89*z0^2 - x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^87*y + x^87*z0 - x^86*z0^2 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 - x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^78*z0^2 + x^79 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^76*y*z0 - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y + x^74*y*z0 - x^74*z0^2 - x^75 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^74 + x^73*y - x^73*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 - x^70*y*z0 + x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 - x^68*y*z0^2 - x^70 - x^69*y - x^68*y*z0 - x^67*y*z0^2 + x^69 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^68 + x^67*z0 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^61*z0 + x^60*y*z0 - x^60*y + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*z0^2 - x^58*y + x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 + x^57*y + x^57*z0 - x^56*y*z0 - x^55*y*z0 + x^56 + x^15*z0, + x^115 + x^114*z0 - x^114 + x^113*z0 + x^113 - x^112*y - x^111*y*z0 - x^111*z0^2 - x^112 + x^111*y - x^110*y*z0 + x^110*z0^2 - x^110*y + x^110*z0 + x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^107*y*z0^2 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^108 - x^106*z0^2 + x^107 - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^103*y - x^102*z0^2 + x^103 - x^102*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 - x^98*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 - x^94*y*z0^2 - x^95*y + x^95*z0 - x^94*y*z0 + x^95 - x^94*z0 + x^93*y*z0 - x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^91*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^89 + x^88*y + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^84 + x^83*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 - x^78*y*z0^2 - x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*z0 - x^76*z0^2 - x^77 - x^76*y - x^75*z0^2 + x^74*y*z0^2 - x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 - x^74*y + x^73*y + x^72*y*z0 - x^71*y*z0^2 - x^73 - x^72*y + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^71*y + x^70*z0^2 - x^71 + x^70*y + x^69*y*z0 - x^69*z0^2 - x^70 + x^69*y - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y + x^68*z0 + x^67*y*z0 + x^66*y*z0^2 - x^67*z0 + x^67 + x^66*y - x^66*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^65 - x^64*y + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^61*y*z0 + x^61*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*y*z0 + x^61 + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*z0 - x^56*y - x^56*z0 - x^56 + x^15*z0^2, + -x^115 - x^114*z0 - x^114 + x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^112 + x^111*y - x^111*z0 + x^110*z0^2 + x^111 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y + x^108*y*z0 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^106*y*z0^2 + x^108 + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^107 - x^106*y - x^105*y*z0 + x^105*z0^2 - x^106 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y + x^103*z0^2 + x^104 + x^103*y + x^102*y*z0 + x^102*z0^2 - x^103 - x^102*y - x^102*z0 + x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 + x^97*y*z0 - x^97*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^97 + x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^94*y*z0 + x^95 + x^94*z0 + x^93*y*z0 - x^94 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*y + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0 + x^84*z0^2 - x^84*z0 - x^83*y*z0 - x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 - x^81*y*z0 - x^80*y*z0^2 + x^82 + x^80*y*z0 + x^79*y*z0^2 - x^80*y + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 + x^74*y*z0^2 - x^76 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 + x^71*z0^2 - x^71*y + x^71*z0 + x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 + x^65*y*z0^2 + x^66*y + x^66*z0 - x^65*y*z0 - x^66 - x^65*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^62*y*z0 + x^62*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 + x^56 + x^15*y, + -x^115 + x^113*z0^2 + x^114 - x^113 + x^112*y + x^112*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^111*z0 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^108*y*z0 + x^108*z0^2 + x^109 + x^108*y + x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y + x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^105*y - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^101*y*z0^2 + x^103 + x^101*y*z0 - x^102 + x^101*y - x^101*z0 + x^100*z0^2 + x^101 - x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 - x^94*y*z0^2 - x^96 - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^95 + x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y + x^92*y*z0 - x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y + x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 - x^89*y + x^89*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^86*y*z0 - x^85*y*z0^2 + x^87 - x^86*y + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*y + x^82*y*z0^2 - x^84 - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y - x^81*y*z0 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 - x^76*y - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 + x^74*z0 - x^73*y*z0 - x^74 + x^73*y - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^72*y - x^72 + x^71*y + x^70*z0^2 + x^69*y*z0^2 + x^71 - x^69*y*z0 - x^70 - x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^68*y - x^68*z0 + x^67*y*z0 + x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^65*y*z0^2 + x^67 - x^65*y*z0 + x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y - x^58*y*z0 - x^59 - x^58*y + x^58*z0 + x^56*y*z0^2 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^15*y*z0, + x^115 + x^114*z0 - x^114 - x^112*z0^2 - x^113 - x^112*y - x^112*z0 - x^111*y*z0 + x^111*y + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^109*y*z0 - x^109*z0^2 + x^109*z0 + x^108*z0^2 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^101*y*z0^2 - x^103 - x^102*y - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^101 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^97*y*z0^2 - x^99 + x^98*y + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*z0 + x^94*y*z0 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*y*z0 + x^90*y*z0^2 - x^92 - x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*y + x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y - x^79*z0^2 + x^80 - x^79*y + x^79*z0 + x^78*z0^2 - x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^76*y*z0^2 - x^78 - x^77*y + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 - x^73*y - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^72 + x^71*y - x^70*y*z0 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^69 - x^68*y + x^67*y*z0 - x^66*y*z0^2 - x^68 - x^65*y*z0^2 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^64*y*z0 + x^64*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^59*y - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^15*y*z0^2, + x^114*z0 + x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^113 - x^111*y*z0 - x^110*y*z0^2 + x^112 + x^110*y*z0 + x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 - x^110 - x^109*y + x^109*z0 - x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^108 + x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 + x^105 + x^104*y + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*z0^2 - x^102*y + x^101*y*z0 - x^100*y*z0^2 + x^102 - x^101*y - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^99*y - x^99*z0 + x^98*z0^2 + x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^97*y + x^96*y*z0 - x^96*z0^2 - x^97 + x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^92*y*z0 - x^91*y*z0^2 - x^93 - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^91*y - x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^89*y*z0 - x^90 + x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^81 + x^80*z0 + x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^78*z0^2 + x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^77*y + x^76*y*z0 - x^76*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 - x^75*y - x^74*z0^2 - x^73*y*z0^2 + x^75 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^73*z0 - x^71*y*z0^2 - x^72*z0 + x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*y + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y + x^65*y*z0 + x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^62*y*z0 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^61*y - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y*z0 - x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 - x^57*z0^2 + x^58 - x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^16, + -x^115 + x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 + x^112*y - x^111*z0^2 - x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*z0 + x^108*y*z0^2 + x^110 + x^109*z0 + x^108*y*z0 - x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^108 - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 + x^107 - x^106*y + x^106*z0 - x^106 - x^105*z0 - x^104*y - x^104*z0 - x^103*z0^2 + x^104 - x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^100*y*z0 + x^100*z0^2 - x^101 + x^99*y*z0 - x^99*z0^2 + x^100 + x^99*y + x^99*z0 - x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^96 + x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*y + x^93*z0 - x^93 - x^92*z0 + x^90*y*z0^2 + x^92 - x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*z0 - x^89*z0^2 - x^88*y*z0^2 - x^89*y - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*z0 - x^88 + x^87*z0 + x^87 + x^86*z0 + x^85*z0^2 - x^86 - x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^84*z0 - x^83*z0^2 + x^84 + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y + x^80*z0^2 + x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*y - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^74*y*z0 + x^74*z0^2 - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*z0 + x^71*y*z0^2 - x^73 - x^72*z0 + x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^71 - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 + x^68*z0^2 + x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y - x^65*y*z0^2 + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*z0^2 + x^65 + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^62*y*z0 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^59*y + x^58*y*z0 + x^57*y*z0^2 + x^58*y + x^58*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 + x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^16*z0, + -x^114*z0 - x^113*z0^2 - x^114 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y - x^111*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^108*z0 - x^106*y*z0^2 - x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0 - x^103*y*z0 - x^103*y + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 - x^102*y - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*y - x^98*y*z0 - x^98*z0^2 - x^99 - x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^98 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y + x^94*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^92*y*z0 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^86*y*z0 - x^85*y*z0^2 + x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y - x^85*z0 + x^84*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*z0^2 - x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*z0 - x^80*y*z0 - x^79*y*z0^2 + x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y - x^77*y*z0 - x^77*z0^2 + x^78 + x^77*y + x^77*z0 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 + x^73*y*z0^2 + x^75 + x^74*y - x^73*y*z0 - x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 - x^69*y*z0^2 + x^70*y - x^69*y*z0 - x^68*y*z0^2 + x^70 - x^68*y*z0 + x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*z0 + x^61*z0^2 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*z0 - x^59*z0^2 - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 + x^57*y - x^57*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^16*z0^2, + x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 + x^113 + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y - x^110*y*z0 + x^110*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*z0^2 - x^107*y*z0^2 - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y + x^105*y*z0^2 + x^107 - x^106*y - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 + x^102 + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^101 + x^99*z0^2 - x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^99 + x^98*y + x^98*z0 - x^97*y*z0 - x^98 + x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^93*y*z0^2 + x^95 + x^94*y + x^92*y*z0^2 - x^94 + x^93*y - x^92*y*z0 - x^91*y*z0^2 + x^92*y + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y + x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*y - x^88*z0 + x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 - x^86*y*z0 - x^86*y - x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y + x^82*z0^2 - x^81*y*z0 + x^81*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*z0 + x^79*z0^2 - x^79*y + x^78*z0^2 + x^79 - x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 + x^75 - x^74*y + x^74*z0 + x^73*y*z0 - x^72*y*z0^2 - x^73*y - x^72*y*z0 - x^72*z0^2 + x^73 - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*y - x^70*y*z0 - x^70*y + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^67*y - x^67*z0 - x^65*y*z0^2 - x^67 + x^66*z0 + x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^65 + x^64*y - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^62*z0 - x^61*y*z0 + x^60*y*z0^2 + x^62 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y + x^16*y, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^111 + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^106*y - x^104*y*z0^2 + x^106 + x^105*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^103*z0^2 - x^102*y*z0^2 + x^103*y - x^103*z0 + x^102*y - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^100*z0^2 - x^100*y - x^99*z0^2 - x^98*y*z0^2 - x^99*y - x^99*z0 - x^98*z0^2 - x^97*y*z0^2 - x^98*y - x^98*z0 - x^97*y*z0 - x^98 + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^96*y + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*y - x^92*z0 - x^91*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*y - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 - x^88*z0^2 + x^87*y*z0^2 + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 - x^85*y*z0^2 + x^86*y - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*y + x^83*z0^2 - x^83*y + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*z0^2 + x^81 + x^79*z0^2 - x^80 - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y - x^77*z0^2 - x^77*y - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 - x^75*z0^2 + x^75*y + x^75*z0 + x^74*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*z0 + x^71*y*z0^2 - x^73 - x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^71 + x^70*z0 + x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 + x^67*y*z0^2 + x^69 + x^68*y - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 - x^65*y*z0^2 - x^66*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^62*z0^2 - x^62*y - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^58 - x^57*z0 + x^56*z0^2 + x^56*z0 + x^56 + x^55*y + x^16*y*z0, + -x^115 - x^114*z0 - x^114 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^111*y + x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 - x^106*y*z0^2 - x^108 + x^107*y + x^106*y*z0 + x^107 + x^106*y + x^106*z0 - x^105*y*z0 - x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 + x^104*y - x^104*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^101*y*z0 + x^101*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*z0^2 + x^97 - x^95*y*z0 - x^94*y*z0^2 + x^96 - x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y - x^94*z0 + x^93*z0^2 - x^93*z0 - x^92*y*z0 + x^91*y*z0^2 - x^93 + x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*z0 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^89 + x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*z0 + x^85*y*z0^2 + x^87 - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 - x^83*y*z0^2 + x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^83 - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^78 - x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^76*y + x^76*z0 + x^74*y*z0^2 + x^76 - x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^74*y + x^74*z0 + x^73*y*z0 - x^72*y*z0^2 - x^74 + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 + x^72*z0 - x^72 + x^71*y - x^71*z0 - x^69*y*z0^2 - x^70*z0 - x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^67 - x^66*z0 + x^65*y*z0 + x^66 + x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^62*y + x^62*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^59*y*z0^2 - x^60*y - x^60*z0 + x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*z0^2 + x^56*z0 - x^55*y + x^16*y*z0^2, + x^115 - x^113*z0^2 + x^114 + x^112*z0^2 + x^113 - x^112*y + x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*z0^2 - x^106*y - x^106*z0 - x^104*y*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*z0 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^98*y*z0^2 - x^99*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^97*z0 - x^96*z0^2 - x^97 - x^96*y + x^96*z0 + x^95*z0^2 + x^96 - x^94*y*z0 - x^94*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^94 - x^93*z0 - x^91*y*z0^2 - x^91*y*z0 + x^91*z0^2 + x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^87*y*z0 - x^86*y*z0^2 - x^88 + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*z0 - x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^82 + x^81*y - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^79*y - x^79*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^77*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^75*y + x^75*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y - x^72*y*z0 - x^71*y*z0^2 - x^73 + x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^71*y + x^70*y*z0 + x^70*z0^2 - x^70*y + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*z0 + x^68*y*z0 + x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y - x^66*z0^2 - x^67 - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 - x^63*y*z0 - x^62*y*z0^2 + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*y - x^57*y*z0^2 + x^59 - x^58*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^55*y*z0 - x^56 + x^55*y + x^17, + x^115 + x^114*z0 + x^112*z0^2 - x^112*y - x^111*y*z0 + x^111*z0^2 + x^112 - x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*z0 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*z0 + x^107*y*z0 + x^108 + x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*z0^2 + x^104*y + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^103 - x^102*y + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 - x^99*y*z0^2 + x^101 - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^98*y*z0 + x^97*y*z0^2 - x^98*y - x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^98 + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y - x^96*z0 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^92*y*z0 + x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*z0^2 + x^92 - x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*z0 - x^86*z0^2 - x^85*y*z0^2 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*y - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^80*y*z0^2 - x^82 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^80 + x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^76 - x^75*y - x^75*z0 + x^75 + x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^71*y*z0 - x^71*z0^2 - x^71*y - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^70*y - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^66*z0 + x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 + x^63*y*z0 - x^62*y*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^63 - x^61*y*z0 + x^61*y + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 - x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^56 + x^55*y + x^17*z0, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 - x^110*y + x^110*z0 + x^109*y*z0 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^109 - x^107*y*z0 + x^108 - x^107*z0 + x^106*y*z0 - x^107 + x^106*y - x^105*y*z0 + x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^99*z0^2 + x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^93*y*z0^2 + x^94*y - x^93*y*z0 + x^92*y*z0^2 + x^94 - x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^93 - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^91 - x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y - x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*z0 + x^87*z0^2 - x^87*y - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 + x^85 + x^84*y - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^80*y*z0 + x^80*z0^2 + x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^77*y*z0^2 - x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 + x^74*z0^2 - x^75 + x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 - x^69*y*z0^2 + x^70*y + x^70*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*y - x^69*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 + x^66*z0^2 - x^67 + x^66*y + x^65*z0^2 - x^64*y*z0^2 + x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^64 + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y - x^62*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y - x^56*y*z0 + x^55*y*z0 + x^17*z0^2, + x^115 - x^113*z0^2 + x^113 - x^112*y + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^110*z0^2 - x^110*y - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y + x^107*y*z0^2 + x^109 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^106*z0 - x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 + x^104 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^102*z0 + x^101*y*z0 + x^101*z0 + x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*z0 + x^97*y*z0^2 - x^98*y + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*z0 - x^95*z0^2 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 - x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^94 - x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 + x^90*y*z0 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^90 + x^89*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y + x^88*z0 - x^87*y*z0 - x^88 + x^87*y - x^86*y*z0 + x^85*y*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^86 - x^85*y - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^74*y + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^72*y*z0 - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*y - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^67*y*z0 + x^66*y*z0^2 - x^68 + x^67*y + x^66*z0^2 + x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^66 + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 - x^62*z0^2 + x^62*y + x^62*z0 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^59*z0 + x^59 + x^58*y - x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^56*y - x^55*y*z0 - x^56 + x^55*y + x^17*y, + x^114*z0 + x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^113 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^110*y*z0 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^109*y + x^108*z0^2 + x^108*y - x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^108 + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 - x^105 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^103 - x^102*y - x^101*y*z0 - x^100*y*z0^2 + x^101 - x^100*z0 - x^98*y*z0^2 + x^100 - x^99*y + x^97*y*z0^2 + x^98*y - x^98*z0 - x^97*y*z0 + x^98 - x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*y*z0 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^95 - x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 + x^91*y*z0^2 + x^92*y - x^92*z0 - x^90*y*z0^2 - x^92 + x^91*y - x^90*y*z0 + x^90*z0^2 + x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 - x^88 + x^87*y - x^87*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*z0^2 + x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*z0^2 - x^82 + x^81*y + x^80*y*z0 + x^79*y*z0 - x^79*z0^2 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*z0^2 - x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*z0 + x^69*y*z0 - x^68*y*z0^2 + x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^67*y*z0 - x^67*z0^2 - x^68 + x^66*z0^2 - x^67 + x^66*y - x^64*y*z0^2 + x^66 - x^65*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^61*y*z0^2 - x^63 + x^61*z0^2 + x^62 - x^61*z0 - x^60*z0^2 + x^60*y - x^60*z0 + x^58*y*z0^2 - x^60 + x^58*z0^2 - x^59 - x^58*y - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^17*y*z0, + -x^115 - x^114*z0 - x^114 + x^113 + x^112*y - x^112*z0 + x^111*y*z0 + x^112 + x^111*y - x^111*z0 + x^110*z0^2 - x^110*y + x^109*y*z0 - x^110 - x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108 - x^107*y - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^102*y*z0^2 - x^104 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*z0 + x^99 + x^98*z0 - x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^95 + x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^94 + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^89 - x^88*y + x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^85*y*z0 - x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^85 + x^84*z0 - x^83*y*z0 - x^84 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^81*y*z0 - x^81*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*y - x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^75*y + x^74*y*z0 - x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^73*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y + x^70*y*z0^2 - x^71*y - x^71*z0 - x^69*y*z0^2 - x^71 + x^70*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^67*y*z0^2 + x^69 + x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*z0 + x^66*y + x^66*z0 - x^65*z0^2 - x^66 + x^65*y - x^65*z0 - x^64*z0^2 - x^65 - x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*z0 + x^62*y*z0 + x^61*y*z0^2 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^55*y*z0 + x^56 - x^55*y + x^17*y*z0^2, + x^115 + x^114*z0 + x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y - x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^110*y - x^109*z0^2 + x^108*y*z0^2 + x^109*y - x^109*z0 + x^108*y*z0 + x^109 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^107 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*y*z0 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^102*y - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*z0 + x^99*z0^2 + x^99*y + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^98 + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 - x^92*y*z0 + x^91*y*z0^2 - x^93 + x^92*y + x^91*z0^2 + x^90*y*z0^2 - x^91*y - x^91*z0 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 - x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^86 + x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^83*y*z0 - x^82*y*z0^2 - x^84 + x^83*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^81*y*z0 + x^81*z0^2 + x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*z0 - x^77*y*z0^2 - x^78*y + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^76 + x^75*y - x^75*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 - x^73*y - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^71*y*z0 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^70 + x^69*y + x^69*z0 - x^68*y*z0 + x^67*y*z0^2 + x^69 + x^66*y*z0^2 - x^67*y + x^66*z0^2 + x^67 - x^66*z0 + x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^65 + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 + x^62 - x^60*z0^2 - x^59*y*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*y + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^18, + -x^114*z0 - x^113*z0^2 - x^113*z0 - x^112*z0^2 - x^113 - x^112*z0 + x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 - x^109 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^106 + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 - x^101*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 - x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^100 + x^99*z0 - x^98*z0^2 + x^97*y*z0^2 - x^97*y*z0 - x^96*y*z0^2 - x^97*y - x^96*y*z0 - x^96*z0^2 + x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*z0 + x^88*z0^2 - x^87*y*z0^2 - x^88*y + x^88*z0 + x^87*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 - x^87 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 + x^84*y*z0 - x^85 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^83*y + x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 - x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y + x^77*y*z0 - x^78 - x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^74 - x^73*y + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*z0^2 - x^70*y - x^70*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 + x^68*y*z0 - x^68*y + x^68*z0 - x^66*y*z0^2 + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^61 + x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 + x^57*z0 + x^56*y*z0 - x^56*y - x^55*y + x^18*z0, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y + x^110*y*z0 + x^109*y*z0^2 - x^111 - x^110*y + x^109*y*z0 + x^109*z0^2 - x^110 - x^109*y + x^109*z0 - x^108*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 - x^105 - x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^97*y - x^96*y*z0 - x^95*y*z0^2 - x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 - x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^91*z0^2 - x^90*y*z0^2 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y + x^88*z0^2 - x^89 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y + x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 + x^80 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^78 + x^77*y + x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^65*z0^2 + x^64*y*z0^2 + x^66 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^63*y - x^63*z0 + x^61*y*z0^2 - x^63 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y + x^59*z0^2 - x^60 - x^59*y + x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*z0^2 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^18*z0^2, + x^114*z0 + x^113*z0^2 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*z0 - x^111 + x^109*z0^2 - x^110 + x^109*y + x^108*y*z0 + x^108*y + x^108*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y + x^103*z0 + x^102*z0^2 + x^101*y*z0^2 - x^101*z0^2 + x^100*y*z0^2 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 + x^96*y + x^96*z0 + x^95*z0^2 + x^96 + x^95*y - x^94*z0^2 - x^93*y*z0^2 + x^94*y + x^93*y*z0 + x^94 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^90*y*z0 - x^91 + x^90*y - x^89*z0^2 + x^90 + x^89*z0 + x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 + x^87*z0^2 - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y - x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^84*y - x^83*z0^2 + x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 + x^81*z0^2 + x^81*y + x^80*z0^2 - x^81 + x^80*y - x^80*z0 - x^80 - x^79*y - x^78*z0^2 + x^79 + x^78*z0 + x^77*y*z0 - x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 + x^74*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*z0 - x^71*z0^2 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^65*y*z0 + x^65*z0^2 + x^65*z0 + x^65 + x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0 - x^56*y*z0^2 + x^58 + x^57*z0 - x^56*y*z0 + x^55*y*z0 - x^56 + x^55*y + x^18*y, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 + x^109*y*z0 - x^110 - x^109*y + x^108*z0^2 + x^109 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^107*y + x^107*z0 - x^106*y*z0 - x^107 - x^106*y - x^106*z0 + x^105*z0^2 + x^105*y + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 - x^102*y*z0 - x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 - x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^101 + x^100*y - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^99*y - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 - x^95*z0^2 + x^94*y*z0 - x^93*y*z0^2 + x^95 + x^94*y + x^93*y*z0 - x^92*y*z0^2 + x^92*y*z0 - x^92*z0^2 - x^93 - x^92*y - x^92 - x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*z0 - x^88*y*z0 + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^85*y*z0 + x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*z0^2 - x^85 + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^83*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^81*y + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*z0 - x^79*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 - x^77*y + x^76*y*z0 + x^76*z0^2 - x^76*y - x^75*z0^2 + x^74*y*z0^2 + x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 + x^70*y*z0^2 + x^72 + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^70*y + x^69*y*z0 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^68 + x^67*y - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y - x^64*z0^2 + x^65 + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*y - x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^18*y*z0, + -x^115 + x^113*z0^2 + x^114 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^109*y - x^109*z0 + x^108*y*z0 + x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*z0 + x^105*y*z0 + x^104*y*z0^2 + x^106 - x^105*y + x^104*y*z0 + x^104*z0^2 - x^105 - x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^102 + x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^97*z0 + x^96*y*z0 + x^95*y*z0^2 - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^93*y*z0 - x^93*z0^2 - x^94 + x^93*y - x^93*z0 + x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^86*y - x^85*y*z0 + x^85*z0^2 - x^86 - x^85*y + x^84*y*z0 + x^85 - x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^84 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^80*y*z0 + x^81 + x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^77*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^77 - x^76*y + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y - x^73*z0 - x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^71*y + x^70*y*z0 - x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^70 + x^69*y - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^65*y*z0^2 + x^67 - x^66*y + x^66*z0 - x^65*z0^2 - x^66 + x^65*y - x^65*z0 + x^63*y*z0^2 - x^64*y - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*y - x^60*y*z0 - x^60*z0^2 - x^61 + x^60*y - x^60*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 - x^58*z0^2 + x^57*y*z0^2 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y + x^57*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y + x^55*y*z0 + x^56 + x^18*y*z0^2, + -x^115 - x^114*z0 - x^114 - x^112*z0^2 - x^113 + x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*z0 - x^105*y*z0 - x^106 + x^105*y - x^105*z0 - x^104*z0^2 - x^105 + x^104*y + x^104*z0 + x^103*y*z0 + x^104 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*z0 + x^99*z0^2 + x^100 - x^99*y + x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y - x^97*z0^2 - x^98 - x^97*y + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*y*z0 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*z0 + x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^90 - x^89*y - x^89*z0 + x^88*z0^2 - x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^88 - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 - x^84*y + x^84*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*z0 + x^82*y*z0 + x^82*y + x^81*y*z0 + x^81*z0^2 + x^81*y - x^80*y*z0 - x^79*y*z0^2 + x^80*y + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 + x^80 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^78 + x^76*z0^2 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^74*z0 - x^73*z0^2 + x^73*y - x^73*z0 - x^72*y*z0 + x^71*y*z0^2 - x^73 - x^72*z0 - x^71*y*z0 - x^72 + x^70*y*z0 + x^70*z0^2 - x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*y - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y + x^65*y*z0^2 - x^67 - x^66*y + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*z0 + x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 - x^58*z0^2 - x^59 - x^58*y - x^58*z0 - x^56*y*z0^2 - x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^55*y*z0 + x^55*y + x^19, + x^114*z0 + x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*z0 - x^110*y*z0 + x^109*y*z0^2 + x^111 + x^110*z0 - x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^103*z0^2 - x^104 + x^103*y - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^102 - x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*y - x^99*z0^2 + x^98*y*z0^2 - x^98*z0^2 - x^97*y*z0^2 - x^97*y*z0 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^96*y - x^96*z0 - x^95*z0^2 + x^96 - x^95*y + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 - x^91*z0^2 - x^92 + x^91*y + x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^88*z0^2 + x^87*y*z0^2 + x^89 - x^87*y*z0 - x^86*y*z0^2 - x^88 + x^87*y + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 + x^83*y*z0 + x^84 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*y*z0 + x^80 + x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 + x^76*z0^2 - x^77 + x^76*y - x^76*z0 - x^74*y*z0^2 - x^76 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y - x^71*y*z0 + x^71*z0^2 + x^71*y + x^70*y*z0 + x^70*z0^2 + x^71 - x^70*y - x^70*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^68 + x^67*y + x^65*y*z0^2 - x^66*z0 - x^65*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 + x^65 - x^64*z0 + x^63*y*z0 + x^62*y*z0^2 + x^64 - x^63*y + x^61*y*z0^2 - x^63 + x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*z0^2 - x^60 + x^59*y + x^57*y*z0^2 - x^59 + x^58*y + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*z0 + x^56*y*z0 - x^55*y*z0^2 + x^57 - x^56*y + x^56*z0 + x^56 + x^19*z0, + x^114 + x^113*z0 + x^112*z0^2 - x^112*z0 - x^111*z0^2 - x^111*y - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^109*y*z0 + x^108*y*z0^2 + x^110 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*z0^2 - x^108 - x^107*y + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^106 + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^104*z0 + x^104 - x^102*y*z0 + x^102*z0^2 + x^103 + x^102*y + x^101*y*z0 + x^100*y*z0^2 + x^102 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 - x^99*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*y + x^97*y*z0 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 + x^92*z0^2 - x^93 - x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 - x^90 + x^89*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^86*z0^2 - x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y - x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*y*z0 + x^77*y*z0^2 + x^78*y + x^77*y*z0 - x^77*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^77 - x^76*y - x^75*y*z0 - x^74*y*z0^2 + x^76 - x^75*y + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 - x^71*z0^2 - x^71*y - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*z0 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y - x^67*z0^2 - x^66*y*z0^2 + x^67*z0 + x^66*z0^2 + x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^64*y*z0 + x^63*y*z0^2 - x^64*y - x^63*y*z0 + x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^62 + x^61*z0 - x^60*y*z0 + x^59*y*z0^2 - x^61 + x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*z0 - x^55*y*z0 + x^19*z0^2, + -x^115 + x^113*z0^2 - x^114 + x^113*z0 + x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^111 - x^110*y + x^109*y*z0 + x^109*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^109 + x^108*y - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^106*z0^2 - x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^105*y + x^105*z0 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*y*z0 + x^102*y*z0^2 - x^104 + x^102*y*z0 - x^101*y*z0^2 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 + x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*z0 + x^99*y*z0 + x^100 + x^99*z0 - x^98*y*z0 + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^93*y*z0^2 + x^95 + x^94*y + x^93*y*z0 + x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^93 - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^91 + x^90*z0 + x^89*y*z0 - x^88*y*z0^2 - x^89*y - x^89*z0 + x^88*z0^2 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^82*z0^2 + x^83 - x^82*y - x^81*y*z0 - x^81*z0^2 - x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*z0 - x^76*y*z0^2 - x^77*z0 + x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 + x^74*z0^2 - x^73*y*z0^2 - x^74*y + x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 + x^72*y + x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 - x^70*y + x^70*z0 - x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 + x^69 - x^68*y + x^68*z0 + x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*z0^2 + x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*y - x^62*z0^2 - x^63 - x^62*y + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 + x^61 + x^59*y*z0 + x^58*y*z0^2 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y - x^58*z0 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^19*y, + x^114*z0 + x^113*z0^2 + x^113*z0 - x^113 - x^111*y*z0 - x^110*y*z0^2 + x^112 + x^111*z0 - x^110*y*z0 + x^111 + x^110*y - x^110 - x^109*y - x^109*z0 - x^108*y*z0 - x^109 - x^108*y + x^108*z0 - x^108 + x^107*y - x^107*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 - x^103*z0^2 - x^102*y*z0^2 + x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 - x^100 - x^99*y + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^96*y*z0 + x^95*y*z0^2 - x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^92*y*z0 + x^92*z0^2 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^85*z0^2 + x^86 - x^85*y - x^85*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y - x^81*y*z0 - x^80*y*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^81 - x^80*z0 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^77*y*z0^2 + x^78*y + x^77*y*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^77 - x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 + x^75 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^74 + x^73*y + x^73*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y + x^71*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 - x^70 + x^69*y + x^68*y*z0 + x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^65*z0^2 + x^65*y - x^64*y*z0 - x^64*z0^2 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 + x^61*y + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 + x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^59 - x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^58 + x^57*y - x^57*z0 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 + x^56 - x^55*y + x^19*y*z0, + x^115 - x^113*z0^2 + x^114 - x^113 - x^112*y - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^110*z0^2 + x^110*y + x^110*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 + x^107*y*z0^2 - x^109 + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 - x^105*y*z0 - x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^101*z0^2 + x^100*y*z0^2 + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*z0^2 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^90*y - x^89*y*z0 - x^89*z0^2 - x^89*y - x^89*z0 + x^87*y*z0^2 + x^89 + x^87*y*z0 + x^86*y*z0^2 + x^88 - x^87*y - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*z0 + x^85*y*z0 + x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 + x^84*y + x^83*y*z0 + x^84 - x^83*z0 - x^82*y*z0 - x^83 - x^82*y - x^82*z0 + x^81*z0^2 + x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y - x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 - x^79 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^77*y - x^76*y*z0 + x^77 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 + x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*z0^2 - x^74 - x^73*z0 + x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 - x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 + x^69 - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 - x^65 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^62*y*z0 + x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^61 - x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^57*y*z0 - x^56*y*z0^2 - x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*z0 + x^56 + x^55*y + x^19*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^113 - x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y - x^107*z0 + x^105*y*z0^2 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*z0 - x^103*z0^2 + x^104 - x^103*y + x^103*z0 + x^102*y*z0 + x^101*y*z0^2 - x^103 + x^102*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 + x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^98 - x^97*y - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*z0^2 - x^96 + x^95*z0 - x^94*y*z0 + x^93*y*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 + x^91*y*z0^2 + x^92*y - x^92*z0 - x^91*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 - x^87*y*z0^2 + x^89 + x^88*y - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^86*y*z0 + x^86*z0^2 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y - x^84*y*z0 - x^84*z0 + x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 + x^82*y*z0 + x^81*y*z0^2 - x^83 - x^81*y*z0 + x^80*y*z0^2 - x^82 + x^81*y + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*z0 - x^79*z0^2 - x^80 + x^79*y + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^77*y*z0 - x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^74*y - x^73*z0^2 + x^74 - x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^73 - x^72*y + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^69 + x^66*y*z0^2 - x^68 + x^67*y - x^65*y*z0^2 + x^67 + x^66*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*y - x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*z0 - x^62*z0^2 + x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 - x^56*z0^2 + x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^20, + x^115 + x^114*z0 - x^114 + x^113*z0 - x^113 - x^112*y - x^111*y*z0 + x^111*z0^2 + x^111*y - x^110*y*z0 + x^110*z0^2 + x^110*y + x^110*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*z0 - x^108*z0^2 - x^107*y*z0^2 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*z0 + x^103*y*z0^2 - x^105 + x^104*z0 + x^103*z0^2 - x^102*y*z0^2 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^102*z0 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^100 - x^99*y - x^99*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^97 + x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 + x^96 + x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^88*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y - x^85*y*z0 - x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^82*z0^2 - x^82*y + x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^82 - x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^77*y*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^75*y - x^75*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^73*z0 - x^72*z0^2 - x^73 - x^72*y + x^71*y*z0 - x^70*y*z0^2 - x^71*y + x^71*z0 - x^69*y*z0^2 + x^71 + x^70*y + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 - x^67 - x^65*y*z0 - x^66 + x^65*z0 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^62*z0^2 - x^62*y + x^62*z0 + x^61*y*z0 + x^60*y*z0^2 - x^62 + x^61*z0 + x^59*y*z0^2 + x^60*z0 + x^59*z0^2 + x^60 + x^59*y - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 + x^58 - x^57*y - x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^20*z0, + x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^112*z0^2 + x^113 - x^112*y + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y + x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y + x^108*y*z0^2 + x^109*y - x^109*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 - x^107*z0^2 - x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^107 - x^106*y + x^106*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 + x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^99*y*z0 - x^100 + x^99*y - x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^99 - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*y + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*z0 - x^90*y*z0 - x^91 + x^89*z0^2 - x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^85*y + x^84*y*z0 - x^83*y*z0^2 + x^84*y - x^84*z0 - x^84 - x^83*y + x^82*y*z0 + x^82*z0 + x^81*y*z0 - x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 - x^80*y*z0 + x^79*y*z0^2 - x^81 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^78*y - x^77*z0^2 + x^78 + x^77*y + x^76*y*z0 - x^76*z0^2 - x^76*z0 + x^75*y*z0 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*y + x^70 + x^69*y - x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^67*z0 - x^65*y*z0^2 - x^66*z0 + x^65*z0^2 - x^66 - x^65*y - x^64*y*z0 - x^63*y*z0^2 - x^64*y - x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^59*y*z0 + x^58*y*z0^2 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*y + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^57 + x^55*y*z0 + x^20*z0^2, + -x^115 + x^113*z0^2 + x^114 + x^112*z0^2 + x^113 + x^112*y - x^110*y*z0^2 - x^112 - x^111*y - x^109*y*z0^2 - x^111 - x^110*y + x^109*z0^2 + x^110 + x^109*y - x^109*z0 - x^108*z0^2 + x^108*y - x^108*z0 + x^107*z0^2 - x^106*y*z0^2 + x^106*y*z0 - x^106*z0^2 + x^107 - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^105*y - x^105*z0 + x^104*z0^2 + x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^101*y*z0 + x^100*y*z0^2 + x^101*y - x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^99*y*z0 + x^99*z0^2 - x^99*y + x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 + x^95*z0^2 - x^94*y*z0^2 - x^95*z0 - x^94*z0^2 - x^94*y - x^93*z0^2 - x^94 - x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^92*y - x^92*z0 + x^91*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*y*z0 - x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^88*z0^2 - x^87*y*z0^2 - x^88*y + x^87*y*z0 - x^87*z0^2 - x^88 + x^87*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^84 - x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y + x^80*z0^2 + x^79*y*z0^2 - x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0 - x^78*z0^2 + x^77*z0^2 - x^76*y*z0^2 - x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^76*z0 - x^74*y*z0^2 - x^75*z0 + x^74*y*z0 - x^73*y*z0^2 - x^75 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^70*y - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^69*y + x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*z0 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^61*y*z0 + x^61*z0^2 - x^62 - x^61*y - x^61*z0 - x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y + x^20*y, + x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*z0^2 - x^111 + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*y - x^104*z0 - x^103*y*z0 - x^104 + x^103*y - x^102*z0^2 - x^102*y - x^101*z0^2 - x^100*y*z0^2 - x^101*z0 + x^100*y*z0 - x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^97 - x^96*z0 + x^95*z0^2 + x^95*z0 - x^94*z0^2 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y + x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 + x^90*y*z0 - x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*z0 + x^89 + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 + x^86*y*z0 + x^87 + x^86*y + x^85*y*z0 + x^85*y - x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^81 + x^79*y*z0 + x^79*z0^2 - x^80 - x^79*z0 + x^78*y*z0 + x^79 + x^78*y + x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*y + x^70*y*z0 + x^69*y*z0^2 - x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^69*z0 - x^67*y*z0^2 + x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*z0 - x^66*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^66 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^65 + x^64*y + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*y + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 - x^57*z0^2 - x^58 + x^57*y + x^56*y*z0 - x^56*z0^2 + x^56*z0 - x^55*y*z0 + x^20*y*z0, + -x^115 + x^113*z0^2 + x^113*z0 + x^112*z0^2 + x^113 + x^112*y + x^112*z0 - x^110*y*z0^2 - x^112 - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 - x^109*y*z0 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*y*z0 + x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 + x^106*y - x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*z0^2 + x^104 - x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^101*y*z0 + x^101*z0^2 - x^102 - x^101*y + x^101*z0 + x^100*z0^2 + x^101 - x^100*z0 - x^98*y*z0^2 + x^100 + x^98*y*z0 + x^99 - x^98*y - x^98*z0 + x^97*y + x^96*y*z0 - x^95*y*z0^2 - x^96*y + x^96*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 + x^94*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^94 - x^92*y*z0 - x^92*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 - x^88*y - x^88*z0 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*z0 - x^81*z0^2 - x^82 - x^81*y + x^80*z0^2 + x^79*y*z0^2 + x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^77*y*z0 - x^76*y*z0^2 - x^77*z0 + x^76*y*z0 - x^77 - x^76*y + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^75*y + x^74*y*z0 - x^75 - x^73*y*z0 - x^73*z0^2 + x^73*y + x^73*z0 + x^72*y*z0 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 + x^69*z0^2 - x^68*y*z0^2 - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^68*z0 - x^67*z0^2 + x^68 - x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*z0^2 + x^64*y*z0^2 - x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y - x^61*y*z0^2 + x^63 + x^62*y + x^61*y*z0 + x^60*y*z0^2 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^60*y - x^60*z0 - x^59*y*z0 + x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^59 - x^57*z0^2 - x^57*z0 + x^56*y*z0 + x^57 - x^56*y + x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^20*y*z0^2, + -x^115 + x^113*z0^2 - x^114 - x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^110 - x^109*y - x^109*z0 + x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*z0 + x^104*y*z0 - x^104*z0^2 + x^105 - x^104*y + x^104*z0 - x^103*y*z0 - x^102*y*z0^2 + x^104 - x^102*y*z0 - x^102*z0^2 + x^103 - x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y - x^101*z0 - x^100*y*z0 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^99*z0 - x^98*y*z0 + x^99 + x^98*y - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^97 + x^96*y - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 + x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*z0 - x^92*z0^2 - x^93 + x^92*z0 + x^91*z0^2 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*y + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^89*y + x^89*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^87 - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^85 - x^84*y - x^84*z0 - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^80*y*z0 + x^80*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^77*z0 + x^76*z0^2 + x^77 + x^76*y - x^75*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 + x^71*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*z0^2 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 + x^67*y*z0 + x^67*y - x^67*z0 - x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y - x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 + x^60*y - x^60*z0 + x^59*y*z0 + x^60 - x^59*z0 - x^58*z0^2 - x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^58 + x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^57 - x^56*z0 + x^55*y*z0 + x^21, + x^115 + x^114*z0 - x^113*z0 - x^112*z0^2 - x^112*y - x^111*y*z0 + x^111*z0^2 - x^112 + x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 + x^106*y*z0 + x^106*y - x^105*y*z0 + x^105*y + x^104*y*z0 + x^104*z0^2 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^104 - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 + x^101*y - x^101*z0 - x^100*y*z0 + x^101 + x^100*z0 - x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^97*y - x^97*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 + x^94 + x^93*z0 - x^91*y*z0^2 + x^93 + x^92*y + x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*y + x^90*y*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y - x^85*y*z0 - x^85*z0^2 - x^85*y - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 - x^81*y*z0 - x^80*y*z0^2 + x^81*y + x^81*z0 - x^80*y*z0 + x^79*y*z0^2 + x^81 - x^80*y - x^79*y*z0 + x^79*y + x^79*z0 - x^78*y*z0 + x^79 - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0 - x^72*y*z0^2 - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 + x^70*y + x^69*z0^2 + x^69*y + x^69*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*z0 - x^66*z0^2 + x^66*y - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^63 - x^62*z0 + x^61*y*z0 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^58*y - x^58*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^21*z0, + -x^115 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^112*y + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^109 + x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 - x^107 + x^105*z0^2 - x^104*y*z0^2 - x^104*z0^2 - x^105 - x^104*y - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^101 - x^100*y + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y + x^98*z0^2 + x^99 + x^98*z0 + x^96*y*z0^2 + x^97*y - x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^95*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*z0 - x^92*y*z0 - x^93 + x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y - x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y + x^90*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*y + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^86*y + x^85*z0^2 + x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^85 - x^84*y - x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*y - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^79 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y + x^73*z0 + x^72*y*z0 + x^71*y*z0^2 + x^73 + x^72*y + x^71*y*z0 - x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^71 + x^70*y - x^69*y*z0 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*y*z0 + x^67*y*z0^2 + x^69 - x^68*y + x^67*y*z0 - x^67*z0^2 - x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*z0 + x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*y + x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^61*y + x^60*y*z0 - x^59*y*z0^2 - x^61 - x^60*y + x^59*y*z0 + x^58*y*z0 + x^57*y*z0^2 - x^58*y + x^58*z0 - x^57*y*z0 + x^56*y*z0^2 - x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^57 - x^56*y - x^55*y*z0 + x^56 + x^21*z0^2, + x^115 - x^113*z0^2 - x^114 - x^113 - x^112*y - x^112*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^110*z0^2 - x^111 + x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^109*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^106*y*z0 - x^105*y*z0^2 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^106 + x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^103*y + x^102*y*z0 - x^102*z0^2 + x^103 + x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^100 + x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 - x^98*y + x^97*y*z0 - x^97*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 + x^97 - x^96*z0 + x^95*y*z0 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*y - x^92*y*z0 + x^92*z0 - x^90*y*z0^2 + x^90*y*z0 + x^89*y*z0^2 - x^91 + x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y + x^87*y*z0 - x^87*z0^2 - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^85*y*z0 + x^84*y*z0^2 + x^85*z0 + x^84*y*z0 - x^83*y*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^80*y*z0^2 + x^82 + x^81*y + x^80*y*z0 - x^80*y - x^79*z0^2 + x^80 + x^78*y*z0 - x^78*z0^2 - x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 - x^76 - x^75*z0 - x^73*y*z0^2 + x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 + x^72*y*z0 - x^72*z0^2 - x^73 - x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^71*y - x^71*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 - x^68*y*z0^2 - x^70 - x^68*z0^2 - x^67*y*z0^2 + x^69 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^65 - x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^63*y + x^62*z0^2 - x^63 + x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y + x^60 + x^59*y - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 + x^57*y*z0 - x^58 - x^57*y + x^56*z0^2 + x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^21*y, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*z0 + x^105*y*z0^2 - x^107 - x^106*y + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 + x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*z0^2 + x^103 + x^102*y + x^102*z0 - x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^100 - x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*z0 + x^95*y*z0 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^94*y + x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*y + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 - x^87*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y - x^84*y*z0 + x^84*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*z0^2 + x^83*y + x^82*y*z0 + x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 - x^82 + x^81*y + x^80*y*z0 - x^80*z0^2 + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*y + x^79*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*y + x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*z0 + x^76*z0^2 - x^77 + x^76*z0 + x^75*y*z0 + x^76 + x^75*y - x^75 + x^74*y + x^74*z0 - x^73*z0^2 + x^74 - x^73*y - x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^70*z0^2 + x^69*y*z0^2 + x^70*y + x^69*y*z0 - x^69*z0^2 + x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*z0^2 + x^68 + x^67*z0 - x^67 + x^66*z0 + x^64*y*z0^2 + x^65*y + x^65*z0 - x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^63*y - x^62*y*z0 + x^63 - x^62*y + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 + x^60*z0^2 + x^61 + x^60*z0 - x^58*y*z0^2 + x^60 - x^59*y - x^58*z0^2 - x^57*y*z0^2 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y - x^57*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^55*y + x^21*y*z0, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^109*y*z0^2 - x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*y - x^108*z0^2 - x^109 - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y - x^102*z0 + x^101*z0^2 + x^102 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*z0^2 - x^98*y*z0^2 - x^99*z0 - x^97*y*z0^2 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^97*z0 - x^96*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0 - x^87*y*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*z0 - x^86*y*z0 - x^87 - x^86*y + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^85*y - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 + x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^81*y + x^81*z0 - x^80*y*z0 - x^79*y*z0^2 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^76*y*z0 - x^76*z0^2 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^74*y + x^74*z0 - x^73*y*z0 - x^72*y*z0^2 + x^74 - x^73 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^70*y + x^70*z0 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^66*z0^2 + x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^64*z0^2 - x^65 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*z0^2 + x^61 + x^60*y - x^59*y*z0 + x^58*y*z0^2 - x^59*y + x^58*z0^2 + x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^57*y - x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^21*y*z0^2, + -x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 + x^111*y*z0 + x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^110*z0 - x^109*z0^2 - x^109*y + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 - x^109 - x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y + x^105*y*z0 + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^102 - x^101*z0 + x^100*y*z0 - x^99*y*z0^2 + x^101 + x^100*z0 + x^99*z0^2 + x^100 + x^99*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^96*y*z0 + x^95*y*z0^2 - x^97 - x^96*y - x^95*y*z0 - x^95*z0^2 - x^96 - x^95*y + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 + x^94 - x^93*z0 - x^92*z0^2 + x^91*y*z0^2 + x^92*y + x^92*z0 - x^90*y*z0^2 + x^91*z0 - x^90*y*z0 - x^91 + x^90*y - x^90*z0 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 - x^87 - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^85*y - x^84*z0^2 + x^85 - x^84*y - x^83*y*z0 - x^84 - x^83*y - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y + x^82 + x^81*y - x^81*z0 - x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^76*y*z0 - x^75*y*z0^2 - x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^75*y + x^75*z0 + x^74*y*z0 - x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^72*y*z0 + x^72*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*z0 - x^65*y*z0^2 + x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*y - x^63*z0^2 + x^64 + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^61*z0^2 - x^60*y*z0 - x^59*y*z0^2 - x^61 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^22, + x^114*z0 + x^113*z0^2 - x^113*z0 + x^113 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 + x^111 - x^110*y - x^109*y*z0 + x^110 + x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*z0^2 + x^108 - x^107*y - x^107*z0 + x^105*y*z0^2 + x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^106 + x^105*y + x^104*y*z0 + x^104*z0^2 - x^105 - x^104*y + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 + x^99*z0^2 + x^100 - x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 + x^94*y*z0^2 + x^96 - x^95*y - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^89*y + x^88*z0^2 - x^89 - x^88*z0 + x^86*y*z0^2 - x^87*y + x^86*y*z0 - x^87 + x^86*y - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 + x^78*z0^2 - x^79 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^76 + x^75*y + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^72*y*z0 - x^73 - x^72*y - x^71*y*z0 - x^70*y*z0^2 - x^72 - x^71*y - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 - x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^68 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*z0 + x^62*y*z0^2 + x^64 - x^62*y*z0 - x^61*y*z0^2 + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*y + x^61*z0 + x^60*z0^2 + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^58*y + x^58*z0 - x^56*y*z0^2 + x^58 - x^57*y - x^56*y*z0 - x^56*z0^2 - x^56*z0 - x^55*y + x^22*z0, + x^114 + x^112*z0^2 + x^113 - x^111*z0^2 - x^111*y - x^109*y*z0^2 - x^111 - x^110*y + x^108*y*z0^2 + x^110 - x^109*z0 + x^108*z0^2 - x^109 + x^108*y + x^107*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y - x^103*y*z0 + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 + x^99*y*z0^2 - x^100*y + x^100*z0 - x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y + x^93*y*z0 - x^93*z0^2 - x^94 - x^92*y*z0 - x^91*y*z0^2 - x^93 + x^92*y + x^91*y*z0 + x^91*z0^2 - x^92 + x^91*y + x^91*z0 - x^89*y*z0^2 + x^90*y + x^89*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^87*z0 - x^86*y*z0 - x^86*z0 + x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^85 - x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*y + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 - x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 + x^78 + x^77*y - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 + x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^71*z0^2 - x^72 - x^71*y + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 + x^69*z0^2 - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*z0 + x^66*z0^2 - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^66 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 - x^64*y - x^64 - x^63*y - x^63*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y - x^62*z0 - x^62 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y + x^56*y*z0 + x^56*z0^2 - x^56*y - x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^22*z0^2, + -x^115 - x^114*z0 + x^113*z0 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^109 - x^108*y + x^107*z0^2 + x^106*y*z0^2 - x^107*z0 + x^106*z0^2 - x^106*y + x^106*z0 + x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^101 + x^100*y - x^100*z0 - x^99*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y + x^97*y*z0 + x^97*z0^2 + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y - x^95*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 - x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^92*z0^2 - x^91*y*z0^2 + x^92*z0 + x^91*y*z0 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 - x^88*y*z0 + x^89 + x^88*y - x^88*z0 + x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 + x^86*y*z0 + x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^86 + x^85*y - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 + x^83 - x^81*y*z0 + x^81*z0^2 - x^82 + x^81*y - x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y + x^75*z0^2 + x^74*y*z0^2 - x^76 - x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*z0^2 + x^71 - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 - x^69*z0 - x^68*z0^2 - x^69 + x^68*z0 - x^67*y*z0 + x^67*y + x^67*z0 + x^65*y*z0^2 - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^64 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*z0 - x^61*y*z0 - x^60*y*z0^2 + x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^56*y - x^56*z0 + x^55*y*z0 + x^22*y, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^111 - x^110*y - x^110*z0 + x^110 + x^108*y*z0 + x^107*y*z0^2 + x^109 + x^108*y + x^107*y*z0 + x^107*z0^2 - x^108 + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y + x^105*y*z0 - x^105*z0^2 - x^106 - x^105*y - x^105*z0 + x^104*y*z0 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*z0^2 + x^101*y*z0^2 + x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^102 - x^100*y*z0 - x^100*z0 + x^99*y - x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^99 + x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*y*z0 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^87*y - x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^83*y*z0^2 - x^85 - x^84*z0 + x^83*y*z0 - x^82*y*z0^2 + x^84 + x^83*y + x^83*z0 - x^83 - x^82*y + x^81*z0^2 + x^82 + x^79*z0^2 + x^80 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^76*z0 + x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 - x^74*z0^2 + x^74*y - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*z0 - x^71*z0^2 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^67*y + x^65*y*z0^2 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^63*y*z0 + x^63*z0^2 + x^64 - x^63*y - x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*z0^2 + x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*z0 + x^60 - x^59*y - x^59 - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^57 - x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^22*y*z0, + -x^115 + x^113*z0^2 + x^112*z0^2 + x^112*y - x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 - x^110*z0 + x^108*y*z0^2 + x^109*y - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*z0 + x^107*y*z0 + x^107*y - x^107*z0 - x^106*z0^2 + x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^104*y*z0^2 - x^106 + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 + x^105 - x^104*z0 - x^104 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^100 - x^99*z0 + x^98*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^97*y - x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^94*y*z0^2 - x^95*y - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*z0^2 - x^90*y*z0^2 - x^91*z0 + x^90*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*z0 + x^88*z0^2 + x^88*z0 - x^87*y*z0 + x^86*y*z0^2 + x^88 + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 + x^85 - x^83*z0^2 - x^82*y*z0^2 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*z0 + x^80*y*z0^2 + x^82 + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y - x^80*z0 - x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 - x^76*y - x^75*y*z0 - x^74*y*z0^2 - x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^73*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^71*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y + x^68*z0^2 + x^67*y*z0^2 + x^68*y - x^67*y*z0 - x^67*z0^2 - x^68 - x^67*y - x^67*z0 + x^67 - x^66*y + x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^59*y - x^59*z0 - x^58*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^57 + x^56*y - x^56*z0 + x^22*y*z0^2, + x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 - x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y - x^103*y*z0^2 + x^105 + x^104*z0 + x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^100*y*z0 + x^100*z0^2 - x^100*y + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y + x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*y + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 - x^93*z0^2 + x^94 + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^90*z0 + x^89*y*z0 + x^90 + x^89*y + x^88*y*z0 + x^87*y*z0^2 - x^88*y + x^87*y*z0 + x^86*y*z0^2 + x^88 - x^86*z0^2 - x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 + x^83*y*z0 + x^82*y*z0^2 - x^83*y + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*y - x^79*y*z0 - x^78*y*z0^2 - x^78*z0^2 - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^76*y + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 + x^69*z0^2 + x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*z0 - x^67*y*z0 + x^66*y*z0^2 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^65*z0^2 - x^64*y*z0^2 + x^65*y + x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 + x^62*y - x^61*y*z0 + x^61*z0^2 + x^61*z0 - x^59*y*z0^2 + x^61 - x^60*z0 + x^59*z0^2 - x^60 + x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^58*y + x^58*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*z0 - x^56 + x^55*y + x^23, + -x^115 + x^114*z0 - x^113*z0^2 + x^113 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^111*z0 + x^111 - x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^110 + x^108*y*z0 - x^108*y + x^108*z0 - x^107*y*z0 - x^106*y*z0^2 - x^108 - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 + x^104*y*z0^2 - x^105*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*z0 - x^103*z0^2 - x^103*y + x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^99*y + x^98*z0^2 - x^98*z0 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y - x^90*y*z0^2 + x^91*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^90 - x^89*y + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^89 - x^87*y*z0 - x^88 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 - x^84 + x^83*y - x^83*z0 + x^82*y*z0 - x^81*y*z0^2 - x^83 - x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^76*y*z0^2 + x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^72*z0 - x^71*y*z0 - x^72 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*z0 - x^67 - x^66*z0 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^63*z0^2 + x^62*y*z0^2 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*z0 + x^58*y*z0^2 + x^60 - x^59*y - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y - x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 + x^56*z0^2 + x^57 + x^56 - x^55*y + x^23*z0, + -x^115 - x^114*z0 - x^113*z0 + x^112*z0^2 + x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^112 + x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^105*y*z0 + x^105*y + x^105*z0 + x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y + x^102 + x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y - x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*y + x^98*z0 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y + x^94*y*z0 - x^93*y*z0^2 - x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^92*z0^2 + x^93 - x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*z0 - x^89*y*z0 + x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^87*y*z0 - x^87*z0^2 - x^87*y - x^87*z0 - x^86*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*z0 + x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 + x^82*z0^2 + x^82*z0 + x^81*y*z0 + x^80*y*z0^2 - x^82 + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^81 - x^80*y + x^79*z0^2 - x^79 - x^78*y - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^76*z0 - x^75*y*z0 - x^76 + x^75*y - x^75*z0 + x^73*y*z0^2 - x^74*y - x^73*y*z0 + x^73*z0^2 - x^74 + x^73*y - x^73*z0 - x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^71*y + x^71*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^70 + x^69*y - x^68*y*z0 + x^68*z0^2 - x^69 - x^68*y + x^68*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^67*z0 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^64 - x^63*z0 + x^62*y*z0 - x^63 + x^62*y - x^61*y*z0 + x^62 + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*z0 - x^58*y*z0^2 + x^59*y - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y + x^57*y*z0 - x^58 + x^57*z0 + x^56*y*z0 - x^57 - x^56*y + x^55*y*z0 - x^55*y + x^23*z0^2, + x^114*z0 + x^113*z0^2 + x^114 - x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 + x^107*y*z0 - x^106*y*z0^2 + x^108 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^103 - x^102*y - x^101*y*z0 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^101 - x^100*z0 - x^98*y*z0^2 - x^100 - x^99*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*y - x^97*y*z0 + x^96*y*z0^2 - x^97*y + x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*z0^2 + x^96 - x^95*y - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^93*y*z0 - x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^93 + x^92*y - x^91*y*z0 - x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 + x^89 - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*y - x^83*z0 - x^82*z0^2 - x^83 - x^82*y - x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^79*y*z0 + x^79*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^75*y - x^75*z0 - x^73*y*z0^2 + x^75 - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*z0 - x^65*y*z0^2 + x^66*y + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^63*y*z0^2 - x^65 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 + x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0 + x^56*z0^2 - x^57 + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^23*y, + -x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 - x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y - x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^106*z0 + x^105*y*z0 - x^106 + x^105*y + x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 - x^103*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^101*y*z0 - x^101*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^101 - x^100*y - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 + x^98*z0^2 - x^98*y + x^98*z0 - x^97*z0^2 - x^98 + x^97*y + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^93*y*z0^2 + x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y + x^91*y*z0 + x^91*z0^2 - x^91*y + x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 + x^87*y*z0^2 - x^89 + x^86*y*z0^2 + x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^86*z0 - x^84*y*z0^2 + x^86 + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^85 - x^84*y - x^83*y*z0 - x^83*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^78*y - x^77*y*z0 + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*y - x^76 - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y - x^71*z0^2 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^69*z0^2 + x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^67*y*z0^2 + x^68*y - x^68*z0 + x^67*y*z0 + x^67*y + x^65*y*z0^2 + x^66*z0 + x^65*z0^2 + x^66 + x^65*y - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 - x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*y*z0 + x^61 - x^60*y + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^58 + x^57*z0 + x^56*z0^2 - x^57 + x^56*z0 + x^55*y*z0 + x^56 + x^23*y*z0, + x^115 + x^114*z0 - x^114 - x^112*z0^2 - x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*z0 + x^106*y*z0^2 - x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*z0 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*z0 - x^95*y*z0 + x^95*y - x^95*z0 + x^94*z0^2 - x^93*y*z0^2 - x^94*z0 - x^93*z0^2 - x^94 - x^93*y - x^92*y*z0 + x^92*y - x^91*y*z0 - x^91*z0^2 - x^92 - x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y + x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^89 + x^88*y - x^87*y*z0 - x^87*z0^2 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 - x^85*z0 + x^84*y*z0 - x^84*y - x^84*z0 + x^84 - x^83*z0 + x^82*y*z0 + x^81*y*z0^2 - x^83 + x^82*y - x^81*z0^2 + x^82 + x^81*z0 - x^80*y*z0 + x^81 - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^79*y + x^79*z0 + x^78*z0^2 - x^78*y - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 - x^74*y - x^73*y*z0 - x^73*z0^2 + x^74 + x^73*y - x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^70*y - x^69*z0^2 - x^70 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^66*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^66 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 + x^58*y + x^57*y*z0 + x^56*y*z0^2 - x^58 + x^57*y - x^57*z0 - x^56*z0^2 + x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^23*y*z0^2, + x^115 + x^114*z0 + x^113*z0 - x^112*z0^2 - x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^112 - x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y - x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y - x^106*y*z0 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^100*y + x^100*z0 - x^99*y*z0 - x^98*y*z0^2 - x^100 - x^99*y + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*y*z0 - x^94*y*z0^2 + x^96 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^93*z0 - x^92*y*z0 + x^91*y*z0^2 + x^93 - x^92*y + x^91*y*z0 + x^90*y*z0^2 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y - x^89*y*z0 + x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^86*y - x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 + x^85 - x^84*y - x^83*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^81*y*z0 - x^80*y*z0^2 + x^81*y + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*z0 + x^75*y*z0^2 - x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^72*z0 - x^71*z0^2 - x^72 + x^70*y*z0 + x^69*y*z0^2 + x^71 - x^70*y + x^69*y*z0 - x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 + x^67*z0^2 + x^68 - x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y - x^65*z0 - x^65 + x^64*y + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^63*y - x^63*z0 + x^62*z0^2 + x^62*y + x^62*z0 - x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 - x^58 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*z0 - x^56 + x^24, + -x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^113 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y + x^106*y*z0 + x^107 - x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y + x^102*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*z0^2 + x^101 - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^97*y*z0 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 + x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^94*y + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 + x^94 + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 - x^90*y*z0^2 - x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y + x^87*z0^2 + x^88 + x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 + x^86 - x^85*y + x^85*z0 + x^84*z0^2 - x^85 - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*z0 + x^79*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*z0^2 - x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*z0 + x^72*y*z0 - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 + x^70*y - x^70*z0 + x^69*z0^2 - x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^66*z0^2 + x^65*y*z0^2 - x^66*z0 + x^64*y*z0^2 + x^66 + x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*y*z0 - x^62*y - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^60*y - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*z0 - x^58*z0^2 + x^59 - x^58*y - x^58*z0 - x^57*z0^2 - x^57*y - x^57 - x^56*y + x^56*z0 + x^55*y*z0 - x^55*y + x^24*z0, + x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113 - x^112*y - x^112*z0 + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 - x^110*z0^2 - x^111 - x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y - x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 - x^106*z0^2 + x^107 + x^106*y + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y + x^102*y*z0 + x^102*z0^2 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y - x^100*y*z0 - x^100*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^98*y - x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^92*y*z0 + x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 + x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^88*y - x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*y + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^82 + x^81*y + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 + x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*z0 + x^75*y - x^75*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^73*z0^2 + x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*z0^2 - x^71 - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 + x^69*y + x^68*y*z0 - x^68*z0^2 - x^69 + x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 - x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^65*y*z0 + x^65*z0^2 - x^66 - x^65*y - x^65*z0 - x^64*z0^2 - x^64*y - x^63*z0^2 + x^63*y + x^63*z0 + x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 - x^61*y*z0 + x^62 + x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^59 + x^58*y + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*z0 + x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*y + x^56 + x^55*y + x^24*z0^2, + x^113*z0 - x^112*z0 - x^111*z0^2 - x^110*y*z0 - x^110*z0^2 + x^111 - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y + x^105*y*z0 - x^105*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^103*y - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*y - x^102*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^100*z0^2 + x^101 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^96 - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^93*z0 + x^92*y*z0 - x^93 + x^92*y - x^92*z0 - x^91*z0^2 - x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*y + x^87*y*z0 + x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 - x^86*z0^2 - x^87 + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^85 + x^83*z0^2 + x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^81*y - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 + x^78 - x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^76*y + x^76*z0 - x^76 + x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^71*y*z0^2 + x^73 + x^72*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y - x^70*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*z0^2 + x^70 + x^69*y - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^68 - x^67*y - x^67*z0 - x^65*y*z0^2 - x^67 + x^66*y + x^65*y*z0 - x^65*z0^2 - x^66 + x^65*y - x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*y*z0 - x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*y*z0 - x^61 - x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 + x^58*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^24*y, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 - x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*z0^2 + x^109*y - x^109*z0 - x^108*y*z0 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^107*z0 + x^105*y*z0^2 + x^107 - x^106*y - x^104*y*z0^2 + x^106 + x^105*z0 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^100*y*z0^2 + x^102 + x^101*y - x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 + x^92*z0^2 - x^93 - x^92*y - x^92*z0 + x^91*y*z0 + x^92 + x^91*y - x^90*y*z0 + x^90*z0^2 - x^91 + x^90*y - x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*y + x^88*y*z0 + x^87*y*z0^2 - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^87*z0 - x^86*z0^2 - x^87 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y - x^85*z0 - x^84*y*z0 + x^85 - x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y + x^79*y*z0^2 - x^80*y + x^79*y*z0 - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 + x^76*y*z0 - x^76*z0^2 + x^76*y - x^76*z0 + x^74*y*z0^2 - x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 + x^74 - x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^73 + x^72*y + x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*z0 + x^71 - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*z0 - x^66 - x^65*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^63*y*z0 + x^64 - x^63*y - x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*z0 + x^62 - x^61*z0 - x^59*y*z0^2 - x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^55*y*z0 - x^56 + x^24*y*z0, + -x^114*z0 - x^113*z0^2 - x^114 + x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 - x^109*y*z0 - x^108*y*z0^2 + x^109*y - x^107*y*z0^2 + x^109 + x^108*y - x^107*y*z0 - x^107*z0^2 - x^108 + x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 + x^105*y*z0 + x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*z0 - x^102*z0^2 - x^103 + x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^102 - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*y + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^99 - x^98*y - x^98*z0 - x^96*y*z0^2 - x^98 - x^97*y - x^96*z0^2 - x^96*y - x^96*z0 - x^94*y*z0^2 - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y - x^93*z0 + x^92*y*z0 - x^93 - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^88 - x^86*z0^2 + x^87 + x^86*z0 + x^85*y*z0 + x^86 + x^85*y - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^83*y*z0 - x^82*y*z0^2 - x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^77*y*z0 + x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 + x^76*y + x^75*y*z0 - x^75*z0^2 - x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*y*z0 - x^72*y*z0^2 + x^74 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^67*y*z0 + x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^65*y + x^64*y*z0 + x^63*y*z0^2 - x^65 - x^64*y + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^60 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 + x^57*y + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y + x^55*y*z0 + x^56 + x^24*y*z0^2, + x^115 - x^113*z0^2 - x^113*z0 - x^112*y - x^112*z0 + x^110*y*z0^2 - x^112 + x^110*y*z0 - x^110*z0^2 + x^111 + x^109*y*z0 + x^109*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 - x^106*y*z0^2 - x^108 - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 - x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^104 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^101*y*z0 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y + x^97*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*z0 - x^95*y*z0 - x^95*y + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 - x^91*y*z0 - x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^89*y*z0 + x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 - x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^86 + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 + x^82*y*z0^2 + x^84 - x^83*z0 + x^82*y*z0 + x^83 - x^82*y + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y - x^79*y*z0 + x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 - x^72*y*z0^2 - x^73*y - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*z0 + x^72 - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 + x^71 - x^70*y - x^69*y*z0 - x^69*z0^2 - x^70 + x^69*y + x^69*z0 - x^68*y*z0 + x^68*y + x^67*y*z0 + x^67*z0^2 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^64*y*z0^2 - x^66 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 + x^63*z0^2 - x^63*y + x^62*y*z0 + x^62*z0^2 - x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^59*y*z0^2 - x^61 - x^60*z0 + x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 + x^56*y*z0 - x^55*y*z0^2 + x^56*z0 - x^56 + x^25, + x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*z0 - x^105*y*z0 - x^104*y*z0^2 - x^106 + x^105*y + x^104*y*z0 + x^105 + x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 + x^102*y - x^101*y*z0 - x^100*y*z0^2 + x^102 - x^101*y - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^97*y*z0 + x^98 - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y - x^95*y*z0 - x^96 + x^95*y - x^94*y*z0 - x^95 - x^94*y + x^93*y*z0 - x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 - x^92*y*z0 + x^93 + x^91*z0^2 - x^92 + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^89*z0 + x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*z0^2 - x^88 + x^87*y + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^86*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0 - x^83*z0^2 - x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^81*z0^2 - x^80*y*z0^2 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*y*z0 - x^80 + x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 - x^74*y*z0^2 - x^75*y + x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^72*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^72 + x^71*z0 - x^70*y*z0 - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y - x^68*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^68 + x^67*z0 - x^66*z0^2 + x^66*y + x^64*y*z0^2 - x^66 - x^65*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^63*z0^2 - x^62*y*z0^2 + x^63*y - x^63*z0 - x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^62 + x^61*z0 + x^60*y*z0 + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*y*z0 - x^57*y*z0^2 + x^59 - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 + x^55*y + x^25*z0, + -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 - x^113 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^110*y*z0 + x^110*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^107 - x^106*y - x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y + x^104*y*z0 + x^105 + x^104*y + x^104*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 + x^100*y*z0 + x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*y + x^99*z0 - x^97*y*z0^2 - x^98*y + x^98*z0 - x^97*y*z0 - x^98 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^95*y - x^93*y*z0^2 + x^95 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 + x^93 - x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*z0^2 + x^87 + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y - x^84*y*z0 + x^84*z0^2 + x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^81 - x^80*z0 - x^79*y*z0 - x^78*y*z0^2 - x^80 - x^79*y + x^78*z0^2 - x^79 + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 + x^77 - x^76*y - x^76*z0 + x^75*z0^2 - x^76 + x^75*y - x^75*z0 + x^73*y*z0^2 - x^75 - x^74*y + x^73*y - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 - x^68*y*z0 - x^67*y*z0^2 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^67*z0 + x^66*z0^2 + x^67 + x^66*y + x^65*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0 + x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^63 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y + x^57*y*z0 + x^56*y*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^25*z0^2, + x^115 - x^113*z0^2 - x^114 - x^113*z0 - x^112*y - x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^111 - x^110*z0 + x^108*y*z0^2 - x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^108 - x^107*y + x^106*y*z0 + x^107 - x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y + x^103*y*z0 + x^104 + x^103*y + x^102*y*z0 - x^102*z0^2 + x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^97 - x^96*y - x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*y - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y - x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 - x^91*y*z0^2 + x^92*y + x^92*z0 + x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^90 + x^89*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^87*z0^2 + x^88 + x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^85*y + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*z0 - x^77*y*z0 - x^78 - x^77*y + x^76*y*z0 + x^77 - x^76*y - x^76*z0 - x^75*z0^2 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y - x^65*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*y*z0 + x^60 + x^58*y*z0 + x^58*z0^2 - x^59 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*z0 + x^56*z0^2 + x^56 - x^55*y + x^25*y, + x^115 + x^114*z0 + x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y - x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y - x^110*y*z0 + x^109*y*z0^2 + x^111 - x^110*y + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*y + x^106*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^103*z0 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^99*z0^2 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y + x^96*y*z0 - x^95*y*z0^2 + x^96*y + x^95*y*z0 - x^96 + x^95*y - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^89*y*z0^2 + x^91 + x^89*y*z0 + x^89*z0^2 + x^89*y + x^88*y*z0 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^84*y*z0 - x^83*y*z0^2 + x^85 + x^84*y + x^84*z0 + x^83*y*z0 + x^84 - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y + x^81*y*z0 + x^80*y*z0^2 + x^82 - x^80*z0^2 + x^81 + x^79*y*z0 - x^79*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y - x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 - x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^69*y - x^69*z0 - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^66*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^64 + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^63 + x^61*y*z0 + x^60*y*z0^2 + x^62 - x^61*z0 - x^59*y*z0^2 + x^59*y*z0 + x^58*y*z0^2 + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^57*y*z0 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^57 - x^56*y + x^25*y*z0, + -x^115 + x^113*z0^2 - x^114 + x^113*z0 - x^113 + x^112*y + x^112*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^106*y*z0^2 + x^108 - x^107*y + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 - x^105*y*z0 - x^104*y*z0^2 + x^106 + x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*z0 - x^103*y*z0 + x^102*y*z0^2 - x^104 + x^103*y + x^102*y*z0 + x^102*z0^2 + x^103 + x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^99*y*z0 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^99 - x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^97*y - x^96*y*z0 + x^95*y*z0^2 - x^97 - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 - x^93*y*z0^2 - x^95 - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 + x^93*y + x^92*y*z0 - x^92*z0^2 + x^92*y + x^91*y*z0 + x^92 + x^91*y - x^91*z0 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 - x^90 - x^89*y + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^85*y*z0^2 + x^86*y + x^86*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*y + x^84*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y + x^82*y + x^82*z0 + x^81*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 - x^80*y - x^79*z0^2 - x^80 - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^74*y*z0 - x^74*z0^2 + x^75 + x^74*z0 - x^73*y*z0 + x^74 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^67*y*z0 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^66*z0^2 - x^67 - x^66*y + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y + x^65*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^61*z0^2 + x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*z0^2 - x^61 + x^60*y - x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^57 - x^56*y + x^56*z0 + x^55*y*z0 - x^55*y + x^25*y*z0^2, + -x^113*z0 + x^113 - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^111 - x^110*y + x^109*z0^2 + x^110 - x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^104*z0^2 + x^105 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^103*z0 + x^102*y*z0 + x^101*y*z0^2 - x^103 - x^102*y + x^101*z0^2 - x^100*y*z0^2 + x^101*y + x^101*z0 - x^100*y*z0 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y + x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^96 - x^95*y - x^94*y*z0 + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^92*y*z0 + x^93 - x^92*y - x^92 + x^91*y - x^91*z0 + x^89*y*z0^2 + x^90*y + x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^86*z0^2 + x^87 + x^86*y - x^85*z0^2 - x^84*y*z0^2 + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^85 + x^84*y - x^84*z0 + x^83*z0^2 - x^82*y*z0^2 + x^83*y + x^82*z0^2 + x^81*y*z0^2 - x^83 + x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y - x^78*y*z0 + x^77*y*z0^2 - x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^62*y*z0 - x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*y*z0 + x^60*y*z0^2 + x^62 - x^61*z0 + x^60*z0^2 - x^60*y + x^59*y*z0 + x^59*z0^2 + x^59*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^57*y + x^57*z0 - x^57 - x^56*y - x^56*z0 - x^55*y + x^26, + -x^115 + x^114*z0 - x^113*z0^2 - x^113*z0 + x^112*z0^2 + x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^108 - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^107 - x^106*z0 + x^105*y*z0 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^103*y*z0 - x^103*z0^2 - x^104 + x^102*y*z0 + x^102*z0^2 - x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*y*z0 + x^94 - x^93*y - x^92*z0^2 + x^93 - x^92*y + x^92*z0 - x^91*y*z0 + x^90*y*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 - x^91 + x^90*y - x^89*y*z0 - x^88*y*z0^2 + x^90 - x^89*y + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y - x^86*y*z0 + x^86*z0^2 + x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 + x^82*y - x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^81 + x^80*z0 - x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^79 + x^77*y*z0 + x^76*y*z0^2 + x^77*y + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^75*z0 + x^73*y*z0^2 - x^75 + x^74*y - x^74*z0 - x^74 + x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^73 + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^69*z0^2 - x^68*y*z0^2 + x^69*y + x^68*y*z0 - x^67*y*z0^2 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^67*z0 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 + x^65*z0 + x^63*y*z0^2 + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y + x^62*y*z0 + x^62*z0^2 - x^63 + x^62*y - x^62*z0 - x^61*y*z0 + x^61*y - x^61*z0 - x^60*z0^2 + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*y + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^56*y*z0 - x^55*y*z0^2 - x^57 + x^56*z0 + x^26*z0, + -x^115 - x^114*z0 + x^113*z0 + x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^112 - x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y + x^108*y*z0 + x^107*y*z0^2 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^107 + x^106*y + x^106*z0 - x^105*y*z0 - x^104*y*z0^2 - x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 + x^101*y*z0^2 - x^102*y + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 + x^99*y*z0 + x^100 - x^99*y - x^99*z0 - x^98*y*z0 - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^96*y*z0 - x^96*z0^2 - x^97 - x^96*y + x^96*z0 - x^94*y*z0^2 - x^96 - x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 - x^89 - x^88*y + x^88*z0 + x^87*y*z0 - x^88 + x^87*y + x^87*z0 + x^87 - x^85*z0^2 - x^86 + x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 - x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*y - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y + x^80*y*z0 - x^80*z0^2 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 - x^78*y + x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^76*z0^2 + x^77 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^75*y + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^74*z0 + x^73*y*z0 - x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*y*z0 + x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 - x^69*y + x^69*z0 - x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^66*z0^2 + x^67 - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^64*y + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*y + x^62*y*z0 + x^62*z0^2 + x^62 + x^61*y + x^60*y*z0 - x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 - x^60 + x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^58*z0 - x^57*y*z0 + x^56*y*z0^2 - x^57*z0 + x^56*y*z0 + x^57 + x^56*z0 + x^55*y*z0 - x^55*y + x^26*z0^2, + -x^115 - x^114*z0 + x^114 + x^113*z0 - x^112*z0^2 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^111*y - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^105*y - x^104*z0^2 + x^105 - x^104*y - x^104*z0 + x^103*y*z0 + x^104 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^100*y - x^99*y*z0 + x^99*z0^2 - x^99*y - x^98*y*z0 + x^98*z0^2 - x^98*y + x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^98 - x^97*z0 - x^96*y*z0 - x^97 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 - x^92 + x^91*y - x^91*z0 + x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^78*y + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y + x^73*y*z0 + x^73*z0^2 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y - x^71*y*z0 + x^71*z0^2 - x^71*y + x^71*z0 - x^69*y*z0^2 - x^71 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^66*z0 - x^66 - x^65*y - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 - x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^59*y - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 - x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^58 - x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^55*y*z0 - x^56 - x^55*y + x^26*y, + x^115 - x^113*z0^2 - x^114 - x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 + x^109*y*z0^2 - x^110*y - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^109 + x^108*z0 - x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^104*y*z0 + x^104*z0^2 - x^105 + x^104*y - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*y*z0 + x^100 + x^98*y*z0 + x^97*y*z0^2 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 + x^95*z0^2 + x^94*y*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^94*y + x^93*y*z0 + x^92*y*z0^2 + x^93*y + x^93*z0 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 + x^90*y*z0^2 + x^92 - x^91*z0 - x^90*y*z0 + x^91 - x^90*y - x^90*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*z0^2 - x^89 - x^88*y + x^88*z0 + x^87*z0^2 - x^87*y - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^85 + x^84*y + x^84*z0 - x^82*y*z0^2 + x^84 + x^83*y - x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*z0^2 - x^82 + x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*y*z0 - x^79 + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 - x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 + x^74*z0 - x^73*y*z0 + x^72*y*z0^2 - x^74 - x^73*y + x^73*z0 + x^72*y*z0 + x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 - x^71*z0 + x^69*y*z0^2 + x^71 + x^70*y - x^69*y*z0 + x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^69 + x^68*y + x^68 - x^67*y - x^67*z0 + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 + x^62*y - x^61*y*z0 + x^60*y*z0^2 + x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y + x^56 + x^55*y + x^26*y*z0, + -x^113*z0 + x^112*z0^2 - x^113 + x^112*z0 + x^112 + x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^110 - x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^107*y*z0 + x^107*z0^2 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 + x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^103*y - x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^102*y + x^101*y*z0 + x^101*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^99*y*z0 + x^100 + x^99*y - x^99*z0 - x^98*z0^2 + x^99 + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^95*z0^2 - x^94*y*z0^2 + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^90*y + x^89*y*z0 - x^88*y*z0^2 + x^90 - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 + x^86*y*z0 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 - x^84*y*z0^2 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y - x^79*y*z0 + x^79*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*z0 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^71*z0 + x^70*z0^2 + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^69 + x^68*y + x^67*z0^2 + x^67*y + x^67*z0 - x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 - x^65*z0^2 + x^66 - x^65*y - x^64*y*z0 + x^64*z0^2 - x^64*y - x^63*z0^2 + x^62*y*z0^2 - x^62*y*z0 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 + x^60 + x^59*y + x^58*z0^2 - x^57*z0^2 + x^58 - x^57*y + x^56*z0^2 - x^56*z0 - x^55*y*z0 - x^55*y + x^26*y*z0^2, + -x^114 - x^112*z0^2 - x^112*z0 + x^111*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^104*z0 - x^103*y*z0 - x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 + x^103 + x^102*y + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*z0 + x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 - x^96 + x^95*y - x^94*y*z0 + x^94*y + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^92 + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^89*y*z0 - x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*z0 - x^85*y*z0 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y + x^83*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^83 - x^82*z0 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^78 - x^77*y - x^76*y*z0 + x^77 + x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y + x^71*z0 + x^69*y*z0^2 + x^71 + x^69*z0^2 - x^68*y*z0^2 + x^69*y - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 - x^65*y*z0 - x^65*z0^2 - x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^65 - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 - x^59*z0 + x^58*y*z0 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^58 - x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 + x^56 + x^27, + -x^115 + x^113*z0^2 + x^114 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 - x^108*y*z0 - x^107*y*z0^2 + x^108*y + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*z0 - x^105*y*z0^2 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^104*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*z0 - x^101*y*z0 - x^102 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 - x^100*y - x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*y*z0 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*y - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 - x^92*y*z0 - x^93 - x^92*y - x^92*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y + x^90*z0^2 - x^91 + x^90*y - x^90*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 + x^85*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^83*y*z0 - x^83*z0^2 - x^83*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^75*y*z0^2 + x^77 - x^76*y - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y + x^71*z0^2 + x^72 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^68*z0 + x^67*y*z0 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 - x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y - x^64*z0 - x^63*z0^2 + x^64 - x^63*y - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*z0 + x^61*y*z0 - x^62 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^60*y + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 - x^58*y*z0 - x^58*z0^2 - x^59 + x^58*y - x^58*z0 - x^57*y*z0 - x^58 - x^57*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56 + x^27*z0, + x^114*z0 + x^113*z0^2 + x^114 + x^112*z0^2 + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^109*y*z0 + x^108*y*z0^2 + x^110 - x^109*y - x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^108 - x^107*y - x^106*y*z0 - x^105*y*z0^2 + x^107 + x^106*y + x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^104*y*z0 + x^104*z0^2 - x^105 + x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 + x^101*z0^2 - x^100*y*z0^2 - x^101*y - x^101*z0 + x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y + x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^96*y*z0 + x^96*z0^2 + x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 + x^93*y*z0^2 - x^95 - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^91 + x^90*y + x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*y - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 - x^86*z0^2 - x^87 - x^86*y + x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^85*z0 + x^83*y*z0^2 + x^85 - x^84*y + x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^81*z0^2 - x^82 - x^81*y - x^80*y*z0 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 - x^79*y + x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^78 + x^77*y - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^75*z0 + x^74*y*z0 + x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 + x^71*y*z0 - x^70*y*z0^2 + x^72 - x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*y + x^69*y*z0 - x^69*z0^2 + x^68*y*z0 + x^69 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^61*y + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*y + x^58*y*z0 + x^58*z0^2 + x^58*y + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y + x^27*z0^2, + x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^113 - x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^111 + x^110*y - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 + x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^107 + x^106*y + x^105*y*z0 - x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^103*y*z0^2 + x^105 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^102 - x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^101 + x^99*z0^2 - x^100 - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 + x^98*y - x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y - x^95*y*z0^2 - x^96*y - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 + x^94*y*z0 - x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 + x^94 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^92*y - x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 + x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 - x^83*y*z0^2 + x^85 + x^84*y - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^82 + x^81*y - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 - x^80*z0 + x^79*z0^2 + x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^78*y + x^78*z0 - x^77*y*z0 + x^78 - x^77*y + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^76*y - x^76*z0 - x^75*z0^2 + x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^71 + x^70*y - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^68 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^64*y*z0 - x^64*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 - x^62*y*z0^2 + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^60 - x^59*y - x^59*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 + x^56*y*z0 - x^56*z0^2 - x^56*y + x^56*z0 + x^55*y + x^27*y, + x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 - x^113 - x^112*y + x^112*z0 + x^111*y*z0 - x^110*y*z0^2 + x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^110 + x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y - x^103*y - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*z0 - x^99*z0^2 - x^99*y + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*z0 + x^94*y*z0 + x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^92*y*z0 - x^91*y*z0^2 + x^93 + x^91*y*z0 - x^91*z0^2 + x^91*y - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 + x^90*z0 - x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 - x^87*y*z0 + x^88 + x^87*y - x^86*z0^2 + x^87 + x^86*y + x^86 - x^84*y*z0 + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y + x^76*y*z0 + x^75*y*z0^2 + x^77 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^74*y*z0 - x^75 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*z0 + x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^66*y*z0^2 - x^68 - x^67*y - x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^63*y*z0 + x^62*y*z0^2 + x^64 - x^63*y + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 - x^59*y*z0^2 + x^61 - x^60*z0 - x^58*y*z0^2 - x^60 + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^56*y - x^55*y*z0 - x^56 + x^55*y + x^27*y*z0, + -x^114*z0 - x^113*z0^2 - x^113*z0 + x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 - x^109*y*z0 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^108 + x^107*y - x^106*z0^2 + x^107 + x^106*y + x^106*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^103*y + x^103*z0 + x^102*y*z0 + x^101*y*z0^2 - x^103 + x^101*z0^2 + x^102 - x^101*y - x^100*y*z0 - x^100*z0^2 + x^100*y + x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^99 - x^98*y - x^98*z0 + x^97*z0^2 - x^98 - x^97*z0 + x^96*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 - x^92*y*z0 - x^91*y*z0^2 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y + x^89*z0^2 + x^88*y*z0^2 - x^88*y*z0 - x^88*z0 - x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^83*y*z0^2 - x^85 - x^84*y + x^84 - x^82*y*z0 + x^82*z0^2 - x^82*y - x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 + x^79*y - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y + x^76*z0^2 + x^77 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*y + x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*y + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*z0 + x^68*y*z0 + x^67*y*z0^2 - x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67 + x^66*y - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 - x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 + x^59 + x^58*y + x^58 + x^57*y + x^57*z0 + x^56*y*z0 - x^56*y + x^56*z0 - x^55*y*z0 - x^56 + x^27*y*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^108 - x^107*y - x^106*z0^2 + x^107 + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^104*y + x^104*z0 - x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 - x^103 - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 + x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^100*z0 + x^99*z0 + x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*z0 + x^94*y*z0 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 + x^93*y - x^93*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 + x^92*y - x^90*y*z0^2 + x^92 - x^91*z0 + x^90*y*z0 + x^89*y*z0^2 + x^91 - x^90*y + x^89*y*z0 + x^89*z0^2 + x^90 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y - x^87*y*z0 + x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^82*y*z0^2 + x^84 - x^83*y + x^83*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 + x^81*y*z0 + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 + x^79*y + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*z0^2 - x^72 - x^71*y + x^70*y*z0 + x^70*z0^2 - x^71 + x^70*y - x^69*y*z0 - x^69*z0^2 + x^70 - x^69*y + x^69 + x^67*z0^2 + x^66*y*z0^2 + x^67*y + x^67*z0 + x^66*z0^2 + x^66*y + x^66*z0 - x^64*y*z0^2 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*y*z0 - x^64 - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^63 - x^62*y - x^61*y*z0 + x^61*z0^2 + x^61*y + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^56 + x^28, + x^115 + x^114*z0 + x^114 - x^113*z0 + x^112*z0^2 + x^113 - x^112*y - x^111*y*z0 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 - x^109*z0^2 + x^110 + x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 - x^107*y*z0 + x^106*y*z0^2 + x^107*y + x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 - x^103*y*z0^2 + x^104*y - x^103*y*z0 + x^103*z0^2 - x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^101*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*z0 - x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^99 - x^98*z0 - x^96*y*z0^2 - x^98 - x^97*y + x^96*y*z0 - x^96*z0^2 - x^96*y + x^96*z0 + x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 - x^92*y*z0 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y + x^90*z0^2 + x^89*y*z0^2 + x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^87 - x^86*y - x^86*z0 - x^84*y*z0^2 - x^85*y + x^85*z0 - x^83*y*z0^2 - x^84*y - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^78 - x^77*z0 - x^76*y*z0 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 - x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y - x^71*y*z0 - x^70*y*z0^2 + x^72 - x^70*y*z0 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 - x^68*y*z0^2 - x^70 + x^69*z0 + x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^66*z0^2 - x^67 + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 - x^64 - x^63*z0 - x^62*y*z0 - x^63 + x^62*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 - x^59*y*z0 - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^58*z0 - x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 + x^56 + x^28*z0, + x^115 + x^114*z0 + x^114 + x^113*z0 - x^113 - x^112*y - x^111*y*z0 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^111 + x^110*y + x^110*z0 - x^110 + x^109*y - x^109*z0 - x^108*y*z0 + x^107*y*z0^2 - x^108*y - x^107*y*z0 - x^108 - x^107*z0 + x^106*z0^2 + x^106*y + x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^100*y*z0 + x^101 + x^100*y + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y + x^94*y*z0^2 + x^96 - x^95*z0 + x^94*y*z0 + x^95 + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^94 + x^93*y + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^92*y - x^90*y*z0^2 - x^92 - x^90*y*z0 - x^90*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^87 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y + x^84*z0 + x^82*y*z0^2 - x^84 + x^83 - x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^82 + x^81*y - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 + x^79*z0^2 + x^79*y + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 + x^77 - x^76*z0 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^73 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*z0 + x^70*z0^2 + x^70*y + x^69*y*z0 - x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^64*y*z0 - x^63*y*z0^2 - x^65 + x^63*y*z0 + x^63*z0^2 + x^64 - x^63*z0 - x^62*y*z0 + x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^62 + x^61 + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^57*y*z0^2 + x^59 - x^58*z0 - x^56*y*z0^2 - x^58 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^28*z0^2, + x^115 - x^114*z0 + x^113*z0^2 - x^113*z0 - x^113 - x^112*y + x^112*z0 + x^111*y*z0 - x^110*y*z0^2 + x^110*y*z0 - x^110*z0^2 + x^111 + x^110*y - x^109*y*z0 + x^109*z0 + x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*z0^2 - x^108 - x^107*y + x^106*z0^2 - x^105*y*z0^2 - x^106*y + x^106*z0 + x^105*z0^2 + x^106 - x^105*y + x^105*z0 - x^103*y*z0^2 + x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^104 + x^103*y - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*z0 + x^98*z0^2 - x^97*y*z0^2 + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 + x^91*y*z0^2 + x^93 - x^91*y*z0 + x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^88*y*z0^2 + x^90 - x^89*y - x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 + x^86 - x^85*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y + x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*z0 - x^82*y*z0 - x^81*y*z0 + x^81*z0^2 - x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^79*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*z0 - x^76*y*z0^2 + x^77*y - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 + x^74*y + x^73*z0^2 + x^74 + x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^71*y - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^67*y*z0 - x^67*z0^2 - x^68 + x^67*y + x^67*z0 + x^65*y*z0^2 - x^66*z0 + x^64*y*z0^2 + x^66 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 + x^63*z0^2 + x^62*y*z0^2 + x^63*z0 - x^62*y*z0 - x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*y*z0 - x^59*y*z0^2 - x^61 + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^59*y + x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*z0 + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 - x^55*y + x^28*y, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 + x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*z0 + x^109*y*z0 + x^108*y*z0^2 + x^110 - x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y + x^107*y*z0 - x^107*z0^2 + x^108 - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 + x^104*y*z0 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 + x^104 - x^103*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*y - x^102*z0 - x^101*y*z0 + x^100*y*z0 - x^99*y*z0^2 - x^101 + x^100*y - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^96*y*z0 - x^97 + x^96*y + x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y - x^89*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 + x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*y - x^85*y*z0 - x^85*z0^2 - x^86 - x^85*y - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^83*z0^2 + x^83*y + x^82*y*z0 + x^81*y*z0^2 - x^83 + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 - x^79*z0 - x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^74 - x^73*y + x^73 - x^72*z0 - x^71*z0^2 + x^71*y + x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 - x^67*y*z0 + x^66*y*z0^2 - x^67*y + x^67*z0 - x^65*y*z0^2 - x^66*y - x^65*z0^2 + x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 - x^62*y*z0^2 - x^63*z0 + x^61*y*z0^2 - x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^59*y*z0^2 + x^60*y + x^60*z0 + x^60 + x^59*y - x^58*y*z0 + x^58*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^58 + x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*y + x^55*y*z0 + x^56 - x^55*y + x^28*y*z0, + -x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 + x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^109*y*z0 - x^109*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^105*y - x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^104*z0 + x^103*y*z0 - x^102*y*z0^2 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^99*y - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*y - x^97*y*z0 + x^97*z0^2 + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^94 - x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^91 + x^90*y + x^89*z0^2 - x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^87 - x^85*y*z0 - x^84*y*z0^2 - x^85*y + x^85*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*z0 + x^83*y*z0 - x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^80*y*z0 - x^79*y*z0^2 - x^80*y - x^79*y*z0 - x^79*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*z0 + x^76*y*z0 - x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 - x^72*y - x^71*y*z0 + x^71*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^67*y - x^67*z0 + x^67 - x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^63 - x^62*y + x^62*z0 + x^61*z0^2 - x^60*y*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*z0 - x^57*y*z0^2 - x^59 - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 + x^55*y*z0^2 - x^57 + x^56*y - x^55*y*z0 - x^56 + x^28*y*z0^2, + x^115 + x^114*z0 - x^114 - x^113*z0 + x^112*z0^2 - x^112*y - x^111*y*z0 + x^111*z0^2 + x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y + x^105*z0^2 + x^106 - x^104*y*z0 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 + x^103*y*z0 - x^102*y*z0^2 - x^104 + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^102*y + x^102*z0 - x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^100*y - x^100*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^96*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*z0^2 - x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^92*y*z0 - x^92*z0^2 - x^93 - x^92*y - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^89 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 - x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^81*y - x^81*z0 - x^80*z0^2 + x^81 + x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^76*y*z0^2 + x^78 + x^77*y - x^76*z0^2 - x^76*z0 + x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*y + x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*z0 + x^65*y*z0^2 - x^67 - x^66*y + x^65*y*z0 + x^66 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*z0 + x^61*y*z0 + x^60*y*z0^2 + x^62 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 + x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*z0 + x^56*y + x^56*z0 + x^29, + -x^115 - x^114*z0 + x^114 + x^112*z0^2 + x^113 + x^112*y + x^111*y*z0 + x^112 - x^111*y - x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*z0^2 - x^109*y - x^109*z0 + x^107*y*z0^2 + x^109 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^106*y + x^105*y*z0 - x^105*z0^2 + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^102*y*z0^2 - x^103*y + x^102*z0^2 + x^103 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^101 + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^94*y*z0 + x^93*y*z0^2 + x^95 + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^94 + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^89*z0^2 - x^90 + x^89*y + x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^88 - x^87*y - x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*y + x^86*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*z0 - x^80*y*z0^2 - x^81*y - x^80*z0^2 - x^81 - x^80*y + x^80*z0 - x^79*z0^2 + x^80 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^77*y*z0 - x^77*z0^2 + x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^75 + x^74*y - x^74*z0 + x^73*y*z0 + x^74 - x^73*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y + x^71*y*z0 + x^71*z0^2 + x^71*y - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y - x^67*z0^2 + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^65*y*z0 - x^66 + x^65*y - x^65*z0 - x^65 + x^64*y + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^60 - x^59*y - x^59*z0 + x^58*z0^2 - x^57*y*z0^2 + x^57*z0^2 - x^58 - x^57*y + x^56*z0^2 - x^56*y - x^56*z0 + x^55*y*z0 + x^55*y + x^29*z0, + -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^110*y*z0 - x^110*y + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109 + x^108*z0 + x^106*y*z0^2 + x^108 + x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y + x^105*y*z0 + x^104*y*z0^2 + x^106 - x^105*y + x^104*z0^2 + x^103*y*z0^2 - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^103*y - x^103*z0 - x^102*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y + x^99*y*z0^2 + x^100*y - x^99*y*z0 + x^99*z0^2 - x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^98*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y - x^93*y*z0 - x^93*z0^2 + x^93*y - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*z0 + x^90*y*z0 - x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^86*y*z0 + x^86*z0^2 - x^87 - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*z0^2 + x^85 - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^83*y + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*y*z0 + x^76*y*z0^2 - x^78 - x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^72*y*z0 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*z0^2 + x^71*y + x^69*y*z0^2 + x^71 + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^58*y*z0^2 - x^60 - x^59*y - x^58*y*z0 - x^58*z0^2 - x^59 + x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 + x^55*y*z0 + x^56 + x^55*y + x^29*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^110*y - x^109*z0^2 - x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^104 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^101*z0^2 - x^102 + x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 + x^98*y*z0^2 + x^99*y - x^99*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 - x^96*y*z0 + x^97 - x^96*y + x^96*z0 - x^95*z0^2 + x^96 + x^94*y*z0 + x^94*y + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 + x^93 + x^92*z0 - x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 + x^89 - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 + x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^81*y - x^80*y*z0 + x^79*y*z0^2 - x^80*z0 - x^78*y*z0^2 - x^80 + x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 + x^78*y - x^77*y*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^76*z0 - x^76 - x^75*y + x^75*z0 + x^74*y*z0 - x^75 + x^74*z0 + x^73*y*z0 - x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^70*z0^2 + x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*y + x^69*z0 + x^68*z0^2 + x^68*y + x^67*y*z0 - x^66*y*z0^2 - x^67*z0 - x^65*y*z0^2 - x^67 - x^65*z0^2 - x^64*y*z0^2 + x^65*y + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 - x^65 + x^64*z0 + x^63*z0^2 - x^63*y + x^62*y*z0 + x^62*z0^2 + x^63 - x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^58*y*z0 - x^58*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 - x^57 + x^55*y*z0 + x^56 + x^29*y, + x^114*z0 + x^113*z0^2 + x^113 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*z0 + x^110*z0^2 - x^110*y + x^110*z0 + x^109*y + x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^109 - x^107*y*z0 + x^107*z0^2 + x^108 - x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 + x^104*y - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 - x^103 - x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^99*y + x^98*y*z0 + x^98*z0^2 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^98 + x^97*y + x^95*y*z0^2 + x^96*y - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^88*y*z0^2 + x^89*y - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*z0 + x^85*y*z0^2 + x^85*y*z0 - x^84*y*z0^2 - x^86 - x^85*y - x^84*y*z0 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 + x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^77*z0 + x^76*y*z0 + x^77 - x^76*y + x^75*z0^2 + x^76 - x^75*y - x^73*y*z0^2 + x^74*z0 - x^72*y*z0^2 - x^74 - x^73*y - x^71*y*z0^2 + x^73 + x^72*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 - x^70*z0^2 - x^71 - x^70*y + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*z0 - x^67*z0^2 + x^68 - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 + x^65*y - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^63*y*z0 - x^62*y*z0^2 + x^63*y + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y + x^61*y*z0 + x^60*y*z0^2 + x^62 + x^61*y - x^60*y*z0 - x^59*y*z0^2 - x^61 - x^60*y + x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^55*y*z0^2 - x^56*y + x^29*y*z0, + -x^115 - x^114*z0 - x^114 - x^113*z0 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 + x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^111 + x^110*y - x^109*y*z0 - x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^107*z0^2 - x^108 + x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 - x^103*y*z0 - x^103*z0^2 - x^104 + x^103*y + x^103*z0 - x^103 + x^102*z0 + x^101*y*z0 + x^102 + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^100*y - x^100*z0 - x^99*y*z0 - x^100 - x^99*y + x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 + x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^93 + x^92*z0 + x^90*z0^2 + x^91 - x^90*y + x^90*z0 - x^89*z0^2 + x^90 - x^89*y + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 + x^84*y*z0 - x^84*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y - x^83*z0 - x^82*y*z0 + x^81*y*z0^2 + x^83 - x^82*y + x^81*y*z0 - x^81*y - x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^77*y*z0^2 + x^79 + x^78*y + x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 + x^76*z0^2 + x^76*y + x^75*y*z0 - x^75*z0^2 + x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^74 + x^73*y + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^68*z0 + x^67*z0^2 - x^68 - x^67*y + x^67*z0 + x^66*z0^2 + x^67 - x^65*y*z0 + x^64*y*z0^2 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 - x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*z0^2 + x^59 - x^58*z0 + x^57*y*z0 + x^56*y*z0^2 - x^57*y - x^57*z0 - x^57 + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^29*y*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 - x^110*y*z0 - x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*y - x^108*z0 + x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*z0^2 + x^105 - x^103*y*z0 + x^103*z0^2 - x^102*z0^2 + x^103 - x^102*z0 - x^101*z0^2 - x^102 - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 - x^96*y*z0^2 - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^97 + x^96*y - x^96*z0 - x^94*y*z0^2 + x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^94 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^89*y - x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*z0^2 + x^85 - x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 - x^81*z0 + x^80*z0^2 + x^81 - x^80*y + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*z0 - x^77*z0^2 + x^78 - x^77*y + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*y + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y - x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^70 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y + x^67*y*z0 + x^66*y*z0^2 + x^68 - x^66*z0^2 - x^65*y*z0^2 - x^66*y + x^65*z0^2 + x^64*y*z0^2 + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 + x^61*y*z0 - x^60*y*z0^2 - x^62 + x^61*y - x^60*y*z0 - x^59*y*z0 + x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*y + x^57*y*z0 + x^58 - x^57*y - x^56*y*z0 + x^56*z0^2 + x^57 - x^56*y + x^55*y*z0 + x^56 + x^30, + -x^114 - x^113*z0 + x^112*z0^2 + x^112*z0 - x^111*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y - x^107*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 + x^102*y*z0^2 + x^104 + x^103*y + x^103 + x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 + x^101*z0 + x^100*z0^2 - x^101 + x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*y + x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^99 + x^98*y - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 - x^95*y*z0^2 + x^96*y + x^96*z0 - x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^92 - x^91*z0 - x^90*z0^2 + x^90*z0 - x^89*z0^2 + x^90 - x^89*y + x^88*y*z0 + x^89 + x^88*y + x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 - x^84*y*z0^2 - x^86 + x^85*z0 + x^83*y*z0^2 - x^85 - x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^84 + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 + x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^80 + x^79*y - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^76 + x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y + x^73*y*z0 - x^74 + x^73*y + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 + x^66*y*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^64*y + x^63*y*z0 - x^63*z0^2 + x^64 - x^63*z0 - x^61*y*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*z0 - x^60*z0^2 - x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^59*z0 + x^58*y*z0 - x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^55*y + x^30*z0, + -x^115 - x^114*z0 + x^114 - x^113*z0 + x^113 + x^112*y + x^111*y*z0 + x^111*z0^2 + x^112 - x^111*y + x^110*y*z0 + x^111 - x^110*y + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y + x^108*z0^2 - x^109 - x^108*y + x^108*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y - x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^102*y + x^101*y*z0 - x^100*y*z0^2 + x^102 + x^101*y - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 - x^98*y*z0^2 - x^100 - x^98*y*z0 + x^98*z0^2 - x^98*y + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^93*z0 - x^92*y*z0 + x^91*y*z0^2 + x^93 + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y - x^90*y*z0 + x^91 + x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*y - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^84*y*z0 + x^84*z0^2 - x^84*y + x^83*z0^2 - x^82*y*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y - x^80*y*z0 - x^80*z0^2 + x^81 + x^80*y - x^79*y*z0 + x^79*z0^2 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^74*y*z0^2 - x^76 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*z0 + x^71*y*z0 + x^70*y*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*z0^2 + x^67*y*z0^2 + x^68*y - x^68*z0 - x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^66 - x^64*y*z0 + x^63*y*z0^2 - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^63*y + x^63*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^61*y - x^60*z0^2 + x^61 + x^60*z0 + x^59*z0^2 + x^60 - x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58 + x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y + x^56 + x^30*z0^2, + x^115 + x^114*z0 + x^114 - x^113*z0 + x^113 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^111 - x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^106*y*z0 + x^105*y*z0^2 + x^105*y*z0 - x^104*y*z0^2 - x^106 + x^105*y + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^104 + x^103*y - x^103*z0 - x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^100*y*z0 - x^100*z0^2 + x^101 + x^99*y*z0 + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 + x^97*y*z0^2 + x^99 - x^96*y*z0^2 - x^98 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*y + x^96*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 + x^94 - x^93*y + x^92*y*z0 - x^92*z0^2 + x^93 + x^92*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^88*y*z0 - x^87*y*z0^2 - x^89 + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^84*y*z0 - x^83*y*z0^2 - x^84*y - x^83*y*z0 - x^83*z0^2 + x^84 - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^83 + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*y + x^77*z0^2 + x^76*y*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0 - x^74*z0^2 - x^75 + x^74*y + x^74*z0 - x^72*y*z0^2 + x^73*y - x^73*z0 - x^73 - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 - x^71 + x^70*y - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*y + x^69*z0 + x^67*y*z0^2 - x^69 - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*z0 + x^67 + x^65*z0^2 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^62*y*z0^2 + x^63*z0 - x^62*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*z0^2 + x^59 - x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y + x^55*y + x^30*y, + -x^115 - x^114*z0 - x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*y - x^112*z0 + x^111*y*z0 + x^112 + x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^110 - x^109*y + x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^106*z0^2 + x^107 - x^106*y + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 - x^104*y*z0 + x^105 - x^104*y + x^103*y*z0 + x^103*z0^2 - x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*z0^2 - x^99*y + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y + x^97*y*z0 + x^97*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^93 + x^92*y + x^92*z0 + x^90*y*z0^2 - x^91*y - x^90*z0^2 - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*y + x^87*z0 + x^87 + x^86*y + x^85*z0^2 - x^84*y*z0^2 + x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 - x^82*y*z0 - x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^80*y*z0^2 + x^81*y - x^81*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*z0 + x^79*y*z0 + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*y - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y + x^75*y*z0 - x^75*z0^2 + x^76 - x^75*y - x^75*z0 + x^74*y*z0 + x^73*y*z0^2 + x^74*z0 - x^73*y*z0 + x^73*y + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y + x^70*y*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^71 - x^70*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 + x^67*z0^2 + x^68 + x^67*z0 - x^67 + x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^64*y + x^64*z0 + x^62*y*z0^2 + x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*z0 - x^61*y*z0 + x^60*y*z0^2 + x^62 - x^61*y + x^60*y*z0 - x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^58*y - x^57*z0^2 - x^58 + x^57*y - x^57*z0 - x^56*y*z0 + x^56*y + x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^30*y*z0, + -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 + x^109*y*z0 - x^108*y*z0^2 - x^110 + x^107*y*z0^2 - x^108*y + x^107*y*z0 + x^108 + x^107*y + x^106*y*z0 + x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^106 - x^105*y - x^104*y*z0 + x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*z0 + x^100*y*z0 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 + x^98*z0^2 - x^97*y*z0^2 + x^97*z0^2 + x^97*y + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^96*y - x^96*z0 + x^95*y*z0 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^93*y*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^93*y - x^92*y*z0 - x^93 - x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*y - x^89*y*z0^2 - x^91 - x^90*y + x^89*y*z0 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y - x^85*y - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y + x^83*y*z0 - x^83*z0^2 + x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*y + x^80*y*z0 - x^80*z0^2 - x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^79*y - x^78*y*z0 + x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y - x^75*y*z0 + x^74*y*z0^2 + x^75*y + x^74*y*z0 + x^74*z0^2 - x^74*y + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 - x^71*y*z0^2 + x^73 + x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^71 + x^69*y*z0 + x^70 - x^69*y + x^68*y*z0 + x^67*y*z0^2 + x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^66 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 + x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y - x^62*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*z0 - x^60*y*z0 - x^61 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^59*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^57 - x^56*y + x^55*y*z0 - x^56 + x^30*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y - x^108*y*z0^2 + x^109*y - x^109*z0 - x^108*z0^2 + x^107*y*z0^2 + x^108*y - x^107*z0^2 + x^108 - x^107*y - x^107*z0 - x^106*y*z0 + x^107 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^105 - x^104*y + x^103*z0^2 + x^102*y*z0^2 - x^103*y + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^101*y*z0 + x^101*z0^2 + x^102 + x^100*y*z0 + x^100*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^99 - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*z0 + x^96*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^91*y*z0 + x^92 + x^91*y + x^89*y*z0^2 + x^91 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*z0 - x^85*y*z0^2 + x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*z0 + x^85 + x^84*y + x^84*z0 - x^83*y*z0 - x^82*y*z0^2 + x^83*y - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*z0 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0 + x^79*y + x^78*y*z0 - x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^77*y - x^76*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*y*z0 + x^76 + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^72*z0 + x^71*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^69*y + x^69*z0 - x^68*y*z0 + x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^67*z0 + x^66*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y - x^64*z0 + x^63*z0^2 + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 - x^61 - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^58*y*z0 - x^57*y*z0^2 - x^58*y - x^58*z0 + x^56*y*z0^2 + x^58 + x^57*y - x^56*y*z0 + x^56*z0^2 + x^57 + x^56*z0 + x^55*y*z0 - x^56 + x^31, + -x^115 + x^113*z0^2 + x^114 + x^112*z0^2 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^109*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 - x^107 + x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^106 - x^105*z0 - x^104*z0^2 + x^105 - x^104*z0 - x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 + x^102*y - x^101*z0^2 + x^102 - x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^100 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 + x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*z0^2 + x^90*y*z0 - x^89*y*z0^2 - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 - x^85*y*z0^2 - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^83*y*z0 - x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 + x^81*y*z0 - x^80*y*z0^2 + x^82 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*z0 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*z0^2 + x^79 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*z0 - x^75*z0^2 - x^76 + x^75*y - x^75*z0 - x^75 - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^74 + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^71*y*z0 + x^70*y*z0^2 - x^71*y + x^71*z0 - x^70*y*z0 + x^69*y*z0^2 - x^70*z0 - x^69*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^60*y*z0 + x^60*z0^2 - x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y - x^58*y*z0 - x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^58 + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 - x^56 + x^31*z0, + -x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^107*y*z0^2 + x^109 + x^107*z0^2 - x^106*y*z0^2 + x^107*y - x^107*z0 + x^106*y*z0 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 + x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 + x^103*y*z0 - x^102*y*z0^2 - x^103*y - x^103*z0 + x^102*z0^2 + x^103 - x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y - x^99*z0^2 - x^100 - x^99*z0 + x^98*z0^2 - x^98*y - x^97*y*z0 + x^97*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 - x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^96 - x^95*y + x^94*y*z0 + x^94*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^94 - x^93*y - x^93*z0 - x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^87*z0^2 - x^86*y*z0^2 - x^88 + x^86*y*z0 + x^86*z0^2 - x^87 + x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y + x^85*z0 - x^84*y*z0 + x^85 + x^84*y - x^83*y*z0 + x^82*y*z0^2 + x^84 + x^83*y - x^83*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^80*y*z0 - x^80*z0^2 - x^81 + x^80*y - x^79*y*z0 - x^78*y*z0^2 - x^79*y - x^79*z0 + x^78*z0^2 - x^77*y*z0^2 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y + x^74*y*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 + x^70*y*z0^2 - x^70*y*z0 - x^70*y - x^69*y*z0 + x^69*z0^2 + x^70 - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 - x^67*z0^2 - x^66*y*z0^2 - x^68 + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y - x^63*z0^2 + x^64 + x^63*y + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*y + x^61*z0 - x^60*y*z0 - x^59*y*z0^2 - x^60*y - x^60*z0 - x^59*z0^2 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 + x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 - x^56 + x^31*z0^2, + -x^115 - x^114*z0 + x^113*z0 + x^112*z0^2 + x^112*y + x^111*y*z0 - x^111*z0^2 + x^111*z0 - x^110*y*z0 - x^109*y*z0^2 - x^111 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^108*y*z0 - x^108*z0^2 + x^108*y + x^106*y*z0^2 - x^107*y + x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*z0^2 - x^102*z0 - x^101*y*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^98 - x^97*z0 + x^96*z0^2 + x^97 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*z0^2 + x^93*y*z0^2 - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^93 - x^92*z0 - x^90*y*z0^2 - x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 + x^91 - x^90*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^88*z0^2 + x^87*y*z0^2 - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 - x^85 + x^84*y - x^84*z0 - x^83*z0^2 + x^84 - x^83*y - x^83*z0 - x^82*y*z0 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y + x^81*z0 - x^80*y*z0 - x^79*y*z0^2 - x^81 + x^80*y - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77 - x^76*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 + x^71*y*z0^2 - x^73 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^71 + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*z0 + x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*y*z0 - x^68 + x^67*y - x^65*y*z0^2 - x^67 - x^66*y - x^65*z0^2 - x^65*y - x^65 - x^64*y - x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^62*z0 - x^61*z0^2 - x^62 + x^61*y - x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*y*z0 + x^60 + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y - x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y + x^56*y*z0 + x^56*z0^2 + x^57 - x^56*y - x^56 - x^55*y + x^31*y, + x^115 + x^114*z0 + x^114 + x^113*z0 + x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*y - x^110*y*z0 - x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 + x^110 - x^108*z0^2 - x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^108 + x^107*y - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 + x^102*z0^2 - x^103 - x^102*y - x^101*y*z0 - x^100*y*z0^2 + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*y*z0 + x^100 + x^99*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^93*y - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^87 + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 - x^82*y + x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^82 - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^76*y*z0^2 + x^78 + x^77*y - x^76*y - x^76*z0 - x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^74 + x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^73 + x^72*y - x^72*z0 + x^72 + x^71*y + x^71*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 + x^63 + x^62*y - x^62*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 + x^59*y*z0^2 + x^60*z0 + x^59*y*z0 + x^58*y*z0^2 + x^60 + x^59*y - x^58*z0^2 + x^57*y*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x^31*y*z0, + x^115 + x^114*z0 + x^114 - x^113*z0 + x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^111*y + x^110*y*z0 - x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^108*y*z0^2 + x^110 - x^109 - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^108 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^107 - x^106*y + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^103*y*z0 + x^104 + x^103*y - x^103*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y + x^101*y*z0 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^96*y*z0^2 - x^98 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*z0 + x^94*y*z0 + x^95 + x^94*y + x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^93*z0 + x^92*z0 + x^92 - x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^91 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^88*y + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y - x^86*y*z0 + x^85*y*z0 + x^85*z0^2 + x^86 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 + x^83*z0^2 - x^84 - x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^81*y*z0 - x^80*y*z0^2 + x^81*y + x^81*z0 + x^80*z0^2 - x^81 - x^79*y*z0 + x^79*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*z0^2 - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^77 + x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y + x^74*y*z0 - x^74*z0^2 - x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^73*z0 + x^72*y + x^71*y*z0 + x^72 + x^71*y - x^71*z0 - x^69*y*z0^2 + x^71 - x^70*z0 - x^69*y + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^61*y*z0^2 + x^63 - x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^59*y*z0 + x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^56*y - x^56*z0 + x^55*y*z0 - x^56 + x^31*y*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^110*y - x^109*y*z0 - x^110 - x^109*y - x^108*y*z0 - x^107*y*z0^2 + x^109 - x^108*z0 + x^107*z0^2 - x^107*y - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^106 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 - x^101*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*z0^2 - x^101 - x^99*z0^2 - x^100 - x^99*y + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*z0 - x^95*z0^2 - x^96 + x^95*z0 + x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^92*y*z0 + x^93 - x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^89 + x^88*y - x^87*y*z0 + x^87*z0^2 + x^86*y*z0 + x^85*y*z0^2 - x^87 - x^86*y + x^85*y*z0 + x^84*y*z0^2 + x^86 - x^85*y - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^84 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 - x^82 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^78 - x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*y*z0 - x^74*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 - x^74 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^70*y*z0 - x^71 + x^70*y - x^70*z0 + x^69*y*z0 + x^70 - x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^69 - x^68*y - x^67*z0^2 - x^68 + x^67*y - x^67*z0 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^64 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^61*y + x^61*z0 - x^60*y*z0 + x^59*y*z0^2 - x^61 + x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^56*y*z0 - x^57 - x^55*y*z0 - x^56 + x^55*y + x^32, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*y + x^110*z0 + x^109*z0^2 - x^110 - x^109*y - x^109*z0 - x^107*y*z0^2 - x^109 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^107*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*z0 + x^104*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 - x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^101*y - x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^101 + x^100*z0 - x^99*z0^2 - x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y - x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 - x^94*y*z0 + x^95 - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 - x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^89*y - x^89*z0 - x^88*y*z0 - x^87*y*z0^2 - x^89 + x^88*z0 + x^87*y*z0 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^86*z0 - x^85*z0^2 - x^86 + x^84*y*z0 + x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*z0 - x^82*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 - x^80 - x^79*y - x^78*y*z0 - x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y - x^76*y*z0 - x^75*y*z0^2 - x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 + x^74 - x^73*y - x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 + x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 - x^68 + x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*z0 - x^65*y*z0 + x^65*y + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^64 - x^63*z0 - x^61*y*z0^2 - x^63 + x^62*y + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^58*y*z0 + x^59 - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^57 - x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^32*z0, + -x^115 + x^113*z0^2 - x^114 + x^112*y + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 - x^108*y*z0^2 + x^110 - x^109*y + x^108*y*z0 + x^109 - x^108*z0 - x^107*z0 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*z0 - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^101*y - x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^101 + x^99*y*z0 + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*z0^2 + x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*y*z0 + x^95*y*z0^2 + x^97 + x^96*z0 + x^95*y*z0 + x^94*y*z0^2 + x^95*z0 + x^94*y*z0 + x^95 - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^89*y*z0^2 + x^91 - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*z0^2 - x^89 - x^88*y + x^88*z0 - x^87*y*z0 - x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 + x^83*y*z0 - x^83*y - x^81*y*z0^2 - x^83 + x^82*y + x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y - x^79 + x^78*y - x^77*y*z0 - x^76*y*z0^2 + x^78 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^76*y + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*z0 + x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^69*y + x^69*z0 - x^68*y*z0 - x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*y - x^65*z0 + x^63*y*z0^2 - x^64*y - x^63*y*z0 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^59*z0^2 + x^60 + x^59*z0 + x^58*y*z0 - x^57*y*z0^2 + x^59 + x^57*y*z0 - x^57*z0^2 + x^58 - x^56*z0^2 - x^55*y*z0^2 - x^55*y + x^32*z0^2, + -x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 - x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^105*y*z0 + x^105*z0^2 - x^105*y + x^105*z0 + x^104*z0^2 + x^105 - x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^102*y*z0 + x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^102 + x^101*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*y - x^98*z0^2 + x^97*y*z0^2 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^96*y - x^96*z0 + x^95*y*z0 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^93 + x^92*z0 + x^91*z0^2 - x^92 - x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y - x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*z0 - x^87*z0^2 + x^87*y - x^86*y*z0 + x^86*z0^2 - x^86*y + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*z0^2 - x^83*y + x^83*z0 + x^81*y*z0^2 - x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^81*y - x^81*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^78*y*z0 + x^77*y*z0^2 + x^78*y - x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^75*y*z0^2 - x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^76 + x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 - x^72 + x^70*y*z0 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y - x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*y*z0 - x^66 - x^65*y + x^65*z0 + x^64*y*z0 - x^63*y*z0^2 + x^65 + x^62*y*z0^2 + x^64 - x^63*z0 + x^62*y*z0 + x^61*y*z0^2 - x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y + x^60*z0^2 + x^61 + x^60*y - x^60*z0 - x^58*y*z0^2 - x^59*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y - x^57 + x^56*y + x^55*y*z0 - x^56 + x^55*y + x^32*y, + x^114*z0 + x^113*z0^2 - x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*z0 + x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^109 - x^107*y*z0 - x^107*z0^2 + x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*z0 + x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y + x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^99*y*z0^2 - x^100*z0 + x^99*y*z0 + x^99*z0 - x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^96*y*z0^2 + x^98 - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*y + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*z0 - x^90*y*z0^2 + x^92 + x^91*z0 + x^91 - x^90*y + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^89*y - x^89*z0 - x^89 + x^88*y + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^81 - x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*y - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^73*y + x^73*z0 + x^71*y*z0^2 - x^73 + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*y - x^69*y*z0 + x^69*z0^2 + x^70 + x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^69 + x^68*y - x^68*z0 - x^66*y*z0^2 + x^67*y - x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 + x^65*z0^2 - x^66 + x^65*y + x^64*y*z0 - x^64*z0^2 + x^64*y + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^63 + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 + x^57*y*z0^2 + x^59 + x^58*z0 + x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56 - x^55*y + x^32*y*z0, + x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^110*y - x^109*y*z0 - x^108*y*z0^2 + x^109*y + x^108*y*z0 - x^107*y*z0^2 - x^109 - x^108*z0 + x^107*z0^2 + x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^100*z0 - x^99*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^98*z0^2 - x^98*y + x^97*y*z0 - x^97*z0 + x^97 - x^96*y + x^96*z0 + x^95*z0^2 + x^96 + x^95*y + x^95*z0 + x^94*y*z0 - x^95 + x^94*y + x^94*z0 + x^94 + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 + x^91*y*z0 + x^91*z0^2 - x^92 - x^91*z0 - x^90*z0^2 - x^89*y*z0^2 + x^90*z0 - x^89*z0^2 - x^90 - x^89*z0 + x^88*z0^2 - x^88*y - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*z0 + x^85*y*z0 - x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 - x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y + x^82*y*z0 - x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*y + x^77*y*z0 + x^77*z0^2 - x^78 + x^77*y + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^74*y*z0 - x^74*z0^2 + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 - x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 + x^69*y*z0^2 - x^71 - x^70*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 + x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y - x^65*z0 - x^64*y*z0 + x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^62*y - x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^60*y + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 + x^56*y*z0^2 - x^58 + x^57*y + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 - x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^32*y*z0^2, + x^115 - x^113*z0^2 + x^113*z0 + x^113 - x^112*y + x^112*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*z0 - x^110*y*z0 + x^111 - x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^109 - x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0 + x^105*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 - x^105 - x^104*y + x^104*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 + x^103 - x^102*y + x^102*z0 - x^101*z0^2 + x^102 + x^101*y + x^100*y*z0 + x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^99 - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 + x^97*y + x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y + x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^94 + x^92*y*z0 + x^92*z0^2 - x^93 + x^92*y + x^92*z0 + x^91*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0 + x^89*z0^2 - x^90 + x^89*y - x^88*z0^2 + x^89 + x^88*y + x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^88 + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^84*y*z0 - x^85 + x^84*y + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*z0 + x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*z0 - x^78*z0^2 + x^78*y - x^78*z0 - x^77*z0^2 + x^78 - x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^75*y - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^72 + x^71*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 + x^70 - x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*z0 + x^66*z0^2 - x^67 + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*z0^2 + x^62*z0^2 - x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 - x^58*y*z0^2 - x^59*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*z0^2 - x^58 - x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^56 + x^55*y + x^33, + -x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^107*y*z0^2 + x^109 + x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^105*y*z0^2 - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*z0 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*z0^2 + x^101*y*z0^2 + x^102*z0 + x^100*y*z0^2 - x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 - x^97*y*z0^2 + x^99 - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 - x^97*y - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 - x^97 + x^96*y + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^94 - x^93*y + x^92*z0 + x^91*y*z0 - x^91*y + x^91*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y - x^89*y*z0 - x^89*z0^2 - x^90 + x^88*y - x^88*z0 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^86*y*z0 + x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 - x^83*y*z0^2 + x^85 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^82*y*z0 + x^82*y + x^82*z0 + x^80*y*z0^2 - x^82 - x^80*y*z0 + x^80*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y - x^76*z0 - x^75*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^73*y*z0^2 + x^75 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 + x^71*y*z0^2 - x^73 - x^72*y - x^71*y*z0 + x^70*y*z0^2 - x^70*y*z0 + x^69*y*z0^2 + x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*z0 - x^68*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^67*y - x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^66 + x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y - x^64*z0 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*z0 + x^60*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^33*z0, + -x^115 + x^113*z0^2 + x^114 + x^112*z0^2 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^111*y - x^111*z0 - x^109*y*z0^2 + x^109*y*z0 + x^109*z0^2 - x^110 - x^109*z0 + x^108*y*z0 + x^109 + x^108*z0 - x^106*y*z0^2 - x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*y + x^104*z0 + x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*y*z0 + x^100*y - x^100*z0 + x^99*y*z0 + x^98*y*z0^2 + x^100 - x^99*z0 - x^98*y*z0 - x^98*y - x^97*y*z0 - x^97*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^96*y + x^95*y*z0 - x^95*z0^2 + x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 - x^94 + x^93*y + x^92*y*z0 - x^93 - x^92*z0 - x^91*y*z0 - x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 - x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 - x^90 + x^89*y + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^86*y*z0 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^84*y*z0^2 - x^86 + x^85*z0 - x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^82*y + x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^82 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*z0 + x^79*z0^2 - x^79*y + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^78*y - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y + x^76*y*z0 + x^77 + x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^74*y - x^74*z0 - x^72*y*z0^2 - x^73*y - x^73*z0 - x^71*y*z0^2 - x^72*y - x^71*y*z0 - x^70*y*z0^2 - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y - x^68*y*z0 + x^68*z0^2 - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^65*y*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^64*y - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y + x^61*y*z0 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^61 - x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 + x^58*y*z0 + x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^57*y - x^56*y*z0 - x^56*z0^2 - x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x^33*z0^2, + x^115 + x^114*z0 - x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y - x^111*y*z0 + x^111*z0^2 - x^112 + x^111*y - x^110*y*z0 + x^109*y*z0^2 - x^110*y + x^110*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*y - x^109*z0 - x^109 - x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^107*y - x^106*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 + x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 - x^103*z0^2 - x^104 - x^103*y + x^102*y*z0 + x^101*y*z0^2 - x^102*y - x^102*z0 - x^100*y*z0^2 - x^101*y - x^101*z0 - x^100*y*z0 - x^101 + x^100*y + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 - x^97*y*z0^2 - x^98*z0 - x^97*y*z0 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 - x^94*y*z0^2 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^89*y*z0 - x^88*y*z0^2 - x^90 - x^89*z0 - x^88*y*z0 - x^87*y*z0^2 - x^89 - x^88*z0 + x^87*y*z0 - x^88 - x^86*y*z0 + x^86*y - x^86*z0 + x^85*y*z0 + x^86 + x^83*y*z0^2 + x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^83 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^79 + x^78*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*z0 + x^75*z0^2 - x^74*y*z0^2 - x^75*y - x^74*y*z0 + x^74*z0^2 - x^75 + x^74*y + x^74*z0 - x^74 + x^73*z0 - x^72*z0^2 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^71*y + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y - x^68*y*z0 - x^67*y*z0^2 + x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^67 - x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 + x^64*y - x^63*y*z0 - x^64 - x^63*y - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^60*z0^2 - x^59*y*z0^2 + x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^58*y + x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 - x^56*y*z0 - x^56*z0^2 - x^57 - x^55*y + x^33*y, + -x^115 + x^113*z0^2 - x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^110*y*z0^2 + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^110 + x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^109 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^107 - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^104*z0 - x^103*y*z0 + x^102*y*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 + x^100*y*z0 + x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*z0^2 + x^99 - x^98*y + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^97 - x^96*y - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 + x^92*y + x^91*y*z0 + x^91*z0^2 - x^91*y - x^91*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^89*z0^2 - x^90 - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*z0^2 - x^88 + x^87*y - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*y + x^82*y*z0 - x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 + x^81*y - x^79*y*z0^2 + x^81 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^77*y - x^77*z0 - x^77 + x^76*y + x^75*z0^2 + x^74*y*z0^2 - x^75*z0 + x^73*y*z0^2 - x^75 - x^74*y - x^73*y*z0 - x^73*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^71*y - x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^70*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*z0^2 - x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^59*y + x^59*z0 + x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^55*y*z0 - x^55*y + x^33*y*z0, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^109*y + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^106*z0 + x^105*y*z0 - x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^103*y*z0 + x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*y - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^101 + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 + x^99 + x^98*y + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*z0 + x^92*y*z0^2 + x^94 + x^93*y + x^92*y*z0 - x^92*z0^2 + x^92*z0 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*y*z0 + x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^90 + x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^89 + x^88*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 - x^86*z0^2 - x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^85*z0 + x^84*z0^2 + x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y + x^83*z0 - x^81*y*z0^2 + x^82*y + x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 - x^80*y + x^80*z0 + x^78*y*z0^2 + x^79*z0 + x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*y + x^76*y*z0^2 - x^78 - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^73*z0^2 - x^74 + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^71*y*z0 - x^71*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 - x^68*y*z0^2 + x^69*y + x^69*z0 - x^68*z0^2 + x^67*y*z0^2 - x^68*y - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 + x^66*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^63*y*z0 - x^63*z0^2 - x^64 - x^63*y + x^61*y*z0^2 + x^63 + x^62*y - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y - x^60*z0^2 + x^59*y*z0^2 + x^59*y*z0 + x^59*z0^2 + x^60 + x^59*y - x^58*y*z0 + x^57*y*z0^2 + x^59 - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^55*y*z0^2 - x^56*z0 - x^56 + x^33*y*z0^2, + x^115 + x^114*z0 + x^114 + x^113 - x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^111*y - x^111*z0 - x^110*z0^2 + x^111 - x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*y + x^105*z0^2 + x^104*y*z0^2 - x^105 - x^104*y - x^103*y*z0 - x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*z0^2 + x^101*y + x^100*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y + x^93*y*z0 + x^93*z0^2 - x^94 - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*z0^2 - x^90 - x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^88 + x^87*y - x^85*y*z0^2 + x^86*y + x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^83*y*z0^2 - x^84*z0 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^79*y + x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y + x^78*z0 - x^76*y*z0^2 - x^78 + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 - x^74*y*z0 - x^74*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*z0 + x^71*y*z0 + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*z0 - x^68*y*z0 - x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*z0 - x^60*y*z0^2 - x^62 + x^61*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*z0 - x^58*y*z0 + x^58*y + x^58*z0 + x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 + x^56*y*z0 - x^55*y*z0^2 + x^57 - x^56*y + x^55*y*z0 - x^56 - x^55*y + x^34, + x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^112*z0^2 - x^112*y - x^112*z0 + x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 - x^109*y*z0^2 - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^110 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*y - x^104*y*z0^2 - x^106 - x^105*z0 + x^104*y*z0 - x^104*z0^2 + x^104*y + x^104*z0 - x^103*y*z0 + x^104 - x^103*y + x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*y + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^101*y + x^101*z0 + x^101 - x^99*y*z0 - x^99*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y - x^95*y*z0 - x^95*z0^2 + x^96 - x^95*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*z0 + x^92*y*z0 + x^93 + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^88*y*z0^2 + x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*y*z0 + x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*z0^2 - x^85*y - x^85*z0 + x^84*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^80*y*z0^2 + x^80*y*z0 - x^79*y*z0^2 - x^81 - x^79*z0^2 - x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^75*z0 - x^74*z0^2 + x^75 - x^74*y + x^73*z0^2 - x^74 - x^73*y - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^68*y + x^68*z0 + x^67*z0^2 - x^66*y*z0^2 - x^67*y + x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*y + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^63*y + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^57*y*z0 - x^57*z0^2 - x^58 + x^57*y + x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*z0 + x^56 - x^55*y + x^34*z0, + x^114*z0 + x^113*z0^2 - x^114 - x^112*z0^2 + x^113 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 - x^108*y*z0^2 - x^110 - x^109*y + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^107*y*z0 + x^107*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 + x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^99*z0^2 - x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 + x^99 + x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 - x^96*y + x^95*y*z0 + x^94*y*z0^2 + x^96 - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^95 - x^94*z0 - x^93*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^91*y*z0 + x^90*y*z0^2 + x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y - x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^89*z0 + x^87*y*z0^2 + x^89 + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 - x^87*y + x^87*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y + x^85*y*z0 + x^84*y*z0^2 + x^85*y + x^84*y*z0 - x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*y + x^80*z0^2 - x^79*y*z0^2 + x^80*y + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 + x^79 - x^78*y - x^77*y*z0 + x^77*z0^2 - x^78 + x^77*y - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*z0 + x^75*y*z0 - x^76 - x^75*z0 - x^74*z0^2 - x^75 - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 - x^72 + x^71*y + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^70 + x^69*y + x^67*y*z0^2 + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 - x^68 + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^65*z0 + x^64*y*z0 + x^63*y*z0^2 - x^63*y*z0 - x^62*y*z0^2 + x^63*y - x^63*z0 + x^62*z0^2 - x^63 + x^61*z0^2 - x^62 + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 - x^58*y*z0 - x^57*y*z0^2 + x^58*y + x^58*z0 - x^57*z0^2 + x^57*y + x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^55*y*z0 + x^56 - x^55*y + x^34*z0^2, + x^115 + x^114*z0 - x^114 - x^113*z0 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 - x^108*y*z0^2 - x^110 - x^108*y*z0 + x^108*z0^2 - x^108*y + x^108*z0 - x^107*z0^2 + x^108 - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 - x^105*y*z0 - x^105*z0^2 - x^105*y + x^104*y*z0 + x^104*z0^2 + x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^104 - x^103*y - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^101*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*y + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^98 - x^97*y + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y + x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 - x^93*y*z0^2 - x^95 - x^93*z0^2 + x^94 - x^93*y - x^93*z0 + x^92*y*z0 - x^93 - x^92*y - x^91*z0^2 + x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 - x^86*y*z0^2 + x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^82*y*z0 - x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*y + x^78*y*z0 + x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 + x^76 - x^75*y + x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^68*y*z0^2 - x^70 + x^68*y*z0 - x^68*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^65*y*z0^2 + x^67 - x^66*z0 - x^65*y*z0 - x^66 + x^64*y*z0 - x^64*z0^2 - x^64*z0 + x^63*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*z0^2 - x^63 + x^62*y + x^62*z0 + x^61*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^60*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^58*y + x^58*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 + x^55*y*z0^2 + x^57 + x^55*y*z0 + x^34*y, + x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 - x^113 - x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^110*y + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*y - x^107*y*z0^2 + x^109 - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*y*z0 - x^102*y*z0^2 - x^104 + x^103*y - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 - x^102 - x^100*y*z0 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*z0^2 + x^99*y - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^96*y + x^96*z0 - x^95*z0^2 + x^96 - x^95*y - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y + x^89*y*z0 - x^88*y*z0^2 + x^89*y - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^88*y + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*z0 + x^83*y*z0 - x^82*y*z0^2 - x^84 - x^82*z0^2 - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^81*y + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^75 - x^74*z0 - x^72*y*z0^2 + x^74 + x^73*z0 - x^71*y*z0^2 + x^72*y - x^71*z0^2 - x^72 + x^70*z0^2 - x^69*y*z0^2 + x^69*y*z0 + x^69*y - x^69*z0 - x^69 + x^68*y - x^68*z0 - x^67*y*z0 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^64*y*z0^2 - x^66 + x^65*y + x^64*z0^2 + x^63*y*z0^2 + x^64*y - x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*z0^2 - x^63 - x^62*y - x^62*z0 + x^61*y*z0 + x^62 + x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^59*y + x^58*z0^2 + x^57*y*z0^2 + x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^57*z0 + x^56*y*z0 + x^57 + x^56*y + x^56*z0 + x^56 + x^34*y*z0, + x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 - x^113 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^109*y - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 + x^106*z0^2 + x^105*y*z0^2 + x^106*y - x^106*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^104*y*z0 - x^105 - x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 + x^103 + x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^102 - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 + x^100*y + x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*y*z0 - x^94*y*z0^2 + x^95*y + x^95*z0 - x^95 + x^94 - x^93*y - x^93*z0 + x^92*z0^2 - x^91*y*z0^2 + x^91*y*z0 + x^90*y*z0^2 - x^91*y + x^90*y*z0 + x^90*z0^2 - x^91 + x^90*y + x^89*y*z0 + x^89*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 + x^88 - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*z0 + x^80*z0^2 - x^81 - x^80*z0 + x^79*z0^2 - x^80 - x^79*y + x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y + x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 - x^75*y*z0^2 - x^76*y + x^75*y*z0 + x^74*y*z0^2 + x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^75 + x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*z0^2 + x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^71*y + x^71*z0 - x^70*z0^2 + x^71 - x^70*y + x^70*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*z0 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^63 + x^61*z0^2 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^61 + x^60*y + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*z0 - x^57*y*z0 - x^58 + x^57*y + x^56*y*z0 - x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 + x^55*y + x^34*y*z0^2, + x^115 + x^114*z0 - x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^106*z0^2 + x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^104*y*z0 + x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 + x^101*y - x^100*y*z0 - x^101 - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 + x^99*y + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^98*y + x^98*z0 + x^96*y*z0^2 + x^98 + x^95*y*z0^2 + x^97 - x^95*y*z0 - x^95*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^92*y + x^91*z0^2 + x^90*y*z0^2 + x^91*y - x^91*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 - x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^89 + x^88*y + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 - x^87*z0 - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^84 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 - x^82 - x^81*y + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^79*y*z0 - x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*z0 + x^75*y*z0^2 + x^76*y + x^76*z0 - x^75*y*z0 - x^74*y*z0^2 - x^76 - x^74*y*z0 + x^75 + x^74*y - x^73*y*z0 + x^73*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*z0^2 + x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 - x^68*z0^2 + x^67*y*z0^2 - x^68*y - x^67*z0^2 - x^66*y*z0^2 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 - x^63*y*z0^2 - x^64*z0 - x^63*y*z0 - x^64 + x^62*z0^2 - x^63 + x^62*y - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^60*y - x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*z0 + x^56*y*z0^2 + x^58 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y + x^56*z0 + x^55*y*z0 + x^56 + x^35, + -x^115 - x^114*z0 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0 + x^110*y*z0 - x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^109*z0 + x^108*y*z0 + x^109 + x^108*z0 + x^107*y*z0 - x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y - x^100*y*z0^2 + x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^98*y*z0^2 - x^100 - x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*z0 + x^96*y*z0 - x^95*y*z0^2 + x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*z0^2 - x^92*y*z0^2 + x^93*z0 - x^92*z0^2 - x^92*y + x^92*z0 + x^91*y*z0 + x^90*y*z0^2 + x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y - x^90*z0 + x^88*y*z0^2 + x^90 - x^89*y - x^88*y*z0 + x^87*y*z0^2 - x^89 + x^88*y + x^87*y + x^87*z0 - x^86*y*z0 - x^87 + x^86*y - x^85*y*z0 + x^84*y*z0^2 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y - x^80*z0^2 - x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*z0 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^76*y*z0 - x^75*y*z0^2 + x^77 + x^76*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^73*y*z0 - x^73*z0^2 + x^74 - x^73*z0 - x^72*z0^2 + x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^69*y - x^68*y*z0 - x^69 + x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 + x^64*y*z0 + x^64*z0^2 + x^65 - x^64*y + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63 - x^62*z0 + x^61*y - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 - x^59*y*z0 + x^60 - x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 - x^55*y*z0^2 + x^56*y - x^55*y*z0 - x^56 + x^55*y + x^35*z0, + -x^115 - x^114*z0 + x^114 - x^112*z0^2 + x^112*y + x^111*y*z0 + x^112 - x^111*y + x^109*y*z0^2 - x^111 - x^109*y + x^109 + x^108*y + x^108*z0 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^106*y + x^106*z0 + x^104*y*z0^2 - x^105*y + x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*z0 - x^101*y*z0 - x^100*y*z0^2 + x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^98*y*z0^2 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^96*y*z0 + x^96*y - x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^92*y*z0 + x^91*y*z0^2 - x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y - x^90*y*z0 + x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*z0 - x^88*z0^2 - x^89 - x^88*z0 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^87 - x^86*y + x^86*z0 + x^85*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 - x^83*y*z0^2 - x^85 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 + x^82*z0^2 + x^82*y + x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*z0 - x^78*y*z0 - x^78*z0 - x^77*z0^2 - x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*z0^2 + x^76 + x^75*y + x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^71*y - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^69*y + x^68*y*z0 - x^68*z0^2 + x^69 + x^68*y - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^64*y - x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^60*y + x^60*z0 + x^58*y*z0^2 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 - x^56 + x^55*y + x^35*z0^2, + -x^115 + x^113*z0^2 + x^114 + x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^112 - x^111*y - x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^110 + x^109*y - x^109*z0 + x^108*z0^2 + x^109 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*y - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^101*y + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^100 + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 + x^98*y - x^98*z0 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 + x^95*y*z0^2 - x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 + x^93*y*z0^2 - x^95 + x^94*y - x^93*z0^2 + x^93*y + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 - x^91*z0^2 + x^92 + x^91*y + x^91*z0 + x^89*y*z0^2 + x^91 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^88*y - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 + x^85*y + x^84*y*z0 + x^84*z0^2 + x^85 - x^84*z0 - x^83*z0^2 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^78*y + x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*z0 - x^76*y*z0 + x^75*y*z0^2 + x^76*y - x^75*y*z0 - x^76 + x^75*y + x^74*y*z0 + x^74*z0^2 + x^75 - x^74*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 - x^72*y*z0 + x^73 - x^71*y*z0 + x^72 - x^71*z0 - x^70*y*z0 + x^70*y - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y + x^69*z0 - x^67*y*z0^2 - x^69 + x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^62*y*z0 + x^62*z0^2 - x^63 - x^62*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 - x^58*y*z0 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 - x^57*y*z0 + x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 - x^56 + x^35*y, + x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y - x^110*y*z0 - x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 + x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 + x^105*y*z0 - x^106 - x^105*y - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 + x^95*y*z0^2 - x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^88*y*z0^2 + x^90 + x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*z0^2 + x^84 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^82*y - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^78*y*z0^2 + x^79*y - x^79*z0 + x^78*y*z0 - x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77*z0 - x^75*y*z0^2 - x^77 - x^75*y*z0 + x^74*y*z0^2 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*z0 - x^73 - x^72*y - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^70*y*z0 + x^71 - x^69*z0^2 + x^68*y*z0 - x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 + x^66*y*z0^2 - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*y - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^62*z0 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^59*y - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^58 + x^57*y + x^57*z0 + x^56*y*z0 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y + x^35*y*z0, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*z0^2 + x^110 - x^109*y + x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*y + x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 - x^104*y*z0 - x^105 + x^104*y - x^104*z0 + x^102*y*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 + x^101*y - x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^97*y*z0 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 + x^96*y - x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^93 - x^92*z0 - x^91*y*z0 - x^90*y*z0^2 + x^92 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y + x^89*z0^2 + x^90 + x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^88*y + x^87*y*z0 + x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 - x^80*z0^2 + x^81 - x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^75*y*z0 + x^75*z0^2 + x^76 + x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^75 - x^74*z0 + x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^71*y*z0 - x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^71 + x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 + x^68*z0^2 - x^69 + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^65*y*z0 + x^65*z0^2 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^56 + x^35*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^113 - x^112*y - x^112*z0 + x^111*y*z0 - x^110*y*z0^2 + x^112 - x^111*y + x^110*y*z0 - x^111 + x^110*y - x^110*z0 + x^109*y*z0 + x^110 - x^109*y + x^109 + x^108*y + x^107*y*z0 - x^107*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^105*y*z0 + x^105*z0^2 + x^106 + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 + x^104*y + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^102*z0^2 + x^102*y + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^98 - x^97*z0 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*z0^2 - x^96 + x^95*y + x^95*z0 + x^94*z0^2 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y + x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y + x^91*y*z0 - x^91*z0^2 + x^92 + x^91*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 + x^90 + x^89*y - x^89*z0 + x^87*y*z0^2 - x^89 + x^88*y + x^87*z0^2 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*y + x^83*y*z0 - x^83*z0^2 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^83 - x^82*y - x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 - x^79*y*z0^2 + x^81 - x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*z0^2 - x^79 - x^78*y + x^77*z0^2 - x^78 - x^77*z0 - x^76*y*z0 - x^77 - x^76*z0 - x^75*z0^2 + x^75*y + x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^71*z0^2 + x^70*y*z0^2 + x^70*y*z0 + x^70*z0^2 + x^71 + x^70*y - x^70*z0 + x^69*y*z0 + x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^67*y + x^67*z0 - x^67 + x^66*z0 + x^65*y*z0 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*y + x^59*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*y + x^57*z0 - x^56*y*z0 + x^55*y*z0^2 + x^57 + x^56*z0 + x^56 + x^36, + x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 - x^111*z0^2 - x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^109*z0 + x^108*y*z0 + x^107*y*z0^2 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^106*y*z0 + x^107 - x^106*y + x^106*z0 - x^105*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 - x^103*y*z0 + x^103*y - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 + x^101*z0 - x^100*y*z0 + x^101 + x^100*y + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^95*z0 + x^94*z0^2 - x^94*y - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^93 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^91 - x^89*y*z0 - x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^85*y*z0^2 - x^86*y + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*z0 + x^81*y*z0 - x^80*y*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 - x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^78*y*z0^2 - x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^74*y*z0 - x^74*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^72*y + x^72*z0 - x^71*y*z0 + x^72 + x^71*y - x^70*y*z0 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^70 - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 - x^64*y - x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y - x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y - x^60*y*z0^2 - x^61*y + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*y + x^59*y*z0 - x^59*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^56*y - x^55*y*z0 + x^56 + x^36*z0, + -x^115 + x^113*z0^2 + x^113*z0 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^109*y*z0 - x^109*z0^2 + x^110 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^108*y + x^108*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*z0 + x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^106 + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*y + x^99*y*z0 - x^99*z0^2 - x^100 - x^99*y - x^99*z0 - x^98*z0^2 - x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 - x^90*y*z0 - x^91 + x^90*z0 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^88*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^86*y*z0 - x^85*y*z0^2 - x^86*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*z0 - x^84*y*z0 - x^83*y*z0^2 + x^85 + x^84*y + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 - x^83*y - x^83*z0 + x^82*y*z0 + x^83 - x^82*y - x^81*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^80*y + x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^79 - x^78*y - x^76*y*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^74*y*z0^2 - x^76 + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^73 + x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*y + x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*y - x^69*y*z0 + x^68*y*z0^2 + x^69*y + x^69*z0 + x^67*y*z0^2 + x^69 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^66*z0^2 - x^67 + x^66*y + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 + x^63*z0 - x^62*z0^2 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^61*y + x^61*z0 + x^60*y*z0 + x^59*y*z0^2 + x^60*y + x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^58*y - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^56*z0^2 + x^55*y*z0^2 - x^57 - x^55*y*z0 + x^56 - x^55*y + x^36*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0 + x^107*y*z0^2 - x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^106*z0 + x^104*y*z0^2 + x^106 + x^105*z0 + x^104*z0^2 - x^104*y - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^101*y + x^101*z0 + x^100*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^99 + x^98*y - x^98*z0 - x^97*z0^2 + x^96*z0^2 + x^97 + x^96*z0 - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0 + x^93*z0^2 + x^93*y - x^91*y*z0^2 - x^93 - x^91*y*z0 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 - x^88*z0^2 + x^89 - x^88*y + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*z0 + x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y + x^81*z0^2 - x^82 + x^81*y + x^81*z0 - x^80*z0^2 + x^81 - x^80*y - x^80*z0 + x^79*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y + x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^72*y + x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y - x^70*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^69*y + x^69*z0 - x^68*z0^2 + x^67*y*z0^2 + x^68*z0 + x^67*y*z0 + x^66*y*z0^2 + x^67*y + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*z0^2 - x^65*y - x^64*y*z0 - x^64*z0^2 - x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^63 + x^62 - x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*z0 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y + x^55*y*z0 + x^56 + x^55*y + x^36*y, + x^115 - x^113*z0^2 + x^114 + x^113*z0 + x^113 - x^112*y + x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^110*y - x^109*z0^2 - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*z0 + x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 - x^104 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y - x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*y - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^97 - x^96*z0 + x^93*y*z0^2 - x^95 - x^93*y*z0 + x^94 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^91*y*z0 - x^90*y*z0^2 + x^91*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^89*y*z0 + x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^88 + x^86*z0^2 + x^85*y*z0^2 + x^86*y + x^85*y*z0 - x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^82*y*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 - x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 + x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 - x^78*y*z0^2 - x^80 - x^79*y + x^77*y*z0^2 + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*z0 - x^73*y*z0^2 - x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 - x^73*y + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^72 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*y + x^70*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*z0 + x^65*y*z0^2 - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y + x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^59*y*z0 - x^58*y*z0^2 - x^60 - x^59*z0 - x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*z0^2 + x^57*y + x^57*z0 + x^56*z0^2 - x^57 - x^56*y + x^56*z0 + x^56 - x^55*y + x^36*y*z0, + -x^115 + x^114*z0 - x^113*z0^2 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y + x^108*y*z0^2 - x^110 + x^109*y - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 + x^107*z0^2 - x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^105*y*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 + x^104*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^102 - x^101*y + x^100*z0^2 - x^99*y*z0^2 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^99*y - x^98*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*z0 + x^95*z0^2 + x^96 + x^95*y - x^95*z0 + x^95 - x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*y*z0 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y + x^84*z0 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*z0^2 + x^81*y + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^77 + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^75*y + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y - x^70*y*z0^2 + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y + x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y - x^63*y*z0^2 - x^65 - x^64*y - x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^62*z0 - x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*y*z0 + x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y - x^58*z0 - x^56*y*z0^2 + x^58 + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y + x^36*y*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^110*y*z0 - x^109*y*z0^2 + x^110*y - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*z0 + x^108*z0^2 - x^109 - x^108*z0 + x^107*y*z0 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^107 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^105*y + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*z0 - x^103*y*z0 - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^103 - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 - x^102 + x^101*y + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 + x^95*y*z0 - x^94*y*z0^2 + x^94*y*z0 - x^94*z0^2 - x^95 + x^94*y - x^93*z0^2 - x^93*y - x^93*z0 - x^91*y*z0^2 + x^92*y - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^88*y - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^86*y*z0 + x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^86 + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 + x^84*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 - x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*y - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*z0 + x^79*y*z0^2 + x^80*y - x^80*z0 - x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 + x^77*y*z0 + x^78 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 + x^74*y*z0 - x^73*y*z0^2 + x^75 - x^74*y - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^73*z0 + x^72*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^68*y*z0 - x^68*z0^2 + x^69 + x^68*y - x^68*z0 - x^67*z0^2 + x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^65*y*z0 + x^64*y*z0^2 - x^66 - x^65*z0 + x^64*z0^2 + x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y - x^63*z0 - x^62*y*z0 - x^61*y*z0^2 - x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 - x^59*y*z0 - x^60 + x^59*y + x^59*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y - x^57*y*z0 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^55*y*z0^2 + x^57 - x^56*y - x^55*y*z0 + x^55*y + x^37, + -x^115 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^112*y - x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^104*z0 + x^103*y + x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^101*y*z0 - x^101*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*z0^2 + x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^95*z0^2 - x^94*y*z0^2 + x^95*z0 + x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*y - x^93*z0 - x^91*y*z0^2 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^85*y*z0 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*z0^2 - x^84*y + x^82*y*z0^2 - x^84 + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0 + x^80*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*y + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 + x^73*y*z0 - x^72*y*z0^2 - x^74 - x^73*y + x^73*z0 + x^73 + x^72*y - x^72*z0 + x^71*z0^2 - x^72 + x^71*y - x^69*y*z0^2 - x^70*y + x^69*y*z0 + x^69*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^69 + x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^66 - x^65*y - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y + x^63*y*z0 + x^63*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 + x^58*y*z0^2 + x^60 + x^59*z0 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^56*y*z0^2 + x^58 - x^57*z0 - x^55*y*z0^2 - x^56*y - x^56*z0 - x^56 - x^55*y + x^37*z0, + x^112*z0^2 - x^112*z0 - x^111*z0^2 - x^112 + x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 + x^107*y*z0 + x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^107 - x^106*y - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 + x^105 - x^104*y + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 - x^102*y - x^102*z0 - x^102 + x^101*y - x^101*z0 - x^99*y*z0^2 - x^101 - x^100*y + x^99*y*z0 - x^100 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^96*y*z0^2 - x^97*y - x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^92*y + x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*z0^2 + x^90 - x^89*y + x^88*z0^2 - x^89 - x^88*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^87 + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^82*y - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^80*y + x^79*z0^2 - x^78*y*z0^2 - x^80 - x^78*y*z0 - x^77*y*z0^2 + x^78*y + x^78*z0 - x^77*y*z0 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 - x^75*y*z0^2 + x^76*y + x^75*y*z0 - x^76 + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*z0^2 - x^72*z0^2 - x^73 - x^72*y + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 - x^70 + x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*z0^2 + x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^65*z0 - x^64*y*z0 - x^63*y*z0^2 - x^64*y - x^63*z0^2 + x^64 - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^63 - x^62*y - x^62*z0 + x^60*y*z0^2 + x^61*y + x^61*z0 - x^60*z0^2 - x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*y*z0 - x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^57*z0 - x^57 + x^56*y - x^55*y*z0 + x^55*y + x^37*z0^2, + -x^115 - x^114*z0 + x^114 + x^113*z0 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^112 - x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 + x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 + x^107*y*z0 + x^107*z0^2 - x^108 - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y + x^106*z0 - x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 + x^103*z0^2 + x^103*y - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^102*y - x^102*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*z0 - x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^100 + x^99*z0 - x^98*y*z0 - x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^97*y - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^92*y*z0 + x^92*y + x^92*z0 + x^91*z0^2 + x^92 + x^91*z0 + x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^88*y*z0 - x^87*y*z0^2 - x^87*y*z0 - x^87*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0 + x^84*y*z0^2 - x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*z0 + x^83*y*z0 - x^84 - x^82*z0^2 + x^83 + x^82*y - x^82*z0 + x^80*y*z0^2 + x^82 - x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y + x^74*y*z0 + x^74*y - x^74*z0 + x^73*y*z0 - x^74 - x^73*y - x^73*z0 + x^71*y*z0^2 + x^72*z0 + x^71*y*z0 + x^72 - x^71*y + x^71*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y + x^69*z0^2 + x^68*y*z0^2 - x^69*y + x^68*y*z0 - x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*y*z0 - x^66*y*z0^2 - x^67*y + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^61*y*z0 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^59*y*z0^2 + x^61 + x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^57*y + x^57*z0 - x^55*y*z0^2 - x^57 + x^56*y + x^37*y, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 + x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 - x^110*y*z0 - x^109*y*z0^2 - x^111 - x^110*y - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y - x^108*y*z0 + x^108*y + x^106*y*z0^2 - x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^106 + x^105*y - x^104*z0^2 - x^104*z0 + x^103*y*z0 + x^102*y*z0^2 - x^104 + x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^100 - x^99*y - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*y*z0 + x^98 - x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 - x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^89*y*z0 - x^88*y*z0^2 - x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*y + x^87*y*z0 + x^86*y*z0^2 - x^87*z0 + x^86*y*z0 + x^85*y*z0^2 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^84*y*z0 - x^83*y*z0^2 + x^84*z0 + x^84 + x^83*z0 - x^82*z0^2 - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^81*y - x^81*z0 + x^80*y*z0 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^78*y*z0 - x^78*y - x^78*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*z0 + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*y - x^75*z0^2 + x^74*y*z0^2 + x^76 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 - x^74*y + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*y - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y - x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 + x^71 - x^70*y + x^70*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^68*z0^2 + x^67*y*z0^2 + x^68*y - x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 + x^67*z0 - x^67 - x^66*y - x^66*z0 + x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^64*z0 - x^62*y*z0^2 - x^64 + x^63*z0 - x^62*z0^2 + x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 + x^58*y*z0^2 + x^59*y - x^59*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 - x^57*z0 + x^56*y*z0 - x^57 - x^56*y + x^56*z0 - x^56 + x^37*y*z0, + x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*y + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y + x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*y*z0 + x^104 - x^103*y + x^102*y*z0 + x^101*y*z0^2 + x^102*y - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 - x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^98*y + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*z0^2 - x^97 - x^96*y + x^96 + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^93*z0^2 - x^93*y + x^92*y*z0 - x^91*y*z0^2 + x^93 - x^92*y + x^92*z0 - x^91*z0^2 - x^92 - x^91*y - x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*y + x^90 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*z0^2 + x^87 + x^86*z0 - x^85*y*z0 + x^86 + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^84 - x^83*z0 - x^82*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 + x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*z0 + x^76*y*z0 + x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*z0 - x^74*z0^2 + x^75 + x^74*y - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y - x^73*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^71 - x^70*y - x^69*z0^2 + x^70 + x^68*y*z0 - x^67*y*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^68 - x^67*z0 - x^66*z0^2 + x^66*z0 + x^64*y*z0^2 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*y - x^63*y*z0 - x^63*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^62*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 - x^59*y*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y + x^58*z0 + x^57*z0^2 + x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^37*y*z0^2, + -x^115 - x^114*z0 + x^114 + x^112*z0^2 - x^113 + x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^112 - x^111*y + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^109*y*z0 - x^108*y*z0^2 + x^110 + x^109*y + x^108*z0^2 - x^107*y*z0^2 - x^108*y + x^108*z0 + x^107*z0^2 + x^108 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 + x^103*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*z0^2 + x^101*y*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*z0^2 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^100 - x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 - x^96*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 - x^93*y*z0 - x^93*z0^2 - x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^93 + x^92*y + x^92*z0 - x^90*y*z0^2 - x^91*y + x^90*y*z0 - x^90*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 - x^89*y - x^88*y*z0 + x^87*y*z0^2 - x^89 + x^88*y + x^87*y*z0 + x^86*y*z0^2 + x^88 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y - x^83*y*z0 + x^83*y + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^82 - x^81*y - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 + x^79*y - x^79 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 - x^76 - x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*z0 - x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 + x^72*y*z0 + x^73 - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*z0^2 + x^69*y*z0^2 + x^70*y - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*z0 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^66 - x^65*y - x^65*z0 - x^64*y*z0 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 + x^64 + x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^59*y*z0 - x^59*y + x^59*z0 - x^57*y*z0^2 - x^59 + x^58*y - x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^57*y + x^56*y*z0 - x^56*z0^2 + x^57 + x^56*z0 - x^56 - x^55*y + x^38, + -x^114*z0 - x^113*z0^2 + x^114 - x^112*z0^2 - x^113 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^108*y*z0^2 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 + x^107*y*z0 + x^108 + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^103*y*z0 - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^101*y + x^101 + x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*y - x^99*z0 - x^98*z0^2 - x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y + x^96*z0 - x^95*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^92*z0^2 + x^91*y*z0^2 - x^92*y - x^91*y*z0 - x^91*z0^2 + x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^91 - x^90*y + x^90*z0 - x^89*y - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 - x^87*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 - x^87 - x^86*y - x^86*z0 + x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^84*y - x^84*z0 - x^82*y*z0 - x^82*z0^2 - x^83 + x^82*y - x^81*y*z0 + x^81*z0^2 - x^82 + x^81*y - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*y + x^77*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*z0^2 - x^77 - x^76*y + x^76*z0 - x^75*z0 + x^74*z0^2 + x^73*y*z0^2 + x^74*z0 - x^73*y*z0 + x^74 + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^71 - x^69*y*z0 + x^70 + x^69*y - x^69*z0 + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^68*y + x^68*z0 + x^67*y*z0 - x^66*y*z0^2 - x^67*z0 - x^66*z0^2 - x^67 - x^66*y + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^64*y*z0 + x^64*z0^2 + x^65 + x^64*y + x^64*z0 - x^62*y*z0^2 + x^63*y - x^63 - x^62*y + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 - x^61 + x^59*y*z0 + x^60 + x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 - x^57*y*z0 - x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^55*y*z0 - x^56 + x^38*z0, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^106*y*z0^2 + x^108 + x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y + x^105*z0^2 - x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^104*y - x^104*z0 - x^102*y*z0^2 + x^104 + x^103*y - x^102*y*z0 + x^102*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^101 + x^100*y + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*z0^2 + x^97*y + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*z0^2 - x^94*y*z0 + x^94*z0^2 + x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^93*z0 + x^92*y*z0 + x^91*y*z0^2 + x^92*y - x^92*z0 - x^90*y*z0^2 + x^91*y + x^91*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 + x^88*z0 + x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^85*y*z0^2 + x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y + x^82*z0^2 - x^83 - x^81*y*z0 - x^81*z0^2 - x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 - x^78*y*z0^2 + x^79*z0 - x^78*z0^2 - x^79 - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 - x^76*y - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^71*y*z0 + x^71*z0^2 - x^72 - x^71*y + x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 - x^66*y + x^65*y*z0 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^60*y - x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^57*y + x^57*z0 - x^56*z0^2 + x^57 - x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^38*z0^2, + x^114*z0 + x^113*z0^2 + x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*z0 - x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^104*y*z0 - x^103*y*z0^2 - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*z0 + x^100*y*z0 + x^101 + x^100*z0 + x^99*y*z0 + x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 + x^98*z0^2 - x^99 + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 + x^95*y*z0 + x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 + x^95 + x^94*y + x^94*z0 + x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 - x^92*y - x^91*y*z0 - x^91*z0^2 - x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^91 - x^90*y + x^89*z0^2 - x^90 - x^89*y - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^88*y - x^88*z0 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y + x^84*y*z0^2 + x^85*y - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^83*y*z0 - x^82*y*z0^2 + x^83*z0 - x^82*y*z0 - x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^80 - x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*y + x^74*z0 + x^73*y*z0 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^73 - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 + x^71*y - x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*z0^2 + x^70 + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^69 + x^68*y - x^68*z0 - x^67*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 - x^63*y*z0^2 - x^65 + x^64*y - x^63*y*z0 - x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^63 + x^62*z0 + x^61*y*z0 + x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^58 - x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y + x^38*y, + -x^114 + x^113*z0 + x^112*z0^2 - x^112*z0 - x^111*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^109*y*z0 + x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^108*y + x^108*z0 + x^107*y - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^105*y*z0 - x^104*y*z0^2 + x^105*y + x^104*y*z0 + x^104*z0^2 + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^104 + x^103*z0 - x^102*y*z0 + x^101*y*z0^2 + x^103 + x^101*y*z0 - x^101*z0^2 - x^102 + x^101*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*z0^2 - x^97*y + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*y*z0 + x^96 + x^95*y + x^95*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^90*y + x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^88 - x^87*y - x^87*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*z0 - x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 - x^84*z0^2 - x^83*y*z0^2 + x^83*y*z0 + x^83*z0^2 + x^84 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^82*y + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^81 - x^80*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 + x^75*y*z0^2 - x^77 - x^76*y + x^76 - x^74*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^72*z0^2 - x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y + x^70*y*z0 - x^70*y + x^69*y*z0 - x^68*y*z0^2 - x^70 - x^69*y - x^68*z0^2 + x^69 - x^68*y + x^67*y*z0 + x^67*z0^2 + x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^66*y + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 + x^63*y*z0^2 + x^64*z0 + x^63*y*z0 - x^63*y - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 + x^62 + x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y + x^59*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y - x^57*z0^2 - x^56*y*z0^2 - x^56*y*z0 + x^56*z0^2 - x^57 - x^56*y - x^55*y*z0 + x^55*y + x^38*y*z0, + -x^115 + x^113*z0^2 + x^113*z0 + x^112*y + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*y + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*z0 + x^101*z0^2 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^94*y + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^92*y*z0 + x^91*y*z0^2 - x^93 + x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^89*y*z0 - x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^85*y*z0^2 - x^87 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^84*y + x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^82*y*z0 - x^82*z0^2 - x^83 - x^82*y - x^82*z0 + x^81*z0^2 - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 - x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^74*y*z0 - x^74*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 + x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^73 - x^72*y + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y + x^70*z0 - x^69*z0^2 + x^70 + x^69*y - x^69*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^67*y*z0 + x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^66*y + x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*z0 + x^61*y*z0 - x^61*y + x^61*z0 - x^59*y*z0^2 - x^61 + x^60*y + x^59*z0^2 + x^60 + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 - x^55*y*z0 + x^56 + x^38*y*z0^2, + x^114*z0 + x^113*z0^2 - x^113*z0 - x^113 + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y + x^109*z0 + x^108*y*z0 - x^107*y*z0^2 + x^108*y + x^108*z0 + x^107*y*z0 + x^106*y*z0^2 + x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*z0 - x^104*z0^2 - x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 - x^98 - x^97*y + x^95*y*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^93*z0^2 + x^93*y + x^93*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y - x^92*z0 - x^91*y*z0 + x^90*y*z0^2 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 - x^87*z0^2 - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y - x^85*z0^2 - x^86 + x^85*y - x^85*z0 + x^83*y*z0^2 - x^84*y + x^83*y*z0 + x^82*y*z0^2 + x^84 - x^83*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 - x^81*y + x^81*z0 + x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^79*y + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 + x^76*y + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*y*z0 - x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^65*z0 + x^64*y*z0 + x^63*y*z0^2 + x^64*y - x^63*y*z0 + x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^63 + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 + x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y + x^57*y*z0^2 + x^57*z0^2 + x^57*y + x^57*z0 - x^56*y*z0 + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y*z0 + x^56 + x^55*y + x^39, + -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 + x^107*z0^2 - x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^107 - x^106*y + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^101 - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y - x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^95*y*z0 - x^95*z0^2 - x^96 + x^95*z0 + x^94*z0^2 + x^95 + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^93 + x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y + x^90*y*z0 + x^90*z0^2 + x^90*y - x^90*z0 - x^89*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^86*y + x^85*z0^2 - x^86 + x^85*y + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^83*z0^2 + x^83 - x^82*y - x^81*y*z0 + x^81*z0^2 + x^82 + x^81*y + x^80*y*z0 + x^80*y + x^79*y*z0 - x^79*z0^2 - x^79*y - x^78*y*z0 - x^78*z0^2 - x^79 - x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y + x^76 + x^75*y + x^75*z0 - x^74*y*z0 - x^75 - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^74 - x^73*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*z0 - x^69*y*z0^2 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^69*z0 - x^69 - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^68 - x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*z0 + x^64*z0^2 + x^65 + x^64*y - x^64*z0 - x^63*y*z0 - x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^56*y*z0^2 + x^58 - x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*z0 + x^55*y*z0 + x^56 + x^55*y + x^39*z0, + -x^115 - x^114*z0 + x^114 - x^113*z0 - x^112*z0^2 + x^112*y + x^111*y*z0 + x^111*z0^2 - x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^109*y*z0^2 + x^111 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*y*z0 - x^108*y + x^108*z0 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 + x^107 + x^105*y*z0 + x^104*y*z0^2 - x^106 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 + x^97*y*z0 - x^96*y*z0^2 + x^98 + x^97*z0 - x^95*y*z0^2 - x^97 - x^96*y - x^95*y*z0 - x^95*z0 + x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 + x^91*y - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^87*y*z0^2 - x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 + x^85*y*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 - x^84*y*z0 - x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*y + x^82*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*z0^2 - x^81 - x^80*y - x^80*z0 + x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*y + x^78*z0 - x^76*y*z0^2 - x^78 + x^77*y + x^76*y*z0 - x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 - x^75*y*z0 - x^76 - x^75*y + x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*z0^2 + x^74 - x^73*y - x^72*y*z0 + x^71*y*z0^2 - x^73 - x^72*y + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 - x^67*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^63*y*z0^2 - x^65 + x^64*y - x^63*y*z0 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^61*y - x^61 + x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^57*y - x^57*z0 + x^56*y*z0 + x^55*y*z0^2 + x^56*z0 - x^55*y*z0 + x^39*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^110*y*z0 + x^109*y*z0^2 - x^110*y + x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^109 + x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*z0 + x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 - x^100*y*z0^2 - x^102 - x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^100 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^97*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 - x^93*y*z0 - x^94 + x^93*z0 - x^91*y*z0^2 + x^93 + x^92*y + x^91*z0^2 + x^92 + x^90*y*z0 + x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^88*y - x^88*z0 + x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 - x^84 - x^83*y + x^83*z0 - x^81*y*z0^2 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0 + x^81 - x^80*y - x^80*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^77*z0^2 - x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 + x^75*y*z0^2 - x^76*y + x^75*y*z0 - x^75*y + x^74*y*z0 - x^73*y*z0^2 - x^74*y + x^73*y*z0 - x^73*z0^2 - x^74 - x^73*z0 + x^72*y*z0 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^72 + x^71*y - x^70*y*z0 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^62*z0^2 - x^63 + x^62*z0 - x^61*y*z0 + x^60*y*z0^2 - x^62 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*y + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^57 + x^56*y + x^55*y*z0 - x^56 + x^55*y + x^39*y, + -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*y*z0 + x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*y - x^108*y*z0 - x^108*z0^2 + x^109 - x^107*y*z0 - x^106*y*z0^2 + x^108 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 - x^105*y*z0 - x^104*y*z0^2 + x^106 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^102*y*z0 - x^102*y - x^102*z0 - x^102 + x^101*y - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^99*y - x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^97 + x^96*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 - x^94*y*z0 - x^93*y*z0^2 + x^94*y - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^92*y - x^92*z0 - x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 - x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*z0 - x^90 - x^89*y - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^88*y + x^86*y*z0^2 + x^87*y + x^87*z0 + x^86*y*z0 - x^87 + x^86*y + x^86*z0 + x^85*z0^2 + x^86 + x^85*y - x^83*y*z0^2 + x^85 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y + x^81*y*z0^2 + x^83 - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 - x^77*y*z0^2 + x^78*y - x^78*z0 - x^77*z0^2 - x^78 - x^77*y + x^77*z0 + x^76*y*z0 - x^75*y*z0^2 - x^77 + x^76*y + x^74*y*z0^2 - x^75*y - x^74*y*z0 + x^73*y*z0^2 - x^74*y - x^74*z0 - x^73*y*z0 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*y - x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0 - x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^67*y + x^67*z0 + x^66*z0^2 + x^67 - x^66*y + x^66*z0 + x^65*z0^2 - x^66 + x^65*y - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^63*y*z0 - x^62*y*z0^2 - x^64 + x^62*y*z0 - x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^61*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 - x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^59 - x^58*z0 - x^57*z0^2 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^56*z0 + x^56 - x^55*y + x^39*y*z0, + x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^112*z0^2 - x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^107*y*z0 - x^106*y*z0^2 + x^108 + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^107 + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^104*z0 - x^103*y*z0 + x^103*z0 + x^102*y*z0 + x^102*z0^2 - x^103 - x^102*y - x^101*z0^2 - x^102 - x^101*z0 - x^100*y*z0 - x^101 - x^100*y - x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^94*y*z0 - x^93*y*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^93*z0 + x^91*y*z0^2 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^89 + x^88*y - x^87*y*z0 + x^86*y*z0^2 - x^88 - x^87*y - x^85*y*z0^2 + x^87 + x^86*y - x^86*z0 + x^85*z0^2 - x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^83*y - x^81*y*z0^2 + x^82*y - x^81*z0^2 + x^81*y + x^81*z0 - x^80*y*z0 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^80 - x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*y*z0 - x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y + x^70*y*z0 - x^70*z0^2 + x^71 - x^70*y - x^68*y*z0^2 + x^70 - x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 - x^66*z0^2 - x^65*y*z0^2 + x^66*y + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^65 - x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^63*z0 - x^62*y*z0 - x^63 + x^62*y + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^61 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^58*y*z0 + x^58*z0^2 - x^58*y - x^57*y*z0 - x^57*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^55*y*z0 - x^55*y + x^39*y*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 + x^113*z0 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^111 + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^110 + x^108*y*z0 + x^107*y*z0^2 + x^108*y - x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^108 - x^107*y - x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*y - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^104*y + x^104*z0 + x^103*z0^2 - x^104 + x^103*y - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^99*z0^2 - x^99*y + x^99*z0 - x^98*y*z0 + x^97*y*z0^2 - x^98*z0 - x^97*y*z0 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y + x^95*z0^2 - x^96 + x^95*y - x^95*z0 + x^95 + x^94*y + x^93*y*z0 + x^93*z0^2 + x^94 - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 - x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^91 + x^90*y - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 - x^83*y*z0^2 - x^85 - x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y + x^79*z0^2 - x^79*y + x^78*z0^2 - x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 + x^74*z0^2 + x^74*z0 + x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*z0 + x^71*z0^2 + x^72 - x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*z0 + x^67*y*z0 + x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 + x^63*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y*z0 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^56*y*z0 - x^55*y*z0^2 - x^57 - x^55*y*z0 + x^40, + -x^115 - x^114*z0 + x^114 + x^112*z0^2 + x^113 + x^112*y + x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y - x^111*z0 - x^109*y*z0^2 - x^110*y + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y + x^108*y*z0 + x^108*z0^2 - x^109 - x^108*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*y - x^105*y*z0 + x^104*y*z0^2 + x^105*y + x^105*z0 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 - x^101*y*z0^2 - x^101*y*z0 + x^101*z0^2 + x^101*y + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^99*y*z0 + x^99*z0^2 + x^99*y + x^99*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*z0 + x^96*y*z0 - x^96*y - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^96 - x^95*z0 + x^94*z0^2 - x^94*y - x^94*z0 + x^92*y*z0^2 - x^94 - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y - x^89*z0 - x^87*y*z0^2 + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^86 - x^85*y + x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y + x^83*z0^2 - x^82*y*z0^2 + x^83*y + x^83*z0 + x^81*y*z0^2 + x^83 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*y*z0 + x^80 - x^79*y - x^79*z0 - x^78*z0^2 - x^78*y + x^78*z0 - x^77*z0^2 - x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y - x^76*z0 - x^74*y*z0^2 - x^76 + x^75*y + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*y + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^73 - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^69*y*z0^2 + x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 + x^67*y - x^66*y - x^65*z0^2 + x^66 - x^65*y + x^65*z0 + x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^61*y*z0^2 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 - x^56 + x^40*z0, + -x^115 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^113 + x^112*y - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^110*y + x^110*z0 + x^109*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*y + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 - x^104*z0 + x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^101*y*z0 + x^101*z0^2 + x^102 + x^100*y*z0 + x^99*y*z0^2 - x^100*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y - x^96*y*z0 - x^96*z0^2 - x^97 + x^96*y - x^95*y*z0 - x^94*y*z0^2 - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^93*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 - x^89*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^88 + x^86*z0^2 - x^86*y - x^86*z0 - x^85*y*z0 - x^84*y*z0^2 + x^86 - x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 - x^80*y*z0^2 - x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 + x^78*z0 - x^78 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^72 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 - x^67*z0^2 - x^68 - x^67*y - x^67*z0 + x^66*z0^2 - x^66*y + x^65*y*z0 + x^64*y*z0^2 - x^65*y - x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^62*y*z0 - x^62*z0^2 + x^63 + x^60*y*z0^2 - x^62 + x^61*y + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^40*z0^2, + x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 + x^111*y + x^110*y*z0 - x^109*y*z0^2 + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^109*z0 - x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^108 + x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0 + x^104*y*z0^2 + x^106 + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^105 + x^103*y*z0 + x^103*z0^2 - x^104 - x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^102*y + x^101*y*z0 - x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y - x^94*y*z0 - x^94*z0^2 - x^95 + x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^92*y*z0 + x^91*y*z0^2 + x^92*z0 + x^90*y*z0^2 - x^92 - x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y + x^90*z0 + x^88*y*z0^2 - x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y + x^87*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y + x^85*y*z0 - x^84*y*z0^2 + x^86 - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*y - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^82*y + x^82*z0 + x^81*y*z0 + x^80*y*z0^2 + x^81*y + x^81*z0 - x^80*z0^2 + x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*y - x^75*y*z0^2 - x^76*y + x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y - x^73*y*z0 - x^73*z0^2 + x^74 - x^73*y - x^73*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^71*z0 + x^70*z0^2 - x^69*y*z0^2 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y - x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^63 + x^61*z0^2 - x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 + x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 + x^56 - x^55*y + x^40*y, + x^115 - x^114*z0 + x^113*z0^2 - x^112*z0^2 - x^113 - x^112*y + x^112*z0 + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^109*y - x^109*z0 - x^108*z0^2 - x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y - x^106*y*z0 + x^106*z0^2 + x^107 - x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^104*y*z0 + x^105 + x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 - x^101*z0 - x^99*y*z0^2 + x^101 - x^99*y - x^99*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*y - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*z0^2 + x^96 - x^95*y + x^95*z0 + x^94*z0^2 - x^94*y - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 - x^92 + x^89*y*z0^2 - x^91 - x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^80*y - x^80*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 + x^76 - x^75*y + x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^71*y - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 + x^69*y - x^69*z0 - x^68*y*z0 - x^69 + x^68*y - x^67*y*z0 - x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^65*y*z0 + x^65*z0^2 - x^66 - x^65*z0 + x^64*z0^2 + x^64*y + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*z0 - x^62*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 + x^60*y - x^59*z0^2 - x^58*y*z0^2 - x^60 - x^58*y*z0 - x^57*y*z0^2 - x^58*y + x^57*y*z0 + x^57*z0^2 - x^57*y - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 - x^56 + x^55*y + x^40*y*z0, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y + x^109*y*z0 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^109 - x^108*z0 - x^107*z0^2 + x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 - x^104*y*z0^2 + x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^104*z0 - x^103*z0^2 - x^104 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*z0 + x^98*z0^2 + x^99 - x^98*y - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97 + x^96*y + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 - x^90*y*z0^2 - x^92 - x^91*y - x^90*y*z0 + x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 + x^87*y*z0 - x^86*y*z0^2 + x^88 - x^87*y - x^86*y*z0 - x^86*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^84*y*z0 - x^83*y*z0^2 - x^85 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 - x^83*y - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^79 - x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y - x^76*y*z0 - x^76*y + x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y - x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y - x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*y + x^65*y*z0^2 + x^67 - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^63 + x^61*y*z0 - x^61*z0 - x^60*z0^2 + x^61 - x^59*y*z0 + x^60 + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^58 + x^57*y - x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^56*z0 + x^56 - x^55*y + x^40*y*z0^2, + -x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 - x^113 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*y - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y + x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*y + x^108*z0^2 - x^107*y*z0^2 + x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0 - x^101*y*z0^2 + x^103 - x^102*z0 + x^102 - x^101*y - x^100*y*z0 - x^100*z0^2 + x^101 + x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^97 - x^95*y*z0 - x^96 + x^95*y - x^95*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^88*y - x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^85 + x^84*y - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^79*y*z0 - x^79*z0^2 + x^80 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*z0^2 + x^77 + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^75*z0 + x^74*z0^2 - x^74*y + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^73*y + x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 - x^70*y*z0 - x^70*y - x^70*z0 + x^69*y*z0 - x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^69 - x^68*y + x^67*y*z0 - x^68 - x^67*z0 + x^65*y*z0^2 + x^67 + x^65*y*z0 - x^64*y*z0 - x^64*z0^2 - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^63*y - x^62*y*z0 - x^61*y*z0^2 + x^62*y - x^62*z0 + x^61*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^58 + x^57*z0 - x^56*y*z0 + x^57 - x^56*z0 - x^55*y*z0 + x^56 + x^41, + x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^113 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y - x^109*z0 + x^109 + x^108*y + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 + x^105 - x^104*z0 + x^103*y*z0 + x^102*y*z0^2 - x^104 + x^103*z0 + x^102*z0^2 + x^101*y*z0^2 + x^100*y*z0^2 - x^102 + x^101*z0 - x^100*y*z0 - x^101 + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^99*y - x^98*y*z0 + x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 + x^98 + x^97*y + x^96*y*z0 - x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 + x^92*y*z0 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 + x^90*y*z0 - x^89*y*z0^2 + x^90*y + x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 - x^87 + x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^83*y + x^82*y*z0 - x^82*z0^2 + x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^80*y*z0 - x^79*y*z0^2 - x^81 + x^80*y - x^79*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 - x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*y + x^77*z0 + x^76*y*z0 + x^77 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^75*y - x^75*z0 + x^74*z0^2 - x^74*z0 - x^73*y*z0 + x^72*y*z0^2 + x^74 - x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^72*y + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*y - x^71*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 - x^64*y*z0^2 - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y + x^63*y*z0 - x^63*y + x^62*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^60*y*z0^2 + x^62 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 - x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^56*y*z0 - x^56*z0^2 + x^57 - x^56*y + x^55*y*z0 + x^55*y + x^41*z0, + x^115 + x^114*z0 + x^114 + x^113*z0 + x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^112 - x^111*y - x^111*z0 - x^110*y*z0 - x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^109 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 - x^105*y*z0^2 + x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*z0^2 + x^102*y + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^100*y*z0 - x^100*z0^2 - x^101 - x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^99*z0 - x^98*z0^2 + x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*z0 + x^96*y*z0 + x^97 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^95*y + x^95*z0 - x^94*y*z0 - x^93*y*z0^2 - x^95 + x^93*y*z0 - x^94 + x^93*z0 + x^91*y*z0^2 + x^93 - x^91*y*z0 + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^90 - x^89*y - x^89*z0 - x^88*z0^2 - x^89 - x^87*y*z0 - x^87*z0^2 + x^88 - x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^86*y - x^86*z0 - x^85*y*z0 - x^84*y*z0^2 - x^86 + x^85*y - x^84*y*z0 + x^83*y*z0^2 + x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 - x^81 + x^80*y + x^79*y + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*z0 + x^76*y*z0^2 - x^78 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y + x^74*y*z0^2 - x^75*z0 + x^74*y*z0 + x^73*y*z0^2 - x^75 - x^73*y*z0 - x^72*y*z0^2 - x^73*y + x^73*z0 + x^71*y*z0^2 + x^72*y - x^72*z0 + x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^71 - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*z0 + x^63*z0^2 + x^62*y*z0^2 - x^63*y - x^63*z0 - x^62*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^60*y*z0 + x^61 + x^60*z0 - x^59*y*z0 - x^59*y + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^56*z0 - x^55*y*z0 - x^56 + x^41*z0^2, + x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^113 - x^112*y + x^111*y*z0 - x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^110 - x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*z0 - x^105 + x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*y - x^99*z0^2 - x^100 + x^99*y - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 - x^95*y*z0^2 - x^97 + x^96*y + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*z0 + x^94*y*z0 + x^94*y - x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*z0 + x^93 - x^92*y + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y - x^90*y*z0 - x^89*y*z0^2 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*y + x^88*z0^2 - x^87*y*z0^2 + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y + x^86*y*z0 - x^87 - x^86*z0 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y - x^83*y*z0 - x^83*z0^2 + x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*y + x^80*y*z0^2 + x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 - x^81 + x^80*z0 + x^79*z0^2 - x^79*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y + x^76*y*z0^2 + x^78 - x^77*y - x^76*z0^2 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^75 - x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*z0 - x^71*y*z0 - x^72 - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*z0 - x^68*y*z0 + x^67*y*z0^2 - x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^66 + x^65*y - x^65*z0 - x^64*y*z0 - x^62*y*z0^2 + x^64 + x^63*y + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^61*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 - x^59*y*z0 - x^58*y*z0^2 + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^59 + x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y + x^56*y*z0 + x^55*y*z0^2 - x^56*y - x^56*z0 - x^55*y*z0 + x^55*y + x^41*y, + -x^115 - x^114*z0 + x^114 - x^113*z0 + x^113 + x^112*y + x^111*y*z0 - x^111*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 - x^111 - x^110*y - x^110*z0 + x^108*y*z0^2 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^109 + x^108*y + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^106*y + x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y + x^105*z0 + x^104*y*z0 - x^104*z0^2 + x^105 + x^104*y + x^104*z0 + x^103*y*z0 + x^104 - x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^99*z0^2 - x^98*y*z0^2 - x^99*y - x^99*z0 - x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*y + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^96*y + x^96*z0 - x^95*y*z0 + x^96 - x^95*y - x^95*z0 + x^94*y*z0 - x^93*y*z0^2 + x^95 + x^94*y - x^93*z0^2 + x^93*y + x^93*z0 - x^92*y*z0 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^92 + x^91*y - x^91*z0 + x^90*z0^2 + x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 + x^88*z0^2 - x^87*y*z0^2 - x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*z0 + x^85*z0^2 - x^86 - x^85*z0 - x^84*y*z0 + x^84*y + x^84*z0 - x^83*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^83 - x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*z0^2 - x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^77 + x^76*y - x^76*z0 + x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*z0^2 - x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^73*y + x^72*y*z0 + x^71*y*z0^2 - x^73 - x^71*y*z0 + x^72 - x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 - x^68*z0^2 + x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^65*y*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y - x^64*y*z0 - x^64*z0^2 - x^65 - x^64*y - x^62*y*z0^2 - x^64 - x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 + x^59*y*z0^2 + x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*y - x^59*z0 - x^58*z0^2 - x^59 - x^58*y + x^56*y*z0^2 - x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*z0 + x^56 + x^55*y + x^41*y*z0, + x^114*z0 + x^113*z0^2 + x^113*z0 - x^112*z0^2 + x^113 - x^111*y*z0 - x^110*y*z0^2 + x^112 - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 + x^110 - x^109*y - x^109*z0 + x^108*y*z0 - x^109 - x^108*y - x^107*y*z0 + x^107*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*y*z0 - x^104*y*z0^2 - x^106 + x^105*y + x^104*y*z0 - x^103*y*z0^2 + x^105 - x^104*y - x^103*y*z0 - x^104 - x^103*y + x^103*z0 - x^102*z0^2 + x^103 - x^102*z0 - x^102 + x^101*y - x^101*z0 + x^100*z0^2 - x^101 - x^100*y + x^99*z0^2 + x^99*y + x^98*y*z0 - x^98*z0^2 + x^97*y*z0 - x^96*y*z0^2 + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^96*z0 + x^95*y*z0 - x^94*y*z0^2 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^89*y*z0^2 + x^91 + x^90*y + x^90*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*y*z0 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^87 + x^85*y*z0 - x^85*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 - x^83*y*z0^2 + x^85 - x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^82*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^81*y + x^81*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*z0^2 + x^73 + x^72*y - x^72*z0 - x^72 - x^71*y + x^70*y*z0 - x^69*y*z0^2 + x^70*z0 + x^69*y*z0 - x^68*y*z0^2 + x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y + x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^65 + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^62*y*z0 - x^62*z0^2 - x^63 - x^62*y - x^61*y*z0 - x^61*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 - x^57*y*z0^2 - x^59 + x^58*y - x^58*z0 - x^56*y*z0^2 - x^58 + x^57*y + x^56*y*z0 - x^56*z0 - x^56 + x^55*y + x^41*y*z0^2, + -x^114*z0 - x^113*z0^2 + x^113*z0 - x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^110*y*z0 - x^110*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^107*y*z0^2 - x^109 + x^108*y - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*y - x^106 - x^105*y - x^104*y*z0 + x^104*z0^2 - x^105 + x^104*z0 + x^103*y*z0 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^102*y + x^102*z0 + x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^101 - x^100*y + x^99*y*z0 - x^99*y + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^95*y*z0^2 - x^97 + x^96*z0 - x^94*y*z0^2 - x^96 - x^94*y*z0 + x^94*z0^2 + x^95 + x^94*y + x^93*y*z0 + x^93*z0^2 + x^94 - x^93*y + x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 - x^91*z0 + x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^89 + x^88*z0 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y - x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y + x^82*y*z0 + x^81*y*z0^2 - x^83 + x^82*z0 + x^81*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y - x^77*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y + x^69*y*z0 - x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*y*z0 + x^68 - x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 + x^65*y + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 - x^58*y*z0 + x^59 + x^58*y + x^58*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 - x^57 - x^56*z0 - x^55*y*z0 + x^55*y + x^42, + -x^115 - x^114*z0 + x^114 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y - x^109*y*z0^2 - x^110*y - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^109*z0 + x^108*z0^2 - x^109 - x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 + x^106 - x^105*y - x^105*z0 - x^105 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 - x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^99 - x^98*y - x^96*y*z0^2 + x^97*y - x^96*y*z0 - x^96*z0^2 - x^96*y + x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y - x^94*y*z0 - x^94*y - x^93*y*z0 + x^92*y*z0^2 + x^94 - x^93*y + x^92*y*z0 - x^91*y*z0^2 - x^92*y - x^92*z0 + x^91*z0^2 - x^92 + x^91*z0 + x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^90 - x^89*z0 - x^87*y*z0^2 + x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^85*y*z0^2 + x^87 + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y - x^84 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y - x^80*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*y - x^76*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^74*z0^2 + x^75 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^70*z0 + x^69*z0^2 + x^68*y*z0^2 - x^69*y - x^69*z0 - x^68*z0^2 - x^68*y - x^68*z0 + x^67*y*z0 + x^68 - x^67*y + x^67 - x^65*y*z0 - x^65*z0^2 + x^66 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^62*y - x^62*z0 - x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^59*y*z0^2 - x^61 + x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*z0 - x^56*y*z0 - x^56*z0^2 + x^57 + x^55*y*z0 + x^42*z0, + x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^113 + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^111 - x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^107*y*z0 + x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*z0^2 + x^107 - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 + x^100*y*z0^2 + x^102 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 + x^99 - x^97*y*z0 - x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*y*z0 + x^97 + x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^95*y + x^95*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^91*y*z0 - x^91*z0^2 - x^92 + x^91*y + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^88*y*z0 - x^88*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 - x^86*y*z0 - x^86*z0^2 - x^86*y + x^85*y*z0 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83 + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^76*z0 + x^74*y*z0^2 - x^76 + x^75*y + x^74*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^71*y*z0^2 - x^73 + x^72*z0 + x^71*y*z0 + x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^69*y*z0 - x^70 - x^69*y - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 - x^68*y - x^68*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^67*z0 + x^66*z0^2 - x^67 + x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^63*y*z0^2 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*y + x^62 + x^61*y + x^61*z0 + x^60*z0^2 - x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^58*y - x^57*z0^2 + x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y + x^56 + x^55*y + x^42*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^108*y*z0^2 - x^110 + x^109*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^107 - x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^106 + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^102*y*z0 + x^102*z0^2 + x^103 - x^102*z0 + x^101*z0^2 + x^102 + x^101*y + x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^99*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^96*y*z0 - x^95*y*z0^2 + x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 + x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 - x^89*y*z0 - x^90 - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^89 - x^87*z0^2 + x^88 + x^87*y + x^85*y*z0^2 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y - x^84*z0^2 + x^85 + x^83*y - x^82*y*z0 + x^82*z0^2 - x^82*y - x^82*z0 + x^81*z0^2 - x^82 + x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y + x^77*y*z0 + x^77*z0^2 + x^77*y - x^76*y*z0 + x^76*z0^2 + x^77 + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^74*z0^2 + x^73*y*z0^2 - x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^70*y - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*y + x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 + x^65 - x^63*y*z0 - x^62*y*z0^2 - x^64 + x^63*z0 - x^62*z0^2 + x^63 - x^62*z0 + x^60*y*z0^2 + x^61*y + x^61*z0 - x^59*y*z0^2 + x^60*y - x^60*z0 + x^58*y*z0^2 - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^58 + x^57*y - x^57*z0 + x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 + x^42*y, + x^115 - x^113*z0^2 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*z0 + x^108*y*z0 + x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 - x^104*z0^2 + x^105 - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^103*z0 - x^102*y*z0 + x^103 - x^102*y + x^101*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^96*y*z0 + x^95*y*z0^2 - x^97 + x^96*y + x^95*z0^2 + x^94*y*z0^2 - x^95*y + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*y - x^93*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^90*y + x^89*y*z0 - x^89*z0^2 + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^83*y + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^81 + x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^78 + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 + x^76*y + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*y*z0 + x^74*y + x^74*z0 - x^73*y*z0 - x^72*y*z0^2 - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y + x^70*y*z0 - x^69*y*z0^2 + x^69*y*z0 + x^68*y*z0^2 + x^69*z0 - x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 - x^66*z0^2 - x^65*y*z0^2 + x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 + x^61*z0^2 + x^62 + x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^61 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*y + x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^57 + x^56*y - x^56*z0 + x^55*y*z0 - x^56 + x^42*y*z0, + x^115 + x^114*z0 - x^113*z0 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^112 - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^111 + x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 + x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*z0 + x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*z0 - x^98*y*z0^2 - x^100 + x^99*y + x^98*y*z0 - x^99 - x^98*z0 + x^97*y*z0 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*y + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^92*z0^2 - x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^89*z0 + x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^84*z0 + x^83*y*z0 + x^83*y + x^83*z0 - x^82*z0^2 + x^83 - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77*z0 + x^75*y*z0^2 - x^76*y - x^76*z0 - x^75*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^75 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*z0 + x^71 - x^70*y - x^69*z0^2 + x^70 + x^69*y + x^69 + x^68*y - x^68*z0 + x^67*y*z0 + x^66*y*z0^2 + x^66*z0^2 + x^67 + x^66*y + x^66*z0 - x^65*y*z0 - x^65*y + x^65*z0 + x^63*y*z0^2 - x^64*y - x^64*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*z0^2 - x^59*y + x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 + x^57 - x^56*y - x^56*z0 + x^56 + x^55*y + x^42*y*z0^2, + x^115 - x^113*z0^2 + x^113*z0 + x^112*z0^2 + x^113 - x^112*y - x^112*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*z0 + x^108*y*z0 + x^107*y*z0^2 + x^109 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*y*z0 + x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 - x^104*y*z0 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^103 - x^101*y*z0 - x^102 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 - x^99*y - x^99*z0 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^98 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 - x^95*z0 + x^94*y*z0 - x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 + x^86*y*z0 - x^87 + x^86*y + x^86*z0 + x^85*y*z0 + x^84*y*z0^2 + x^85*y - x^85 + x^83*z0^2 - x^83*y - x^83*z0 - x^82*y*z0 - x^81*y*z0^2 - x^83 + x^82*y + x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^79*y + x^79*z0 - x^78*y*z0 + x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y - x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 - x^68 - x^67*y - x^67*z0 - x^65*y*z0^2 - x^67 - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^64 + x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^62*y - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^57 - x^56*z0 - x^55*y*z0 + x^56 + x^43, + -x^115 + x^114*z0 - x^113*z0^2 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^110*z0^2 - x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^107*y*z0^2 - x^109 - x^108*z0 - x^107*y*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 + x^103*z0^2 + x^104 - x^103*y - x^103 + x^102*y + x^102*z0 - x^100*y*z0^2 + x^102 - x^101*y - x^100*z0^2 - x^100*y - x^100*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^98*y*z0 - x^98*z0^2 + x^98*y - x^98*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*z0^2 - x^94*y*z0^2 + x^95*z0 - x^94*z0^2 - x^95 + x^94*y - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^93*z0 - x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*y*z0 - x^92 - x^90*y*z0 - x^90*z0^2 - x^90*y + x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 + x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^85*y + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^82*y*z0 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^81*y - x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^79 + x^78*y - x^78*z0 - x^77*z0^2 + x^78 - x^77*y - x^77*z0 + x^76*z0^2 - x^77 - x^76*y + x^76*z0 + x^75*y*z0 + x^75*y + x^75*z0 + x^74*z0^2 + x^73*y*z0^2 + x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^70*y - x^70*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0 + x^67*z0^2 + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*z0 + x^65*z0^2 + x^65*z0 + x^64*y*z0 + x^63*y*z0^2 - x^65 - x^64*y + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y - x^62*z0 - x^60*y*z0^2 + x^62 + x^61*y - x^60*z0^2 - x^61 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^59*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y*z0 + x^43*z0, + x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y - x^107*z0 + x^106*z0^2 + x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*z0 - x^103*y*z0^2 - x^105 + x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^102*y*z0 - x^102*z0^2 - x^103 - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^101 - x^100*y - x^100 + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^96*y*z0^2 + x^97*y - x^97*z0 + x^96*z0^2 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 + x^91*y*z0^2 + x^93 - x^91*z0^2 - x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^89*y*z0 + x^88*y*z0^2 + x^90 + x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^87*z0 - x^86*y*z0 + x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*z0^2 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^84 + x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*z0 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y + x^75*y*z0^2 + x^76*y + x^76*z0 - x^75*y*z0 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*y - x^74*z0 - x^73*y*z0 + x^72*y*z0^2 - x^73*y - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*y*z0 + x^70*y - x^69*z0^2 - x^69*y - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^65*y*z0 - x^65*z0^2 + x^65*y + x^64*y*z0 - x^64*z0^2 + x^65 - x^64*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^59*y*z0 - x^59*z0^2 - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 + x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 + x^58 - x^56*y*z0 + x^55*y*z0^2 - x^56*y + x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^43*z0^2, + x^114*z0 + x^113*z0^2 - x^114 + x^112*z0^2 - x^113 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^105*y - x^104*y*z0 - x^104*z0^2 + x^105 - x^103*y*z0 - x^103*z0^2 + x^103*y - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 - x^97*z0^2 + x^98 - x^97*y - x^96*y*z0 + x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 + x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*y + x^86*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^84*y*z0 + x^84*z0^2 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^84 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 - x^80*y - x^80*z0 + x^78*y*z0^2 - x^79*y + x^78*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^78 - x^77*y + x^77*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^75*y*z0 - x^75*z0^2 - x^75*y + x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^75 - x^74*y + x^73*y*z0 - x^72*y*z0^2 + x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^73 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*z0 - x^69*z0^2 - x^70 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^69 - x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^67 + x^66*y + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 - x^62*z0^2 + x^63 - x^62*y - x^61*y*z0 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 + x^60*y + x^60*z0 + x^59*z0^2 + x^60 + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 - x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^43*y, + -x^115 - x^114*z0 + x^114 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^106*y*z0^2 + x^108 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*y - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 - x^104*z0^2 - x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^97*y*z0^2 + x^98*y + x^96*y*z0^2 - x^98 - x^96*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^93*y - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^90*z0^2 - x^89*y*z0^2 - x^90*y + x^90*z0 - x^89*z0^2 + x^90 - x^89*y - x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 - x^87*y*z0 - x^86*y*z0^2 + x^88 - x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*y - x^86 - x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*y*z0 - x^80 + x^79*y - x^79*z0 + x^77*y*z0^2 - x^79 - x^78*y + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^77 - x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^74 + x^73*y + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^70*y*z0^2 + x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^68*y*z0^2 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 + x^66*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 - x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 + x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*z0 + x^58*y*z0 - x^59 + x^58*z0 - x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^56*z0 + x^55*y*z0 - x^56 + x^43*y*z0, + -x^115 + x^114*z0 - x^113*z0^2 + x^113*z0 - x^112*z0^2 + x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y - x^108*z0^2 - x^109 + x^108*y - x^106*y*z0^2 + x^108 - x^106*y*z0 - x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^104*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 + x^103*y + x^102*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0 + x^101 + x^100*y + x^100*z0 + x^99*y*z0 - x^100 + x^99*z0 + x^98*z0^2 + x^97*y*z0^2 - x^98*y + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*y - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y + x^90*z0^2 - x^89*y*z0^2 - x^89*y*z0 + x^88*y*z0^2 + x^89*y - x^89*z0 + x^87*y*z0^2 + x^89 - x^88 - x^87*y + x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^82*y*z0 - x^81*y*z0^2 + x^83 + x^82*y - x^81*y*z0 + x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*y + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^75*y - x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 + x^72*y*z0^2 - x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 - x^70*y*z0^2 - x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 + x^68 - x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 - x^63*y*z0^2 + x^65 - x^64*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^62*y*z0 - x^62*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^60*y*z0^2 - x^61*y + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*z0 - x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^43*y*z0^2, + x^115 + x^114*z0 - x^114 + x^112*z0^2 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^112 + x^111*y - x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y - x^105*y*z0^2 - x^106*y + x^105*y*z0 - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^104*y - x^104*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y + x^103*z0 + x^102*z0^2 + x^103 - x^102*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^99*y*z0^2 - x^100*z0 - x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^99 - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^97*z0 + x^95*y*z0^2 - x^97 - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^94*y*z0 + x^93*y*z0^2 + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0 - x^92*z0^2 - x^93 + x^91*y*z0 - x^90*y*z0 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^87*y*z0 + x^87*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 + x^87 + x^86*y + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^84 + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*y + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^78*y*z0^2 + x^80 + x^79*z0 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y + x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^75*y + x^75 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^73*y + x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^72*z0 + x^71*z0^2 - x^72 + x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^71 - x^70*y + x^70*z0 + x^69*y*z0 - x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^68*y + x^68*z0 + x^67*y*z0 - x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*z0^2 + x^66 - x^65*y - x^64*y*z0 - x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 + x^63*y*z0 - x^62*y*z0^2 - x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y - x^61*y*z0 + x^60*y*z0^2 - x^61*y - x^61*z0 + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*y - x^57*y*z0^2 - x^59 - x^58*y + x^57*y*z0 + x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 + x^55*y*z0^2 - x^57 + x^56*z0 + x^56 + x^44, + x^115 - x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 - x^112*y + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*z0 - x^108*y*z0^2 - x^110 - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^108 + x^107*z0 + x^106*y*z0 + x^106*z0 + x^104*y*z0^2 - x^106 - x^105*z0 - x^104*z0^2 - x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^104 - x^103*y - x^103*z0 - x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^100*y - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^99*y - x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y + x^97*z0^2 + x^98 + x^97*y - x^97*z0 + x^96*z0^2 + x^96*y - x^96*z0 + x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*z0 + x^94*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93 - x^92*y - x^92*z0 - x^91*y*z0 + x^92 - x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^88*y*z0^2 + x^90 + x^89*y - x^88*y - x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 - x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^80 + x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 - x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^75 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 + x^70 + x^69*y - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^67*z0^2 - x^68 - x^66*z0^2 - x^65*y*z0^2 + x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^66 - x^65*z0 + x^64*y*z0 + x^64*y - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^62*y + x^62*z0 + x^61*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 - x^59*z0^2 - x^60 - x^59*y + x^59*z0 - x^57*y*z0^2 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56*y - x^56*z0 + x^55*y*z0 - x^56 + x^44*z0, + -x^115 - x^114*z0 - x^114 - x^113*z0 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*y*z0 + x^110*y - x^110*z0 - x^109*y*z0 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^109 - x^108*z0 + x^107*y*z0 - x^108 - x^106*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*z0^2 - x^105*z0 - x^103*y*z0^2 - x^104*z0 - x^103*y*z0 + x^103*y + x^102*y*z0 - x^103 - x^102*y + x^101*y*z0 + x^101*y + x^101*z0 - x^100*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y - x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y - x^95*z0^2 - x^94*y*z0^2 + x^95*z0 - x^94*y*z0 + x^95 - x^94*y - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*y + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^89 + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^86*z0 + x^84*y*z0^2 + x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y - x^83*z0^2 - x^82*y*z0^2 - x^83*y - x^83*z0 - x^82*z0^2 + x^83 + x^81*z0^2 + x^81*y - x^81 + x^80*y + x^80*z0 + x^78*y*z0^2 + x^79*y - x^78*y*z0 - x^77*y*z0^2 - x^79 + x^77*y*z0 + x^78 - x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 - x^73*z0^2 - x^74 - x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^72*z0 - x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*z0^2 - x^68*y*z0^2 - x^70 - x^69*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y - x^67*y*z0 - x^67*y + x^66*z0^2 + x^66*z0 + x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*z0^2 - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^60*y*z0^2 + x^62 + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 - x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 - x^56*y - x^56 - x^55*y + x^44*z0^2, + -x^112*z0^2 - x^112 - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*z0 + x^109*z0^2 + x^110 + x^109*y + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y + x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^103*y*z0 - x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 + x^102*y - x^101*y*z0 - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^101 + x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y + x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^94*y*z0 - x^95 - x^94*y + x^93*z0^2 + x^92*y*z0^2 + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^93 + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^90 + x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^88 - x^87*y - x^87*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^85*y + x^85*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^84 + x^82*y*z0 + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^81 - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^74*y*z0^2 + x^76 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y - x^74*z0 + x^73*y*z0 + x^74 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^71*y*z0 + x^71*z0^2 - x^71*y + x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*z0^2 + x^68*y*z0^2 + x^69*z0 - x^68*z0^2 - x^69 + x^68*z0 + x^67*y*z0 - x^66*y*z0^2 + x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^66 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^65 - x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^62*y - x^61*y*z0 + x^61*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 + x^59*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y + x^55*y*z0 - x^56 + x^55*y + x^44*y, + x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 - x^113 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^110*y*z0 + x^110*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*z0^2 + x^107 + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*y - x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^103*y + x^102*y*z0 + x^102*z0^2 + x^103 - x^102*y + x^101*y*z0 - x^101*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y - x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^97*y - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 - x^93*y + x^93*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*y + x^91*y*z0 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 + x^91 - x^90*y + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^87*z0 - x^86*y*z0 + x^85*y*z0^2 + x^87 - x^86*y + x^85*y*z0 - x^86 - x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^83*y + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^81*z0^2 + x^80*y*z0^2 + x^81*z0 + x^79*y*z0^2 + x^81 - x^80*y - x^80*z0 + x^79*z0^2 + x^80 + x^79*z0 - x^78*y*z0 + x^79 + x^78*y - x^78*z0 + x^77*y*z0 - x^78 - x^77*z0 + x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*y - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0 + x^69*z0^2 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*z0^2 - x^65 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 - x^62*z0^2 + x^62*y + x^62*z0 - x^61*z0^2 + x^62 + x^61*y + x^60*y*z0 + x^59*y*z0^2 - x^61 + x^60*y + x^59*y*z0 - x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^57*y + x^56*y*z0 + x^56*z0^2 - x^55*y + x^44*y*z0, + -x^114*z0 - x^113*z0^2 + x^114 - x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 - x^109*y*z0 - x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^107*y*z0 + x^107*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*y*z0 + x^107 + x^105*y*z0 + x^104*y*z0^2 + x^104*y*z0 + x^103*y*z0 + x^102*y*z0^2 - x^104 + x^103*y - x^103*z0 - x^101*y*z0^2 + x^103 + x^102*y - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y - x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^97*y*z0 - x^96*y*z0^2 - x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^92*z0 + x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^85 - x^84*y + x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^80 + x^79*y + x^77*y*z0^2 - x^79 + x^78*z0 - x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^76*y - x^76*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*y*z0 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*z0 + x^70*y*z0 - x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^65*y + x^65*z0 - x^64*z0^2 - x^64*y - x^64*z0 - x^64 + x^63*y - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 + x^61*y*z0 + x^60*y*z0^2 + x^62 + x^60*z0^2 + x^61 + x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 + x^58 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^56*z0 - x^55*y*z0 + x^55*y + x^44*y*z0^2, + x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^107*y*z0^2 - x^109 + x^108*z0 + x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 + x^107 - x^106*y + x^106*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 - x^102*z0 - x^100*y*z0^2 - x^101*y + x^100*z0^2 - x^101 - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*z0 - x^98*z0^2 + x^99 - x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^97*y - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 - x^94 + x^93*y - x^92*y*z0 + x^91*y*z0^2 + x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^90*y*z0 + x^89*y*z0^2 - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 + x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^89 + x^88*y - x^88*z0 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*z0 + x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^77*z0 + x^76*z0^2 + x^75*y*z0^2 + x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^73*y*z0^2 - x^75 - x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^73*z0 + x^71*y*z0^2 + x^72*y + x^72*z0 - x^70*y*z0^2 + x^72 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0 + x^69*z0^2 + x^70 + x^69*z0 + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^68 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^66 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*y*z0 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 + x^60*y*z0 + x^59*y*z0^2 - x^60*y + x^59*z0^2 + x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*z0 - x^58 + x^55*y*z0^2 - x^57 + x^56*y - x^56 + x^55*y + x^45, + x^115 - x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^110 + x^109*y - x^108*y*z0 + x^107*y*z0^2 + x^108*y + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^104 - x^103*y + x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^102 - x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 - x^99 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^95 - x^94*z0 + x^93*y*z0 + x^94 + x^93*y - x^93*z0 + x^92*z0^2 - x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^85*y*z0 - x^84*y*z0^2 + x^86 + x^85*y - x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 + x^83 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^80*y - x^80*z0 - x^79*y*z0 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 + x^77*y*z0^2 + x^79 + x^78*y + x^77*y*z0 + x^77*z0^2 + x^77*y + x^77*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 - x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 - x^74*y + x^72*y*z0^2 + x^74 + x^73*y + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^70*y*z0^2 + x^72 + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^68*y*z0 + x^67*y*z0^2 + x^68*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^66*z0^2 + x^65*y*z0^2 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 - x^64*z0 + x^63*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^62*y - x^62*z0 - x^61*z0^2 + x^62 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y - x^59*z0 + x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^56*y*z0 - x^56*z0^2 + x^57 - x^56*y - x^55*y*z0 + x^45*z0, + x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 + x^113 - x^112*y + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*y*z0 - x^110*y - x^109*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^109 - x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 - x^105*y*z0 + x^106 - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^103*z0^2 + x^104 - x^103*z0 + x^102*z0^2 - x^103 - x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^100*z0^2 - x^99*y*z0^2 + x^101 + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 - x^97*z0 - x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*z0 - x^91*y*z0 + x^91*z0 + x^90*z0^2 - x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^89 + x^88*z0 + x^87*z0^2 - x^88 - x^87*y + x^87*z0 - x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^84 - x^83*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^80*y*z0 - x^79*y*z0^2 + x^81 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^79 - x^78*z0 - x^77*y*z0 - x^78 + x^77*y + x^76*z0^2 + x^77 + x^76*z0 + x^75*y*z0 - x^74*y*z0^2 + x^76 - x^75*y - x^73*y*z0^2 + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^71*y - x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^71 + x^69*y*z0 + x^69*z0^2 - x^69*y + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*z0 - x^67*z0^2 - x^68 + x^67*y - x^66*z0^2 + x^67 - x^66*y + x^66*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y + x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^60*y + x^60*z0 + x^58*y*z0^2 + x^60 - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^57*y*z0 - x^57*z0^2 + x^57 + x^56*y - x^56*z0 - x^56 - x^55*y + x^45*z0^2, + x^114*z0 + x^113*z0^2 + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*z0 - x^111 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^108*y*z0 - x^108*z0^2 + x^108*y - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 + x^105*z0^2 - x^106 + x^105*y + x^105*z0 + x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^104 - x^103*z0 - x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 - x^101*y*z0 - x^102 - x^100*y*z0 - x^99*y*z0^2 + x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 - x^94*z0^2 - x^95 - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 + x^92*z0^2 - x^92*y - x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 + x^88*z0^2 + x^89 + x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*y - x^87*z0 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^85 - x^84*y + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^80*z0^2 + x^79*y*z0^2 - x^81 - x^79*y*z0 + x^79*z0^2 - x^80 - x^79*y - x^79*z0 + x^78*y*z0 + x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 - x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^73 - x^72*y - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^67*y*z0^2 - x^68*z0 - x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*y + x^65*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^63*y*z0 - x^63*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 + x^63 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^59*z0 + x^59 + x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^57 - x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^45*y, + x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*z0 - x^103*z0^2 - x^104 - x^103*y + x^103*z0 - x^102*z0^2 + x^103 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^100 - x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*z0 - x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^96 - x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^93*z0^2 + x^94 + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 + x^90*y*z0^2 - x^92 - x^91*z0 + x^89*y*z0^2 - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^90 - x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 - x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^83*y*z0 - x^83*z0^2 + x^84 - x^83*y + x^83*z0 - x^82*z0^2 - x^81*y*z0^2 + x^82*y + x^81*y*z0 + x^82 + x^81*z0 - x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 - x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*y - x^75*y*z0 + x^75*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y - x^73*y*z0 + x^72*y*z0^2 - x^74 + x^73*y - x^72*z0^2 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^69*y + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y - x^68*z0 - x^67*z0^2 - x^68 - x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^64*y*z0^2 - x^64*z0^2 + x^63*y*z0^2 + x^64*z0 - x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 + x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^56*y - x^55*y*z0 + x^56 - x^55*y + x^45*y*z0, + -x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^110 - x^109*z0 + x^108*y*z0 - x^107*y*z0^2 + x^109 + x^107*y*z0 + x^107*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 - x^104*y*z0^2 - x^106 + x^105*z0 - x^104*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y + x^100*z0^2 - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^97*y*z0^2 - x^99 - x^97*y*z0 + x^97*z0^2 + x^98 + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^96*z0 - x^95*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 - x^91*y*z0^2 + x^93 + x^91*y*z0 - x^91*z0^2 - x^92 + x^91*y - x^90*y*z0 - x^90*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 + x^88*y - x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y - x^86*z0 + x^85*y*z0 - x^86 + x^85*y - x^85*z0 - x^83*y*z0^2 - x^84*y - x^82*y*z0^2 + x^84 - x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^81*y - x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*y - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*z0 - x^76*y*z0^2 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y + x^75*y*z0 - x^74*y*z0^2 + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^73*y*z0 + x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^72*z0 + x^71*y*z0 - x^70*y*z0^2 + x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*y - x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^68 + x^67*y - x^66*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*z0 + x^63*y*z0^2 - x^65 + x^64*y + x^62*y*z0^2 - x^64 + x^63*y - x^62*z0^2 + x^61*y*z0^2 + x^62*z0 + x^61*y*z0 - x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 - x^61 + x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*y + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^57 - x^55*y*z0 + x^56 - x^55*y + x^45*y*z0^2, + -x^115 + x^113*z0^2 - x^114 + x^112*y + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^111 + x^110*z0 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*y + x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^106*y + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^92*y + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^87*y*z0^2 - x^89 + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 - x^87*y - x^86*y*z0 + x^86*z0^2 + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 + x^84*y*z0 + x^83*y*z0^2 - x^84*y + x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^80 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^77 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y + x^72*z0 - x^71*z0^2 + x^71*y - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^69 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*y + x^63*y*z0 + x^63*z0^2 + x^63*z0 + x^62*y*z0 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*z0 - x^59*z0^2 + x^60 - x^59*y - x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 - x^56*y*z0^2 - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^55*y*z0 - x^55*y + x^46, + x^115 - x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 - x^112*y - x^112*z0 + x^110*y*z0^2 + x^111*y + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^109*z0 - x^107*y*z0^2 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^106 + x^105*y + x^105*z0 - x^104*z0^2 - x^104*y - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^102*z0 - x^100*y*z0^2 + x^101*y + x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^99*y*z0 - x^99*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 + x^95*z0^2 - x^94*y*z0^2 + x^95*y - x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y + x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*y - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y - x^88*y*z0 - x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*z0^2 + x^87 + x^86*y - x^85*y*z0 - x^85*z0^2 + x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^84 - x^83*y - x^82*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 + x^80*y*z0^2 - x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^80*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y - x^77*y*z0 - x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^76 - x^75*y - x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 - x^71*y - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 + x^70*y - x^70*z0 - x^68*y*z0^2 - x^70 + x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y + x^65*y*z0 - x^65*z0^2 - x^66 + x^65*y + x^64*z0^2 + x^63*y*z0^2 + x^64*y - x^63*y*z0 + x^62*y*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 - x^61*y*z0^2 + x^62*y + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^61 + x^59*y*z0 - x^59*z0^2 + x^60 - x^59*y + x^59*z0 - x^58*z0^2 - x^57*y*z0^2 + x^58*y - x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56 + x^46*z0, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*y - x^110*z0 + x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 + x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*y*z0 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^105 - x^104*y + x^104*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 + x^102*y*z0 + x^103 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^95*y + x^95*z0 - x^94*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^91*y*z0 + x^92 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^89*y*z0 - x^89*z0^2 - x^89*y + x^89*z0 + x^88*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^88 - x^86*y*z0 + x^86*z0^2 - x^86*y + x^86*z0 - x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^84*y + x^84*z0 - x^84 - x^83*y + x^82*y*z0 + x^83 - x^82*y + x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*y - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^77 + x^76*y + x^75*y*z0 - x^74*y*z0^2 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*z0 - x^73*y*z0 + x^72*y*z0^2 + x^74 - x^73*z0 - x^72*z0^2 + x^73 - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*z0 - x^70*z0^2 - x^70*y - x^69*z0^2 + x^68*y*z0^2 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^67 + x^66*z0 + x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*z0^2 - x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y + x^59*y*z0 - x^58*y*z0^2 - x^60 + x^57*y*z0^2 - x^58*y + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^57*z0 + x^56*y*z0 + x^55*y*z0^2 - x^57 - x^56*y + x^55*y + x^46*z0^2, + -x^115 - x^114*z0 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^112 + x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^110*y - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^104*y*z0 - x^103*y*z0^2 - x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 - x^103 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^100*y*z0 + x^101 + x^100*z0 - x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y + x^97*z0^2 - x^96*y*z0^2 + x^97*y - x^96*y*z0 + x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^96 + x^95*z0 + x^94*y*z0 - x^93*y*z0^2 + x^95 + x^94*y - x^93*y*z0 - x^92*y*z0^2 + x^93*y + x^93 + x^92*y - x^91*y*z0 - x^91*z0^2 + x^92 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 + x^89*y + x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^88*y + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 - x^77*z0 + x^76*y*z0 - x^75*y*z0^2 - x^76*z0 - x^75*y*z0 + x^74*y*z0^2 + x^76 - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^70 - x^69*y - x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^68 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^65*z0^2 + x^64*y*z0^2 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 - x^64*y - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^61*y + x^60*y*z0 + x^60*z0^2 + x^61 - x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^60 + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^58*y + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^46*y, + -x^115 - x^114*z0 + x^113*z0 + x^112*z0^2 + x^112*y + x^111*y*z0 + x^111*z0^2 + x^112 - x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 - x^108*y*z0^2 - x^110 - x^109*y + x^108*y*z0 + x^107*y*z0^2 - x^109 + x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 - x^107 - x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^106 + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^104*z0 - x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 + x^101*y*z0^2 - x^102*y - x^101*y - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^99*y*z0 + x^98*y*z0^2 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^99 - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y - x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^95 + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^89*y + x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*y - x^83 - x^82*y - x^81*y*z0 + x^82 - x^81*y - x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*z0 + x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 + x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^78 + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 - x^77 + x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 + x^74 - x^73*y + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 + x^70*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^69*y - x^69*z0 - x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 + x^68 - x^67*y - x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*z0^2 + x^63*y*z0^2 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^62 - x^61*z0 + x^60*y*z0 + x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*z0^2 - x^59 - x^57*y*z0 + x^57*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^57 - x^56*y + x^55*y*z0 - x^56 + x^55*y + x^46*y*z0, + -x^114*z0 - x^113*z0^2 - x^114 + x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*y - x^108*z0 - x^108 - x^107*y + x^107*z0 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*y + x^104*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^100*y*z0 - x^99*y*z0^2 - x^100*y - x^100*z0 - x^98*y*z0^2 + x^99*y - x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*y + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 + x^94*z0^2 - x^94*y - x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y + x^92*y*z0 + x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*z0^2 - x^89 - x^88*y - x^88*z0 - x^86*y*z0^2 + x^88 - x^87*z0 + x^86*z0^2 + x^87 + x^86*y - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^85 + x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y - x^83 + x^82*y - x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 + x^80*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 - x^79*y - x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y + x^75*z0 + x^74*y*z0 - x^75 + x^74*y - x^74*z0 - x^73*y*z0 - x^73*y - x^73*z0 - x^72*z0^2 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^71*y + x^69*y*z0^2 + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^70 - x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*y + x^66*z0 - x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*z0^2 + x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 + x^60*y + x^59*y*z0 - x^59*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^57*z0 - x^56*z0^2 + x^55*y*z0^2 - x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^46*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 + x^113 - x^112*y - x^112*z0 + x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 - x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^110 + x^109*y - x^109*z0 - x^108*y*z0 - x^109 - x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y + x^105*z0^2 + x^106 - x^105*z0 - x^104*z0^2 + x^105 + x^104*y + x^104*z0 - x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^103 - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^99*y*z0^2 - x^100*y - x^100*z0 - x^98*y*z0^2 + x^100 + x^99*z0 - x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*z0^2 - x^96*y + x^95*y*z0 - x^94*y*z0^2 - x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^94*y + x^94*z0 + x^92*y*z0^2 - x^94 + x^93*y + x^92*z0^2 - x^93 - x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*y + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y + x^86*y*z0 - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^86 + x^85*y + x^85*z0 - x^83*y*z0^2 + x^85 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0 + x^80*z0^2 - x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^79*y - x^79*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^76*y*z0^2 - x^78 - x^76*y*z0 + x^76*z0^2 + x^77 + x^76*y - x^76*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 + x^73*y*z0^2 - x^74*y - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 + x^73 - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y + x^69*z0^2 + x^68*y*z0^2 - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^68 + x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*y + x^65*z0 + x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 + x^62*y*z0^2 + x^63*y + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*y - x^61*z0 - x^60*y + x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y*z0 + x^55*y + x^47, + x^114 + x^113*z0 - x^112*z0^2 - x^113 - x^112*z0 + x^112 - x^111*y - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^109*y - x^108*z0^2 - x^107*y*z0^2 + x^108*y - x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^105*y*z0^2 + x^107 - x^106*y - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y + x^103*y*z0 - x^103*z0^2 - x^103*z0 + x^102*y*z0 - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^100 - x^98*y*z0 - x^98*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*y*z0 - x^94 + x^93*y + x^93*z0 + x^92*z0^2 - x^93 + x^92*y - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^91*z0 - x^90*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 - x^89*y + x^88*y*z0 + x^87*y*z0^2 - x^88*y - x^88*z0 + x^87*y*z0 + x^88 + x^87*y - x^86*y*z0 - x^86*z0^2 - x^87 - x^85*y*z0 + x^85*z0^2 + x^86 + x^85*y + x^85*z0 - x^84*y*z0 - x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 - x^82*y*z0^2 - x^83*y + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*y - x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^78*y*z0^2 - x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y + x^77*z0^2 - x^77*y - x^77*z0 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y + x^75*z0 + x^74*z0^2 + x^73*y*z0^2 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 - x^73 + x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 + x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 + x^68*y*z0 - x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^64*z0^2 - x^65 + x^64*y - x^64*z0 - x^63*y*z0 + x^63*y + x^63*z0 - x^61*y*z0^2 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 + x^61 - x^60*y + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^56*y*z0 - x^55*y*z0^2 - x^56*y - x^55*y*z0 + x^47*z0, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^111*y - x^111*z0 + x^110*y*z0 - x^111 + x^109*y*z0 + x^109*z0^2 + x^110 + x^108*y*z0 + x^108*z0^2 - x^109 + x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 - x^106*y*z0 + x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 - x^105 + x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 + x^102*y - x^101*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^97*y - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*z0 + x^95*y*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y + x^93*y*z0 + x^94 + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 - x^91*z0^2 - x^90*y*z0 + x^89*y*z0^2 - x^91 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y + x^88*y*z0 + x^87*y*z0^2 + x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^85*y*z0 - x^85*y + x^83*y*z0^2 + x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y + x^80*z0 + x^79*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^79 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y + x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*y*z0 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 - x^75 + x^74*y + x^74*z0 - x^73*y*z0 - x^74 - x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 - x^71*y*z0 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^70 + x^69*y + x^68*y*z0 + x^68*z0^2 + x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*z0 + x^66*z0^2 - x^67 - x^66*z0 - x^64*y*z0^2 - x^65*y + x^64*y*z0 + x^65 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^63*z0 + x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^56*y*z0 - x^56*y - x^56*z0 - x^55*y + x^47*z0^2, + -x^115 - x^114*z0 - x^114 - x^112*z0^2 + x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^112 + x^111*y - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*z0^2 + x^107*y*z0^2 - x^108*y - x^108*z0 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^105*y*z0^2 - x^107 - x^106*y - x^105*y*z0 + x^104*y*z0^2 - x^105*y + x^104*z0^2 + x^105 - x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^101*y*z0 + x^100*y*z0^2 + x^101*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 - x^99*z0^2 - x^99*y + x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 + x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 - x^92*z0^2 + x^92*z0 - x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*z0^2 + x^91 - x^90*y - x^89*y*z0 - x^89*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^83*y*z0 - x^82*y*z0^2 - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 - x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*z0 - x^76*y*z0^2 - x^77*y + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^76 + x^75*y + x^74*y*z0 - x^73*y*z0^2 - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^73*y + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 - x^69*y*z0^2 + x^71 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*z0 + x^66*z0^2 - x^66*y + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y - x^63*y*z0 - x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 + x^62*z0^2 + x^63 + x^62*y - x^62*z0 - x^60*y*z0^2 + x^61*z0 - x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 + x^59*y*z0 + x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^58 - x^57*y + x^57*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^47*y, + x^114*z0 + x^113*z0^2 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*z0^2 - x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 + x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y - x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 - x^105*y*z0 + x^106 - x^104*y*z0 - x^105 - x^104*y - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 + x^102*y*z0 + x^103 + x^102*y + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^100 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^98 - x^97*y + x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^96*z0 - x^95*z0^2 - x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^94*y - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 - x^92 + x^90*y*z0 + x^90*y - x^90*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*z0 - x^85*y*z0 - x^84*y*z0^2 - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*y - x^82*y*z0 + x^81*y*z0^2 - x^83 + x^82*z0 - x^81*y*z0 - x^80*y*z0 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*y + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^73*y - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^71*y - x^71*z0 + x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 + x^69 - x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 - x^63*y*z0 + x^62*y*z0^2 - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*y*z0 + x^57 + x^56*z0 + x^47*y*z0, + -x^113 - x^112*z0 + x^111*z0^2 + x^112 - x^111*z0 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y + x^108*y*z0 + x^108*z0^2 + x^109 + x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 - x^103*z0^2 + x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*y - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 - x^98*y*z0 + x^97*y*z0^2 - x^98*y - x^97*z0^2 + x^96*y*z0^2 - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*z0^2 + x^96 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y - x^94*z0 + x^93*y*z0 + x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*y - x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 - x^84*y*z0^2 - x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^83*y*z0 + x^83*z0^2 - x^84 + x^83*y + x^83*z0 + x^83 + x^82*y - x^81*y*z0 - x^81*y + x^81*z0 - x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*z0 + x^79*y*z0 + x^78*y*z0^2 + x^79*y + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*z0 + x^76*y*z0^2 - x^77*y - x^76*y - x^75*y*z0 - x^74*y*z0^2 + x^75*y - x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*y + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^70*y - x^70*z0 - x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 - x^63*y*z0^2 - x^65 - x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^62*z0^2 - x^63 + x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^60*y*z0 - x^60*z0^2 - x^60*y - x^60*z0 + x^58*y*z0^2 + x^60 - x^59*y - x^58*y*z0 - x^58*z0^2 + x^59 + x^58*y - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^57*z0 - x^56*z0^2 + x^57 - x^56*y - x^56*z0 - x^56 + x^47*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^112*y + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 + x^110*z0^2 + x^111 + x^109*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^106*y*z0^2 - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 - x^101*z0^2 - x^102 + x^101*y + x^101 + x^100*y - x^99*z0^2 - x^99*y - x^98*y*z0 + x^97*y*z0^2 + x^98*z0 - x^97*y*z0 + x^96*y*z0^2 - x^98 + x^97*z0 + x^96*y*z0 + x^95*y*z0^2 - x^96*y - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*z0 - x^89*y - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 - x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*z0^2 + x^83*z0 + x^82*y*z0 - x^82*y + x^81*y*z0 - x^81*z0^2 + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^77*z0^2 + x^76*y*z0^2 + x^76*z0^2 + x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 - x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^71 - x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^70 + x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 + x^67*y - x^66*z0^2 + x^65*y*z0^2 - x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y - x^65*z0 - x^64*y*z0 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y + x^62*y*z0 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^61 + x^60*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*y - x^58*y*z0 + x^57*y*z0^2 + x^59 - x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^58 - x^57*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56*y - x^56*z0 + x^55*y*z0 - x^55*y + x^48, + x^115 + x^114*z0 - x^113*z0 - x^112*z0^2 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^112 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^107 + x^106*y - x^105*y*z0 + x^105*z0^2 + x^106 + x^105*y + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^104 + x^103*y - x^102*y*z0 + x^102*z0^2 - x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^95*z0 - x^94*y*z0 + x^93*y*z0^2 + x^95 - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^92*y*z0 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 + x^90 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*z0 - x^87*y*z0 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^87 - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^84 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y + x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y + x^77*y*z0^2 - x^79 - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^75*y + x^75*z0 + x^75 - x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*z0 - x^70 - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^68*y + x^68*z0 - x^67*y*z0 + x^68 - x^66*z0^2 - x^67 - x^66*y + x^66*z0 - x^65*z0^2 - x^66 - x^65*y + x^65*z0 + x^64*z0^2 - x^65 - x^64*y + x^64*z0 - x^63*y*z0 - x^64 + x^63*y - x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^63 + x^62*y + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^60*y*z0 - x^60*z0^2 + x^61 - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*z0 - x^56*y*z0 - x^57 - x^56*y - x^55*y*z0 - x^55*y + x^48*z0, + -x^115 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^112*y - x^112*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 + x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*z0 + x^109*y*z0 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^108*y - x^107*y*z0 - x^107*z0^2 - x^108 - x^107*y + x^106*y*z0 + x^105*y*z0^2 - x^107 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^104*y*z0 - x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 - x^104 + x^103*y + x^103*z0 + x^102*z0^2 - x^103 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 - x^100*y + x^98*y*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^95*z0^2 - x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*y + x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 + x^91*z0^2 - x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^90*y + x^90*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y - x^89*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 + x^86*y*z0^2 - x^87*y - x^87*z0 - x^86*y*z0 + x^87 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^85 + x^84*z0 - x^83*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^81*y*z0 - x^80*y*z0^2 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^78*y*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y + x^76*y*z0 - x^76*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*y*z0 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^73*y + x^73*z0 + x^71*y*z0^2 - x^72*y + x^71*y*z0 + x^70*y*z0^2 - x^72 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*z0 - x^67*y*z0^2 - x^69 + x^68*y - x^67*z0^2 + x^66*y*z0^2 - x^68 + x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^65 + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y - x^62*y*z0 - x^61*y*z0^2 + x^63 + x^62*y - x^61*z0^2 + x^60*y*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 + x^60 + x^59*y - x^59*z0 + x^57*y*z0^2 - x^59 + x^56*y*z0^2 - x^58 + x^56*z0^2 + x^55*y*z0^2 - x^56 + x^48*z0^2, + -x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^109 + x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*y + x^104*z0 - x^103*z0^2 - x^103*y + x^102*z0^2 + x^103 + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*y - x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 - x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y + x^97*z0 - x^97 - x^96*y - x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*z0 - x^92*y*z0 - x^91*y*z0^2 + x^92*z0 + x^91*y*z0 + x^91*y - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^88*y + x^88*z0 + x^87*y*z0 + x^88 + x^87*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^84*y - x^84*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^83 - x^82*z0 - x^80*y*z0^2 + x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^78*y + x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*y + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^75*y*z0 + x^75*z0^2 + x^76 + x^75*y + x^75*z0 - x^73*y*z0^2 - x^75 + x^74*y - x^73*z0^2 + x^72*y*z0^2 - x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^69 - x^68*y + x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 - x^65*y*z0^2 + x^67 - x^66*y + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 + x^65*y - x^65*z0 - x^64*y*z0 + x^63*y*z0^2 - x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 - x^59*z0 + x^57*y*z0^2 + x^59 - x^58*y + x^58 - x^57*y - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^55*y*z0 - x^56 - x^55*y + x^48*y, + -x^114*z0 - x^113*z0^2 - x^113*z0 + x^111*y*z0 + x^110*y*z0^2 + x^112 + x^110*y*z0 + x^110*z0^2 + x^111 - x^110*z0 - x^109*z0^2 - x^110 - x^109*y - x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y - x^105*y*z0 + x^105*z0^2 + x^105*y - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^100*y*z0 - x^100*z0^2 + x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^100 - x^98*y*z0 - x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^96*y*z0^2 + x^97*y - x^96*y*z0 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 - x^93*y*z0^2 - x^94*y - x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 + x^92*z0^2 - x^93 + x^92*y + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*z0 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 + x^86*z0^2 - x^87 - x^86*y + x^86*z0 + x^85*y*z0 - x^86 - x^85*y + x^85*z0 - x^83*y*z0^2 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 - x^83*y - x^83 + x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^80*z0^2 - x^79*y*z0^2 + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^79*y + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 - x^76 - x^75*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 + x^74 - x^73*z0 - x^71*y*z0^2 - x^73 + x^71*y*z0 - x^70*y*z0^2 + x^72 + x^69*y*z0^2 - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*y - x^67*y*z0^2 - x^69 + x^68*y - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 + x^56*y*z0 + x^55*y*z0^2 + x^55*y*z0 - x^56 - x^55*y + x^48*y*z0, + -x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^113 - x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^105*y - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^101*y*z0 + x^101*z0^2 + x^101*y - x^101*z0 + x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*y + x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y + x^98*y*z0 + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^97 - x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y - x^94*y*z0 - x^94*y - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^92 + x^91*y + x^91*z0 + x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^88*y*z0 + x^88*z0^2 + x^89 + x^88*y - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^87*y - x^86*y*z0 + x^85*y*z0^2 + x^87 + x^85*y*z0 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^81*y*z0 - x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 - x^81 + x^80*z0 - x^79*z0^2 - x^80 - x^79*y + x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y + x^76*y*z0^2 + x^77*y + x^77*z0 + x^75*y*z0^2 - x^77 - x^76*z0 + x^76 + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^74*y - x^74*z0 + x^73*y*z0 - x^72*y*z0^2 - x^74 - x^72*y*z0 - x^73 + x^72*z0 + x^70*y*z0^2 - x^72 + x^71*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 + x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^65*y*z0^2 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^64*y*z0 + x^65 - x^64*y - x^64*z0 - x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^59*z0 - x^57*y*z0^2 - x^58*y + x^57*y*z0 + x^57*z0^2 - x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^55*y*z0 + x^56 + x^48*y*z0^2, + x^114*z0 + x^113*z0^2 - x^113*z0 - x^113 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 + x^112 - x^111*z0 + x^110*y*z0 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^110 - x^109*y - x^109*z0 + x^108*y*z0 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*z0 - x^100 + x^99*y - x^99 - x^98*y + x^98*z0 + x^97*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y - x^94*z0 + x^93*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*y + x^91*z0^2 - x^90*y*z0^2 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*z0^2 + x^83*y*z0^2 + x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 + x^83 + x^82*z0 - x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 - x^80*z0 - x^79*y*z0 - x^78*y*z0^2 + x^80 - x^79*y - x^78*y*z0 - x^78*y - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^76 - x^75*y - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^74 - x^73*z0 + x^72*z0^2 + x^73 + x^72*y - x^71*y*z0 + x^71*z0^2 + x^72 + x^71*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y + x^68*y*z0 + x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^66 + x^65 + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 + x^63 - x^62*z0 + x^61*z0^2 + x^62 - x^61*y - x^60*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^59 - x^58*y + x^58 + x^57*y + x^57*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 + x^56 + x^55*y + x^49, + -x^114*z0 - x^113*z0^2 + x^114 - x^112*z0 + x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 - x^110*z0^2 + x^111 + x^109*y*z0 + x^109*z0^2 - x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*z0 + x^106*z0^2 + x^107 + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0 - x^100 + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*z0 - x^95*y*z0^2 - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^96 - x^95*y + x^95*z0 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^92 - x^91*y - x^91*z0 - x^89*y*z0^2 - x^90*y + x^89*z0^2 - x^88*y*z0^2 + x^89*z0 - x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 + x^86*y + x^86*z0 - x^84*y*z0^2 + x^86 - x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 - x^84 + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^83 - x^82*y - x^82*z0 + x^81*z0^2 + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^77*z0 + x^76*y*z0 + x^77 + x^76*z0 + x^75*y*z0 - x^76 - x^75*z0 - x^74*z0^2 + x^75 + x^73*y*z0 - x^74 - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^71*y - x^70*y*z0 + x^70*z0^2 + x^71 - x^70*y + x^70*z0 + x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^68*y + x^67*y*z0 - x^66*y*z0^2 - x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 - x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*z0 - x^63*y*z0^2 - x^65 + x^64*y - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^61 - x^60*y - x^59*z0^2 + x^58*y*z0^2 + x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 - x^56 + x^49*z0, + x^115 + x^114*z0 + x^114 + x^113*z0 + x^112*z0^2 - x^113 - x^112*y - x^111*y*z0 - x^112 - x^111*y - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y - x^109*z0^2 + x^110 + x^109*y + x^109*z0 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^107 + x^106*y - x^105*y*z0 - x^105*z0^2 + x^105*y - x^105*z0 + x^104*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 + x^104 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*z0^2 + x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^99*y - x^98*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^98 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^93*y*z0 - x^93*z0^2 + x^94 - x^93*y - x^93*z0 - x^92*y*z0 - x^91*y*z0^2 - x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*y - x^86*y*z0 - x^86*z0^2 + x^86*y - x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^85 - x^84*z0 + x^83*z0^2 - x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*y + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^82 - x^81*y - x^80*y*z0 - x^80*y - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^79*z0 + x^78*z0^2 + x^79 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^78 + x^77*y - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^76*y - x^75*y*z0 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 + x^74*z0^2 + x^75 - x^74*y - x^73*z0^2 + x^72*y*z0^2 + x^74 - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71 + x^70*y + x^70*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^67 + x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^63*y*z0^2 - x^64*y + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*y - x^63 - x^62*y - x^61*y*z0 + x^61*z0^2 + x^62 + x^61*y + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y + x^59*y*z0 - x^59*z0^2 + x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^58*y + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*z0 + x^55*y*z0 - x^56 + x^49*z0^2, + x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*y + x^110*y*z0 - x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*y + x^109*z0 - x^109 - x^108*z0 - x^107*y*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 + x^104*z0^2 - x^105 - x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y + x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*z0 + x^92*y*z0^2 - x^94 - x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*y + x^92*z0 - x^91*z0^2 - x^90*y*z0^2 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*z0 - x^89*y*z0 - x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 + x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*z0^2 + x^81*y - x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y - x^78*y*z0 - x^77*y*z0^2 + x^79 + x^78*y - x^76*y*z0^2 - x^78 + x^77*y + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^73*y*z0^2 + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*z0 + x^72*z0^2 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^71 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^68*y*z0 - x^68*z0^2 - x^68*y - x^68*z0 - x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 + x^66*z0^2 - x^67 - x^66*y - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*y + x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^63*y*z0 + x^62*y*z0^2 - x^64 + x^62*z0^2 - x^63 - x^62*y + x^62*z0 + x^61*z0^2 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^58*y*z0^2 - x^60 - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y + x^58*z0 + x^57*y*z0 - x^58 - x^56*y*z0 - x^56*y + x^55*y*z0 - x^55*y + x^49*y, + x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 + x^112*z0^2 - x^113 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*z0 - x^110*y*z0 - x^109*y*z0^2 + x^110*y - x^109*z0^2 - x^108*y*z0^2 - x^109*y - x^108*y*z0 - x^108*z0^2 + x^109 + x^108*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^101*y*z0 + x^100*y*z0^2 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^99*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^98 + x^96*y*z0 + x^95*y*z0^2 - x^96*y - x^96*z0 - x^94*y*z0^2 - x^95*y - x^95*z0 + x^94*y*z0 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 + x^94 - x^93*y - x^92*y*z0 - x^93 + x^92*y - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^91*z0 + x^90*y*z0 + x^89*y*z0^2 + x^91 + x^90*z0 - x^89*z0^2 + x^90 - x^89*y + x^89*z0 + x^88*y*z0 - x^88*y + x^88*z0 - x^87*z0^2 - x^87*y - x^87*z0 + x^86*z0^2 + x^87 - x^86*y - x^86*z0 + x^86 + x^85*y - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*y*z0 + x^84 + x^83*y - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y + x^81*y*z0 - x^81*z0^2 - x^82 + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^79*y*z0 - x^79*z0^2 + x^80 - x^79*y - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 - x^76 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^74*y + x^73*y*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 + x^72*z0^2 + x^73 - x^72*y + x^70*y*z0^2 - x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 + x^69*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^69 + x^68*z0 - x^67*y*z0 - x^68 + x^67*y + x^66*z0^2 - x^67 - x^66*y + x^66*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^64*y + x^64*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*z0 + x^60*y*z0^2 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y + x^58*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^55*y*z0 - x^55*y + x^49*y*z0, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y + x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 - x^108 - x^107*y + x^107*z0 - x^105*y*z0^2 - x^106*y - x^105*y*z0 - x^105*z0^2 + x^106 - x^105*y + x^105*z0 + x^104*z0^2 - x^105 + x^104*y - x^103*y*z0 - x^103*y + x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^101 + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^97 - x^96*y - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^95 - x^94*z0 + x^92*y*z0^2 + x^94 - x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*y + x^92*z0 + x^90*y*z0^2 - x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^86*y*z0^2 + x^88 - x^87*y + x^87*z0 + x^86*z0^2 + x^87 + x^85*y*z0 - x^84*y*z0^2 - x^86 + x^84*y*z0 - x^84*z0^2 - x^84*z0 - x^83*y*z0 - x^82*y*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^82 - x^81*y + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^80*y + x^79*y*z0 - x^80 + x^79*z0 + x^77*y*z0^2 - x^79 - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 + x^75*z0^2 + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^73 - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*y + x^70*y*z0 + x^70*z0^2 - x^70*z0 + x^69*z0 - x^68*y*z0 - x^67*y*z0^2 - x^69 + x^68*z0 + x^67*z0^2 - x^65*y*z0^2 + x^65*y + x^65*z0 + x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y + x^61*y*z0 + x^61*z0^2 + x^62 + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^60*y - x^60*z0 - x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*y + x^58*y*z0 - x^58*z0^2 - x^59 - x^58*z0 - x^57*z0^2 + x^58 + x^57*z0 - x^56*y*z0 - x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^55*y + x^49*y*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^110*y + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*z0 + x^108*z0^2 - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^106*z0^2 + x^107 + x^106*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^104*y - x^104*z0 + x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^103*z0 + x^102*z0^2 + x^101*y*z0^2 + x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^99*y*z0^2 + x^101 + x^100*y - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^99*y + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^97*y - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 - x^96 - x^95*y - x^95*z0 + x^94*y*z0 + x^95 - x^93*z0^2 + x^94 + x^93*z0 + x^91*y*z0^2 - x^93 - x^92*y + x^91*y*z0 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^90*y + x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 + x^87*y - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y - x^85*y*z0 - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^84 + x^83*y + x^83*z0 - x^82*z0^2 - x^83 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*y*z0 + x^79 + x^77*y*z0 + x^76*y*z0^2 + x^78 - x^76*y*z0 + x^76*z0^2 + x^77 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^72*y + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^71*y - x^71*z0 + x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^69 - x^68*z0 - x^66*y*z0^2 - x^68 + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^61*y*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^56*y - x^56*z0 - x^55*y*z0 + x^55*y + x^50, + x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 + x^109*y*z0^2 - x^111 - x^110*y - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*z0^2 + x^109 + x^108*y - x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^107 + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y + x^102*z0^2 - x^101*y*z0^2 + x^103 + x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^100*y - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 + x^93*z0^2 - x^93*z0 - x^92*z0^2 + x^91*y*z0^2 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 - x^90 - x^89*y + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^89 + x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^84*y*z0 - x^84*z0^2 - x^85 + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^84 - x^81*y*z0^2 - x^83 - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^81*y - x^80*z0^2 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y - x^78*y*z0 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^75*y + x^74*y*z0 - x^75 + x^73*y*z0 - x^72*y*z0^2 - x^74 + x^73*y - x^72*y*z0 - x^72*z0^2 - x^72*y - x^71*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y + x^67*z0^2 + x^67*y + x^67*z0 - x^67 + x^66*y + x^66*z0 + x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 + x^65 + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*z0 - x^62*y*z0 - x^63 + x^61*z0^2 + x^60*y*z0^2 - x^61*y - x^60*y*z0 + x^61 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^59 + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^57 + x^56*z0 - x^56 + x^50*z0, + x^115 + x^114*z0 - x^114 + x^113*z0 - x^112*z0^2 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^112 + x^111*y - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*z0 - x^109*y*z0 - x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 - x^108*z0^2 + x^108*y - x^107*y*z0 - x^107*z0^2 + x^108 + x^105*y*z0^2 + x^107 + x^105*y*z0 - x^104*y*z0^2 + x^106 + x^104*y*z0 + x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*y*z0 - x^102*y - x^101*z0^2 + x^102 + x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y + x^99*z0^2 - x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*y + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^94*y*z0^2 - x^95*y + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^94 - x^93*y - x^92*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^84*z0 - x^83*z0^2 + x^83*y + x^83*z0 + x^82*z0^2 - x^83 + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*z0 - x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^79 + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*z0 - x^75*y*z0 - x^76 + x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^74 - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^73 - x^72*z0 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0 + x^68*y*z0^2 - x^70 + x^69*y + x^68*y*z0 + x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*z0^2 - x^65 + x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^61*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 + x^58*z0^2 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y*z0 + x^56 + x^55*y + x^50*z0^2, + -x^115 + x^113*z0^2 + x^112*z0^2 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 + x^109*y*z0 + x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^108*y - x^107*y*z0 + x^107*z0^2 + x^108 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*z0^2 - x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y + x^103*y*z0 + x^103*z0^2 - x^104 + x^103*y + x^103 + x^102*y + x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*y + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^95*y - x^95*z0 - x^94*z0^2 - x^95 + x^93*y*z0 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y - x^91*z0 - x^90*z0^2 + x^90*y + x^90*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*z0 + x^85*y*z0 + x^84*y*z0^2 + x^85*y - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 - x^84*y - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^82*y*z0 - x^82*z0^2 + x^82*z0 - x^82 - x^81*y + x^80*y*z0 - x^80*z0^2 + x^81 - x^80*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*y - x^79*z0 + x^77*y*z0^2 - x^79 + x^78*y + x^77*y*z0 + x^76*y*z0^2 + x^77*y - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^74*y*z0^2 - x^76 + x^75*z0 + x^74*y*z0 - x^73*y*z0^2 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 + x^69*y*z0 - x^69*y - x^68*z0^2 - x^69 - x^68*y + x^67*y*z0 + x^66*y*z0^2 + x^68 - x^67*z0 + x^65*y*z0^2 + x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^61*y*z0 + x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^57*y*z0 - x^57*y + x^55*y*z0^2 + x^57 + x^56*y - x^56 + x^55*y + x^50*y, + -x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 + x^111*y*z0 + x^110*y*z0^2 - x^111*y - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*y - x^109*y*z0 + x^109*z0^2 - x^110 + x^109*z0 + x^107*y*z0^2 + x^109 - x^108*z0 + x^107*z0^2 - x^106*y*z0^2 + x^107*y - x^107*z0 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 - x^102*y*z0 + x^102*z0^2 + x^103 + x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y - x^101*z0 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*y*z0 + x^98*y*z0^2 - x^100 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y + x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^91*y - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 + x^89*y + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^86*y*z0 + x^85*y*z0^2 + x^86*y - x^85*y*z0 - x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^83*y - x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^80*y - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*z0 - x^75*z0^2 + x^76 + x^75*y + x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y + x^72*y*z0^2 + x^74 - x^73*z0 - x^71*y*z0^2 + x^73 + x^72*y - x^71*y*z0 - x^71*z0^2 + x^72 + x^71*y + x^69*y*z0^2 - x^71 - x^70*y + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^67 + x^66*y - x^66*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y - x^64*z0^2 - x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*z0 - x^62*y*z0 + x^63 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 + x^60*z0^2 - x^60*y - x^59*y*z0 + x^59*z0^2 + x^59*y + x^58*y*z0 - x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^55*y*z0^2 + x^57 + x^56*y - x^55*y*z0 - x^56 + x^50*y*z0, + x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 + x^112*z0^2 - x^112*y + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y - x^109*z0 + x^107*y*z0^2 - x^109 - x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*z0 - x^105*z0^2 + x^106 - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^103*y*z0 + x^103*z0^2 + x^104 - x^103*y + x^103*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^100*z0^2 + x^99*y*z0^2 + x^100*y + x^100*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^97 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y + x^94*y*z0 - x^93*y*z0^2 - x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*z0 - x^92 - x^91*y - x^90*y*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y - x^89*z0 - x^88*y*z0 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 + x^85*z0^2 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^81*z0 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^78*y*z0^2 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*z0^2 - x^74*y*z0^2 - x^75*y + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*z0 + x^70*y*z0^2 - x^71*y - x^71*z0 - x^70*y*z0 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^67*y*z0 + x^66*y*z0^2 - x^68 - x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66 - x^65*y + x^65*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^63*y*z0 - x^63*z0^2 + x^63*y - x^61*y*z0^2 - x^63 + x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^59*y - x^59*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^57*y + x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^56*y + x^56*z0 - x^55*y*z0 - x^55*y + x^50*y*z0^2, + -x^115 + x^113*z0^2 - x^112*z0^2 - x^113 + x^112*y + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^109*y*z0^2 - x^111 + x^110*y - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^108*z0^2 + x^108*y + x^108*z0 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 - x^107 + x^106*y - x^105*y*z0 - x^105*z0^2 - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^105 + x^104*y - x^104*z0 - x^104 - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*y - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*y + x^98*y*z0 - x^97*y*z0^2 + x^98*y - x^98*z0 - x^97*y*z0 + x^98 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^88*y + x^88*z0 + x^86*y*z0^2 + x^88 + x^87*y + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^85*y + x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 + x^84*z0 - x^83*y*z0 - x^84 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^80*y + x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*z0^2 - x^79 + x^78*y - x^78*z0 - x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*y - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^70*y + x^69*y*z0 + x^69*z0^2 + x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^68*y + x^68*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^64*z0^2 - x^63*y*z0^2 + x^64*z0 - x^64 + x^62*y*z0 - x^61*y*z0^2 - x^62*y - x^62*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 + x^60*y*z0 + x^60*y - x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*z0^2 - x^58*y + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y - x^56*y*z0 - x^56*z0^2 - x^56*y + x^55*y*z0 - x^56 + x^51, + x^115 - x^114*z0 + x^113*z0^2 - x^113*z0 + x^113 - x^112*y + x^111*y*z0 - x^110*y*z0^2 - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^110*y - x^109*z0^2 - x^110 - x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^107 + x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^103*z0^2 - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^103 + x^101*y*z0 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*z0 + x^93*y*z0 + x^94 + x^93*y - x^93*z0 - x^92*y*z0 + x^91*y*z0^2 - x^93 + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*z0 + x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^89 - x^88*y + x^86*y*z0^2 - x^88 + x^87*y + x^86*y*z0 - x^86*z0^2 + x^87 + x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^86 + x^84*z0^2 - x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 + x^82*z0^2 - x^83 + x^82*y - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*z0 + x^80*y*z0 + x^80*y + x^79*z0^2 - x^80 + x^79*z0 + x^77*y*z0^2 + x^79 - x^77*y*z0 + x^77*z0^2 + x^77*y + x^76*z0^2 + x^77 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*z0 + x^73*z0^2 + x^72*y*z0^2 + x^73*y - x^73*z0 + x^72*y*z0 + x^73 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^70 - x^69*z0 - x^68*y*z0 - x^69 - x^68*y - x^67*y*z0 + x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y + x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y - x^62*z0^2 + x^63 + x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*z0 - x^59*y*z0^2 - x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 + x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^59 - x^57*z0^2 - x^56*y*z0^2 + x^57*z0 - x^56*z0^2 + x^57 - x^56*y + x^55*y*z0 - x^56 + x^55*y + x^51*z0, + -x^113*z0 - x^112*z0^2 + x^113 + x^111*z0^2 - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^109*z0^2 - x^108*y*z0^2 - x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^108*y + x^106*y*z0^2 - x^108 + x^106*y*z0 + x^107 + x^106*z0 + x^105*y*z0 + x^104*y*z0^2 + x^106 + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^104*y + x^104*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^101*z0^2 - x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^100*y + x^100*z0 + x^98*y*z0^2 - x^100 - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^98*y + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 - x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*z0 + x^90*y*z0 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^89 + x^88*z0 + x^87*z0^2 + x^88 - x^87*y + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*z0^2 + x^82 + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^80*y - x^79*y*z0 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^76*y + x^76*z0 - x^76 + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^73*y - x^72*y*z0 - x^72*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 + x^68*y*z0^2 - x^70 - x^69*y + x^68*z0^2 - x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 - x^67*z0 + x^66*z0^2 - x^66*y + x^66*z0 - x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 + x^64*z0^2 + x^64*y - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^61*y*z0 + x^61*z0^2 - x^62 + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60 + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 - x^55*y*z0^2 - x^57 - x^56*y + x^55*y*z0 - x^55*y + x^51*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^111*y + x^110*y*z0 - x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 + x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^108 + x^106*z0^2 + x^105*y*z0^2 - x^106*z0 - x^105*y*z0 + x^106 + x^105*y + x^105*z0 + x^104*y*z0 - x^103*y*z0^2 + x^104*y + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102 + x^101*y + x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 - x^98*y*z0^2 - x^100 - x^99*y + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*z0^2 + x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 + x^91*z0^2 + x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^90*z0 - x^90 + x^89*y + x^88*y*z0 - x^89 - x^88*y - x^87*y*z0 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*z0 + x^85*y*z0 + x^85*y + x^84*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^84 + x^83*y - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^76*y*z0 + x^75*y*z0^2 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^75*z0 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^73 + x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^70 - x^69*y - x^69*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^67*z0^2 + x^66*y*z0^2 - x^67*z0 - x^67 - x^66*y + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 + x^64*y*z0 - x^65 - x^64*y - x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 - x^61*y*z0^2 + x^63 - x^62*y + x^61*z0^2 + x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 + x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^56*y + x^55*y*z0 - x^55*y + x^51*y, + -x^115 + x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*z0^2 + x^108*y*z0^2 - x^108*z0^2 + x^107*y*z0^2 - x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 - x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^102*z0 - x^102 - x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 - x^98*z0 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^95*y*z0^2 + x^97 + x^96*y - x^95*y*z0 - x^94*y*z0^2 + x^96 - x^95*y + x^94*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^91*y*z0^2 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*y + x^89*z0 - x^88*z0^2 + x^89 - x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^88 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 + x^85*y - x^85*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 - x^83*y*z0 + x^84 - x^83*z0 + x^82*y*z0 - x^81*y*z0^2 - x^83 + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^81 - x^80*y + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^78 - x^77*y + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^73*z0 + x^72*z0^2 + x^73 + x^72*y - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 - x^70*z0^2 - x^71 + x^70*y - x^70*z0 - x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*y + x^67*z0 - x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 + x^59*z0^2 - x^59*y - x^58*y*z0 + x^58*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^51*y*z0, + -x^115 + x^114*z0 - x^113*z0^2 - x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 - x^111 + x^110*y + x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^109 + x^108*y - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^104*y*z0 + x^103*y*z0^2 + x^104*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*z0 + x^97*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 + x^92*y*z0^2 + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*z0 + x^91*y*z0 - x^92 - x^90*z0^2 - x^91 - x^90*y + x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^89*y + x^88*y*z0 - x^88*y - x^87*y*z0 + x^87*z0^2 - x^88 + x^87*y + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^86*y + x^85*y*z0 - x^86 + x^85*y - x^84*y*z0 + x^84*z0^2 + x^85 + x^84*z0 - x^83*z0^2 - x^84 + x^83*y - x^83*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*y - x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 + x^79*y + x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^75*z0^2 - x^76 + x^74*y*z0 - x^74*z0^2 + x^74*z0 + x^73*y*z0 - x^74 - x^73*y - x^72*y*z0 + x^71*y*z0^2 - x^72*y - x^71*y*z0 - x^71*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 - x^71 + x^70*y + x^70*z0 + x^68*y*z0^2 + x^70 - x^69*y - x^68*y*z0 + x^68*z0^2 - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 - x^66*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^61*y*z0 - x^60*y*z0^2 + x^62 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 - x^58 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^57 + x^55*y*z0 - x^56 - x^55*y + x^51*y*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^103*y*z0^2 + x^105 - x^104*z0 - x^103*y*z0 - x^104 - x^103*y - x^102*y*z0 + x^102*z0^2 + x^103 - x^102*z0 - x^101*y*z0 - x^102 + x^100*z0^2 - x^99*y*z0^2 + x^101 + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^96*z0 + x^95*z0^2 - x^94*y*z0^2 + x^95*y + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^93*y - x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^92*y + x^92*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^90*y + x^89*y*z0 - x^88*y*z0^2 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^84*y*z0^2 + x^86 + x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^77*z0^2 - x^76*y*z0^2 + x^77*y - x^76*z0^2 + x^75*y*z0^2 - x^74*y*z0 + x^73*y*z0^2 - x^74*y + x^74*z0 - x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 - x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^72*z0 - x^70*y*z0^2 + x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^70*y - x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 + x^65*y*z0^2 + x^67 + x^66*z0 + x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^61 - x^60*y + x^60*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^57*y*z0^2 + x^58*y + x^57*z0^2 + x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^56 + x^55*y + x^52, + x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 + x^113 - x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*y - x^106*z0 + x^105*y - x^105*z0 - x^105 - x^104*y + x^104*z0 + x^102*y*z0^2 + x^103*z0 + x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^97 + x^96*z0 + x^94*y*z0^2 - x^96 + x^95*y - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^94 - x^93*y - x^91*y*z0^2 - x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*z0 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^88*y*z0 + x^88*z0^2 - x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 + x^85*y*z0 - x^84*y*z0^2 - x^86 - x^85*y + x^84*y*z0 - x^84*y + x^83*z0^2 - x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*y + x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^78*y*z0 + x^77*y*z0^2 - x^79 - x^77*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y - x^72*z0 - x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^70*y - x^70*z0 + x^69*z0^2 - x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^64*y*z0 + x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^64 - x^63*y + x^62*z0^2 + x^62*z0 - x^61*y*z0 + x^62 - x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y + x^57*z0 - x^55*y*z0^2 + x^57 + x^56*z0 + x^56 + x^52*z0, + x^115 + x^114*z0 - x^114 + x^113*z0 - x^113 - x^112*y - x^111*y*z0 - x^111*z0^2 + x^111*y - x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^111 + x^110*y + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^108*z0 - x^106*y*z0^2 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^106*z0 - x^106 - x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 - x^102*y*z0^2 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 + x^102 + x^101*y - x^101*z0 - x^100*y*z0 - x^100*y - x^98*y*z0^2 + x^100 - x^99*y + x^99*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 - x^95*y*z0^2 + x^97 - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y + x^92*z0 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 - x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 + x^87 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 - x^80*y + x^79*y*z0 - x^79*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 + x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^77 + x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^72*z0 - x^70*y*z0^2 + x^71*y + x^70*y*z0 - x^70*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*z0^2 - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^65*y + x^64*y*z0 - x^64*z0^2 - x^65 - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^62 + x^61*z0 - x^60*y*z0 - x^59*y*z0^2 + x^61 + x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^55*y*z0^2 + x^56*y + x^55*y*z0 + x^56 + x^52*z0^2, + -x^115 + x^113*z0^2 + x^112*y + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*z0 - x^110*z0^2 - x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^106*y*z0 - x^105*y*z0^2 + x^106*y + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^101*y + x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^93*z0 + x^92*y*z0 - x^93 - x^92*z0 - x^91*z0^2 - x^90*y*z0^2 - x^90*z0^2 + x^89*y*z0^2 - x^90*y + x^90 - x^89*z0 + x^88*z0^2 - x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*z0 - x^86*y*z0 - x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*z0^2 + x^83*z0 - x^83 - x^82*y + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^80 - x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*z0 + x^76*y*z0 + x^77 - x^76*y - x^76*z0 + x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^70 + x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^67*y*z0 - x^67*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y + x^66*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^64*z0^2 - x^63*y*z0^2 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^63*z0 - x^62*z0^2 - x^63 + x^62*y - x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*z0 + x^57*y*z0 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 - x^55*y*z0^2 - x^57 - x^56*z0 + x^56 + x^52*y, + -x^115 - x^114*z0 + x^114 - x^112*z0^2 + x^112*y + x^112*z0 + x^111*y*z0 - x^112 - x^111*y - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*z0 - x^107*y*z0 - x^108 + x^107*y - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y + x^106*z0 + x^104*y*z0^2 - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 - x^103*y*z0 + x^102*y*z0^2 + x^103*y + x^103*z0 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 + x^100*y*z0^2 - x^102 - x^101*y - x^100*y*z0 + x^100*z0^2 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^99*y - x^99*z0 - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^97*y + x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 + x^95*y*z0 + x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^93*z0^2 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^93 - x^92*y + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*y + x^89*y*z0^2 + x^91 + x^90*y + x^89*y*z0 + x^89*z0^2 + x^89*z0 + x^87*y*z0^2 - x^88*y + x^87*y*z0 - x^87*z0^2 + x^87*y + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 - x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^83*y*z0 - x^82*y*z0^2 - x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 + x^81*y + x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 - x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^74*y*z0 + x^73*y*z0^2 + x^73*y*z0 + x^73*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 - x^72*y - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 + x^65*y*z0^2 + x^67 + x^66*z0 + x^65*y*z0 - x^66 - x^65*y + x^65*z0 + x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*y + x^64*z0 - x^63*y*z0 - x^62*y*z0^2 - x^64 + x^63*y + x^62*y*z0 + x^62*z0^2 - x^63 - x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y + x^60*y*z0 + x^59*y*z0^2 - x^60*y - x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 + x^58*y*z0 + x^59 - x^58*z0 + x^57*y*z0 + x^56*y*z0^2 - x^57*y + x^57 - x^56*y + x^55*y*z0 + x^56 + x^55*y + x^52*y*z0, + -x^115 + x^113*z0^2 - x^112*z0^2 - x^113 + x^112*y + x^112*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y - x^105*y*z0 + x^105*z0^2 - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^103*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 + x^98*y - x^97*y*z0 - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 - x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^94 - x^93*y - x^93*z0 + x^92*y*z0 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^89*y - x^89*z0 - x^87*y*z0^2 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y + x^85*z0 - x^84*z0^2 + x^85 + x^84*y + x^84*z0 + x^83*y*z0 - x^84 - x^83*y - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^79 - x^77*y*z0 - x^77*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 + x^76 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^73*y*z0 + x^73*z0^2 - x^74 + x^73*z0 - x^72*y*z0 - x^72*y + x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^71 - x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*y*z0 + x^67*y*z0^2 - x^69 - x^68*y - x^66*y*z0^2 + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*z0 - x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 + x^61*y + x^59*y*z0^2 - x^61 + x^60*z0 + x^58*y*z0 + x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*z0^2 + x^58 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 + x^52*y*z0^2, + x^115 + x^114*z0 - x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^111*y - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^107*z0 - x^105*y*z0^2 + x^107 + x^105*z0^2 + x^105*z0 - x^104*y*z0 - x^105 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*z0 + x^101*y*z0 - x^102 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*z0 + x^99*z0^2 - x^98*y*z0^2 - x^99*z0 + x^98*y*z0 + x^99 - x^98*z0 - x^97*z0^2 + x^96*y*z0^2 - x^97*z0 + x^96*y*z0 - x^95*y*z0^2 + x^97 + x^96*z0 - x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 - x^94*y - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y + x^90*z0 + x^89*y*z0 - x^88*y*z0^2 - x^90 + x^89*y - x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y + x^86*z0 - x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^82*y - x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^81*y - x^80*y*z0 - x^80*z0^2 - x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*z0 - x^75*y*z0 + x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y - x^73*z0^2 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^69*y + x^69*z0 - x^68*y*z0 + x^69 + x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y + x^66*z0^2 + x^66*y + x^66*z0 + x^64*y*z0^2 - x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 + x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^58 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^57 - x^56*z0 + x^55*y*z0 + x^55*y + x^53, + x^115 - x^113*z0^2 + x^112*z0^2 - x^112*y - x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*z0 - x^110*z0^2 - x^109*y*z0^2 + x^108*y*z0^2 + x^110 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*z0 + x^107*z0^2 + x^108 + x^107*y + x^106*y*z0 - x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^105*y + x^104*z0^2 + x^105 + x^104*y + x^104*z0 - x^103*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 + x^102*y + x^101*z0^2 + x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^94 - x^92*y*z0 - x^92*z0^2 - x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*z0^2 - x^91 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^89*y + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^84*z0^2 - x^84*y - x^82*y*z0^2 - x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*y + x^81*z0 + x^80*z0^2 + x^81 - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 - x^78*y - x^78*z0 - x^77*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*z0^2 - x^76*y + x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*z0 - x^71*z0^2 - x^71*y - x^71 - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^69*z0 - x^68*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^63*z0^2 + x^64 + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^61*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 - x^60*y - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^57*y*z0 + x^56*y*z0^2 - x^58 - x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y + x^53*z0, + -x^112*z0^2 - x^113 - x^112*z0 - x^111*z0^2 + x^112 - x^111*z0 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^108*y - x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 - x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 - x^104*y*z0^2 - x^106 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^103*z0^2 + x^102*y*z0^2 - x^103*y - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^100*z0^2 - x^99*y*z0^2 - x^100*z0 - x^99*y*z0 - x^100 + x^99*y - x^99*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^97 - x^96*z0 - x^95*y*z0 - x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^90*y - x^89*y*z0 + x^89*z0^2 - x^90 - x^89*y - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 - x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^81 + x^80*y + x^79*z0^2 - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 - x^76*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 + x^74*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^73*z0 - x^72*z0^2 + x^72*y - x^72*z0 + x^70*y*z0^2 + x^71 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^68*y*z0 - x^68*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 - x^65*y*z0 - x^64*y*z0^2 + x^66 + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*y + x^64*z0 + x^62*y*z0^2 + x^63*z0 - x^62*y*z0 - x^61*y*z0^2 + x^63 - x^62*y - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0 + x^56*z0^2 + x^56*z0 + x^53*z0^2, + -x^115 + x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^112*y + x^112*z0 - x^110*y*z0^2 + x^112 + x^111*z0 + x^110*y*z0 + x^109*y*z0^2 - x^109*y*z0 + x^109*z0^2 - x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^109 - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^106*y + x^106*z0 - x^105*y*z0 + x^104*y*z0^2 + x^106 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 + x^103*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^102 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^100*z0 + x^99*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y - x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^97 + x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*z0 + x^91*y*z0^2 + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^90*y*z0 + x^90*z0^2 + x^91 + x^90*y + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^87*y - x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 + x^77*z0^2 + x^78 - x^77*y - x^76*y*z0 - x^76*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^66 + x^65*z0 + x^64*y*z0 + x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y - x^61*y*z0 - x^60*y*z0^2 + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^59*z0 + x^57*y*z0^2 + x^58*y - x^58*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^53*y, + -x^115 + x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y + x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 + x^107*y*z0^2 - x^109 - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y - x^103*z0^2 - x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^102*y - x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*y - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*z0 + x^98*z0^2 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*y*z0 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 + x^92*z0 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^90*z0 + x^89*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 + x^87*y + x^86*y*z0 - x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 - x^84*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*z0^2 - x^84 + x^83*y + x^82*y*z0 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^81 + x^80*y - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^78*y*z0 - x^79 + x^78*y - x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 - x^76*z0 + x^75*z0^2 + x^75*z0 - x^74*z0^2 + x^75 + x^74*z0 - x^73*y*z0 - x^72*y*z0^2 - x^72*y*z0 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*z0 + x^69*y*z0^2 + x^71 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y - x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*y*z0 - x^65 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y*z0 + x^62 - x^61*z0 - x^59*y*z0^2 - x^61 - x^60*y - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 - x^57*y*z0 + x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^56*z0 + x^55*y + x^53*y*z0, + x^115 + x^114*z0 - x^114 + x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*y - x^111*z0 - x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0 - x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^99 + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^98 + x^97*y - x^96*z0^2 - x^95*y*z0^2 - x^97 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^94*y + x^93*z0^2 + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 - x^91 + x^90*y + x^89*y*z0 - x^88*y*z0^2 - x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 + x^87*z0^2 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 + x^85*y*z0 - x^86 + x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^84 + x^83*y + x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^80*y*z0 + x^80*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^78*z0^2 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^77*y - x^77*z0 + x^75*y*z0^2 + x^76*y + x^76*z0 - x^75*y*z0 + x^74*y*z0^2 + x^76 - x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y + x^70*y*z0 - x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 - x^70 + x^69*y + x^68*y*z0 + x^67*y*z0^2 + x^69 + x^68*y - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*y - x^67*z0 + x^66*z0^2 + x^67 - x^66*y + x^66*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^61*y*z0^2 + x^62*y - x^61*y*z0 - x^61*z0^2 - x^62 + x^61*y - x^60*z0^2 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 - x^60 + x^59*y + x^58*y*z0 + x^59 - x^57*y*z0 - x^58 - x^56*z0^2 + x^55*y*z0^2 + x^56*y - x^56*z0 - x^55*y + x^53*y*z0^2, + x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 - x^113 - x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^111*z0 - x^110*y*z0 + x^109*y*z0^2 + x^111 + x^110*y + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^109 - x^108*y - x^108*z0 + x^106*y*z0^2 + x^108 + x^107*y - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 + x^105*y*z0 - x^105*z0^2 - x^105*y + x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*z0 + x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^99 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^96*z0 - x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^95 + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 + x^93*y + x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^91 - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*z0 + x^87*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^86*z0 - x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^84*y*z0 - x^84*z0^2 + x^84*y + x^84*z0 + x^83*y*z0 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^78*y*z0^2 + x^80 - x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*z0 + x^76*z0^2 + x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*z0 + x^74*z0^2 - x^75 + x^74*y + x^73*y*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y - x^71*y*z0 - x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*z0 - x^66*y*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y - x^65*z0 - x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 - x^63*y*z0 + x^62*y*z0^2 - x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0 + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60 - x^59*z0 - x^59 + x^58*y + x^58*z0 + x^57*z0^2 + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56 + x^54, + -x^115 - x^114*z0 + x^114 - x^112*z0^2 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^112 - x^111*y - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*z0 - x^105*y*z0^2 + x^107 + x^105*y*z0 - x^105*z0^2 + x^105*y + x^104*y*z0 - x^104*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*z0 - x^102*y*z0 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^102 + x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^94*y*z0 + x^93*y*z0^2 + x^95 - x^94*y + x^93*y*z0 + x^93*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^93 + x^92*y + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^90 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y + x^87*y*z0 - x^87*z0^2 - x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y + x^83*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*y + x^79*z0 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^74*y + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 - x^72 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 + x^61*z0^2 - x^60*y*z0^2 - x^61*y + x^61*z0 + x^60*y*z0 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 + x^59*y + x^59*z0 - x^58*z0^2 + x^59 - x^58*y - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0 - x^56 + x^54*z0, + x^115 + x^114*z0 + x^114 - x^113 - x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^108*y*z0 - x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^107*y - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^107 - x^106*z0 - x^105*z0^2 + x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*y*z0 - x^99*y*z0^2 - x^100*z0 - x^99*y*z0 - x^99*y + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 - x^95*y + x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*z0^2 - x^94 + x^93*z0 + x^92*y*z0 + x^93 - x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 + x^90*y*z0 + x^89*y*z0^2 - x^91 + x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^89*y + x^88*y*z0 - x^87*y*z0^2 - x^88*y - x^87*z0^2 - x^88 - x^87*y - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*z0 - x^84 - x^83*y - x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^82 - x^81*y - x^80*y*z0 - x^79*y*z0^2 + x^80*y - x^79*y*z0 - x^80 + x^78*y*z0 + x^79 + x^78*y - x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y + x^75*y*z0 + x^75*z0^2 + x^76 - x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y - x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 + x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*y - x^68*z0 + x^67*z0^2 + x^68 + x^67*y + x^67*z0 + x^66*y - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*z0 + x^64*y*z0 - x^65 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 + x^61*y*z0^2 + x^62*y + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 + x^58*y*z0^2 - x^60 - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 - x^57*y*z0 - x^57*z0^2 + x^58 + x^57*y + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y - x^56 - x^55*y + x^54*z0^2, + -x^115 + x^114*z0 - x^113*z0^2 + x^113*z0 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^111*z0 - x^110*y*z0 + x^111 - x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 - x^108*y*z0 - x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^107*y + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^106*y - x^106*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^103*y - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^101*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*y*z0 - x^101 - x^100*y + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^99*y + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*y + x^95*z0^2 + x^96 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*y - x^92*z0 + x^91*y*z0 + x^90*y*z0^2 + x^91*y - x^90*z0^2 - x^91 + x^90*y - x^90*z0 + x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^87 - x^86*y - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^83*y*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 + x^84 + x^83*z0 - x^81*y*z0^2 + x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^80 + x^79*y - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*y*z0 + x^78 - x^77*y - x^76*y*z0 - x^75*y*z0^2 - x^76*y + x^76*z0 + x^75*y*z0 - x^76 - x^75*z0 + x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*z0 + x^73*y*z0 - x^74 - x^73*y + x^73*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^71 - x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 + x^66*y*z0^2 - x^68 - x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 - x^65 + x^64*y - x^64*z0 - x^63*y*z0 - x^62*y*z0^2 + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^61*y + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^57*y*z0 - x^57*z0^2 - x^58 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 + x^55*y + x^54*y, + x^115 + x^114*z0 + x^114 - x^112*z0^2 + x^113 - x^112*y - x^111*y*z0 - x^111*z0^2 - x^111*y + x^111*z0 + x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^105*y*z0^2 + x^107 - x^106*y + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^103*z0 - x^102*z0^2 + x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*z0 + x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 + x^93*y*z0^2 + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 - x^92*z0 - x^91*y*z0 + x^90*y*z0^2 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 + x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*z0^2 + x^88 + x^87*y - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 - x^81*y + x^80*y*z0 + x^79*y*z0^2 - x^81 - x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^80 - x^78*y*z0 - x^78*z0^2 + x^79 - x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^75*z0^2 - x^76 + x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y + x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^70 + x^69*y - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^67*y*z0 + x^68 + x^67*y + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^64*y - x^63*y*z0 + x^63*z0^2 + x^64 - x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^57*z0 + x^55*y*z0^2 - x^57 - x^56*z0 + x^55*y*z0 - x^55*y + x^54*y*z0, + -x^115 + x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y + x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 - x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*y - x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*y*z0 - x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^103 - x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^98*y - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^96*y*z0 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 - x^94*y + x^94 - x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^91*y - x^91*z0 + x^90*y*z0 + x^91 + x^90*y - x^90*z0 + x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^88*y - x^87*y*z0 - x^86*y*z0^2 + x^87*y + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^84*z0^2 - x^83*y*z0^2 - x^83*y*z0 + x^84 - x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^79*z0 + x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^78 + x^76*y*z0 + x^76*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 + x^75*z0 + x^74*z0^2 - x^75 - x^74*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 - x^72 - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^71 + x^70*z0 - x^69*z0^2 + x^70 + x^69*y - x^68*y*z0 + x^67*y*z0^2 - x^68*y + x^67*y*z0 + x^68 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y - x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^63 - x^62*y - x^61*y*z0 - x^61*z0^2 - x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^60*y + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y + x^58*y*z0 - x^58*z0^2 + x^58*y - x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^56*y*z0 - x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 + x^55*y*z0 + x^54*y*z0^2 - x^56, + -x^115 - x^114*z0 - x^114 - x^113*z0 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^111 + x^110*y - x^109*y*z0 + x^108*y*z0^2 + x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^107*z0^2 + x^107*y + x^106*z0^2 + x^105*y*z0^2 + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 - x^104*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 - x^104 + x^103*y + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^101*y - x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^98*y - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^96*y*z0 + x^97 + x^94*y*z0^2 + x^96 - x^95*y + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 - x^92 - x^91*z0 + x^90*y*z0 - x^89*y*z0^2 + x^91 + x^90*z0 + x^88*y*z0^2 + x^89*y + x^89*z0 + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y - x^86*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*z0^2 - x^85 + x^84*z0 + x^83*z0^2 + x^84 + x^83*y + x^83*z0 + x^82*y + x^82*z0 + x^82 + x^81*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*y*z0 + x^79*y - x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^76*y*z0 + x^77 - x^76*y - x^74*y*z0^2 + x^75*y + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*y + x^74*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 - x^71*y*z0 + x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^68*y*z0^2 + x^69*z0 - x^67*y*z0^2 + x^69 - x^68*z0 + x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*z0 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^65 + x^63*y*z0 - x^63*z0^2 - x^63*z0 - x^62*z0^2 - x^63 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^57*y*z0^2 - x^59 - x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 - x^56*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^55, + -x^114*z0 - x^113*z0^2 - x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^109*y*z0 - x^108*y*z0^2 + x^110 + x^109*y - x^109*z0 + x^107*y*z0^2 - x^108*y - x^108*z0 + x^107*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^102*y*z0^2 + x^104 + x^103*y + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y + x^101*z0^2 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^98*y - x^98*z0 + x^97*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*y*z0 - x^97 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*z0^2 - x^95 - x^93*y*z0 - x^93*z0^2 + x^94 + x^93*y + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y + x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y - x^89 + x^88*y + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*z0 - x^83*y*z0 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*z0^2 + x^80 - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^78*y + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*y - x^75*y*z0 + x^74*y*z0^2 - x^76 - x^75*y - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^71*y - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^65*y - x^65*z0 + x^63*y*z0^2 + x^65 + x^64*y - x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^62*y*z0 - x^61*y*z0^2 + x^63 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 - x^57*z0^2 - x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*z0, + x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 + x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^110 + x^109*y + x^108*y*z0 - x^108*z0^2 + x^108*y - x^107*y*z0 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^107 - x^106*y + x^106*z0 - x^105*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 - x^102*y + x^100*y*z0^2 + x^102 - x^101*y + x^100*y*z0 + x^99*y*z0^2 + x^101 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*z0 + x^98*y*z0 + x^99 - x^98*y + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^94*z0^2 + x^93*y*z0^2 - x^94*z0 + x^93*y*z0 + x^93*y + x^93*z0 - x^92*z0^2 - x^91*y*z0^2 - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 + x^88 + x^87*z0 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^85*y - x^84*z0^2 + x^83*y*z0 - x^83*z0^2 - x^84 + x^83*z0 + x^82*y*z0 - x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^80*y*z0^2 - x^82 - x^81*y + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*y - x^77*y*z0^2 - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 + x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y - x^72*y*z0^2 - x^73*z0 + x^72*y*z0 + x^72*z0 - x^71*z0^2 - x^71*y - x^71*z0 - x^69*y*z0^2 - x^71 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 + x^68*z0^2 - x^68*y + x^68*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^63*y + x^62*y*z0 - x^61*y*z0^2 - x^63 + x^62*z0 - x^61*z0^2 - x^62 + x^61*y + x^60*z0^2 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 - x^59*y - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^57 - x^56*z0 + x^55*z0^2 + x^56] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[((-x^2*z0 + y)/y) * dx, + (1/y) * dx, + (z0/y) * dx, + (z0^2/y) * dx, + (x/y) * dx, + (x*z0/y) * dx, + ((-x^3 + x*z0^2)/y) * dx, + (x^2/y) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lpseud_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_lment(threhold = 30)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....:  if omega.valuation() < 0: +....:  print(omega, omega.trace(), omega - omega.group_action([1]))[?7h[?12l[?25h[?25l[?7l....:  print(omega, omega.trace(), omega - omega.group_action([1])) +....: [?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....:  if omega.valuation() < 0: +....:  print(omega, omega.trace(), omega - omega.group_action([1])) +....:  +[?7h[?12l[?25h[?2004l((x^4 + x^2*z0^2 + y*z0)/y) * dx ((-x^2)/y) dx ((x^2*z0 - x^2 - y)/y) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lat_most_poles_orms(1)[?7h[?12l[?25h[?25l[?7lt_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lsage: AS.at_most_poles_forms(1) +[?7h[?12l[?25h[?2004l[?7h[((-x^2*z0 + y)/y) * dx, + ((x^4 + x^2*z0^2 + y*z0)/y) * dx, + (1/y) * dx, + (z0/y) * dx, + (z0^2/y) * dx, + (x/y) * dx, + (x*z0/y) * dx, + ((-x^3 + x*z0^2)/y) * dx, + (x^2/y) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1): +....:  if omega.valuation() < 0: +....:  print(omega, omega.trace(), omega - omega.group_action([1]))[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_form(1) +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1;3S[?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +[?2004l ┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Using Python 3.11.1. Type "help()" for help. │ +│ Enhanced for CoCalc. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [2], line 1 +----> 1 AS + +NameError: name 'AS' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7las_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y], prec = 200) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-3 + 2*t^2 + 2*t^3 + t^8 + t^9 + 2*t^14 + 2*t^15 + t^17 + 2*t^18 + 2*t^20 + 2*t^24 + 2*t^26 + t^27 + 2*t^29 + t^35 + 2*t^42 + t^47 + 2*t^48 + 2*t^51 + 2*t^53 + t^54 + 2*t^56 + 2*t^60 + 2*t^62 + t^68 + 2*t^74 + t^78 + t^81 + 2*t^83 + 2*t^87 + t^89 + 2*t^93 + O(t^97) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-1 + t^4 + t^5 + t^9 + t^10 + 2*t^14 + t^15 + t^17 + t^19 + 2*t^23 + 2*t^25 + 2*t^27 + t^28 + t^30 + 2*t^32 + t^34 + t^41 + 2*t^43 + 2*t^44 + 2*t^45 + t^49 + 2*t^50 + t^53 + 2*t^54 + t^55 + t^63 + 2*t^69 + 2*t^71 + t^73 + 2*t^75 + 2*t^77 + t^81 + t^82 + t^84 + 2*t^90 + t^94 + 2*t^98 + O(t^99) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(place = 1) +[?7h[?12l[?25h[?2004l[?7h2*t^-1 + t^4 + 2*t^5 + 2*t^9 + t^10 + 2*t^14 + 2*t^15 + 2*t^17 + 2*t^19 + t^23 + t^25 + t^27 + t^28 + t^30 + 2*t^32 + t^34 + 2*t^41 + t^43 + 2*t^44 + t^45 + 2*t^49 + 2*t^50 + 2*t^53 + 2*t^54 + 2*t^55 + 2*t^63 + t^69 + t^71 + 2*t^73 + t^75 + t^77 + 2*t^81 + t^82 + t^84 + 2*t^90 + t^94 + 2*t^98 + O(t^99) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7l= AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7lsage: omega = AS.at_most_poles_forms(1)[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega.expansion + omega.expansion  + omega.expansion_at_infty + + + [?7h[?12l[?25h[?25l[?7l + omega.expansion  + + [?7h[?12l[?25h[?25l[?7l_at_infty + omega.expansion  + omega.expansion_at_infty[?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega.expansion_at_infty(place = 0) +[?7h[?12l[?25h[?2004l[?7ht^-1 + t + t^3 + t^5 + t^7 + t^9 + 2*t^10 + 2*t^12 + t^13 + t^14 + 2*t^15 + t^16 + t^18 + 2*t^19 + 2*t^20 + t^21 + 2*t^22 + t^23 + t^24 + t^25 + t^27 + t^31 + 2*t^33 + 2*t^35 + 2*t^36 + 2*t^37 + 2*t^38 + t^39 + t^40 + t^42 + t^44 + t^45 + t^46 + t^47 + t^48 + t^49 + t^50 + t^51 + 2*t^52 + 2*t^53 + 2*t^55 + 2*t^56 + t^57 + 2*t^59 + t^60 + 2*t^61 + 2*t^62 + t^63 + t^64 + t^66 + 2*t^67 + t^68 + t^69 + t^71 + 2*t^72 + t^73 + t^74 + 2*t^76 + t^77 + 2*t^78 + 2*t^79 + t^81 + t^82 + t^84 + t^85 + t^86 + 2*t^87 + t^88 + 2*t^89 + 2*t^91 + t^92 + t^93 + t^94 + 2*t^95 + 2*t^96 + 2*t^97 + t^99 + 2*t^100 + t^101 + t^102 + 2*t^104 + t^105 + 2*t^106 + t^107 + t^108 + t^110 + 2*t^111 + 2*t^113 + 2*t^114 + 2*t^115 + 2*t^116 + 2*t^117 + 2*t^120 + 2*t^122 + 2*t^123 + t^125 + 2*t^126 + 2*t^127 + 2*t^129 + t^131 + t^134 + t^136 + t^139 + t^141 + 2*t^142 + 2*t^143 + 2*t^144 + t^145 + t^146 + 2*t^147 + 2*t^148 + t^149 + 2*t^150 + 2*t^154 + t^156 + t^157 + 2*t^159 + t^160 + t^161 + 2*t^162 + 2*t^165 + 2*t^167 + 2*t^169 + 2*t^170 + 2*t^171 + 2*t^172 + t^175 + 2*t^177 + 2*t^180 + t^181 + 2*t^182 + t^183 + t^184 + t^186 + t^187 + 2*t^188 + t^189 + t^192 + t^193 + O(t^195) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty(place = 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: omega.expansion_at_infty(place = 1) +[?7h[?12l[?25h[?2004l[?7h2*t^-1 + 2*t + 2*t^3 + 2*t^5 + 2*t^7 + 2*t^9 + 2*t^10 + 2*t^12 + 2*t^13 + t^14 + t^15 + t^16 + t^18 + t^19 + 2*t^20 + 2*t^21 + 2*t^22 + 2*t^23 + t^24 + 2*t^25 + 2*t^27 + 2*t^31 + t^33 + t^35 + 2*t^36 + t^37 + 2*t^38 + 2*t^39 + t^40 + t^42 + t^44 + 2*t^45 + t^46 + 2*t^47 + t^48 + 2*t^49 + t^50 + 2*t^51 + 2*t^52 + t^53 + t^55 + 2*t^56 + 2*t^57 + t^59 + t^60 + t^61 + 2*t^62 + 2*t^63 + t^64 + t^66 + t^67 + t^68 + 2*t^69 + 2*t^71 + 2*t^72 + 2*t^73 + t^74 + 2*t^76 + 2*t^77 + 2*t^78 + t^79 + 2*t^81 + t^82 + t^84 + 2*t^85 + t^86 + t^87 + t^88 + t^89 + t^91 + t^92 + 2*t^93 + t^94 + t^95 + 2*t^96 + t^97 + 2*t^99 + 2*t^100 + 2*t^101 + t^102 + 2*t^104 + 2*t^105 + 2*t^106 + 2*t^107 + t^108 + t^110 + t^111 + t^113 + 2*t^114 + t^115 + 2*t^116 + t^117 + 2*t^120 + 2*t^122 + t^123 + 2*t^125 + 2*t^126 + t^127 + t^129 + 2*t^131 + t^134 + t^136 + 2*t^139 + 2*t^141 + 2*t^142 + t^143 + 2*t^144 + 2*t^145 + t^146 + t^147 + 2*t^148 + 2*t^149 + 2*t^150 + 2*t^154 + t^156 + 2*t^157 + t^159 + t^160 + 2*t^161 + 2*t^162 + t^165 + t^167 + t^169 + 2*t^170 + t^171 + 2*t^172 + 2*t^175 + t^177 + 2*t^180 + 2*t^181 + 2*t^182 + 2*t^183 + t^184 + t^186 + 2*t^187 + 2*t^188 + 2*t^189 + t^192 + 2*t^193 + O(t^195) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty(place = 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: omega.expansion_at_infty(place = 0) + omega.expansion_at_infty(place = 1) +[?7h[?12l[?25h[?2004l[?7ht^10 + t^12 + 2*t^14 + 2*t^16 + 2*t^18 + t^20 + t^22 + 2*t^24 + t^36 + t^38 + 2*t^40 + 2*t^42 + 2*t^44 + 2*t^46 + 2*t^48 + 2*t^50 + t^52 + t^56 + 2*t^60 + t^62 + 2*t^64 + 2*t^66 + 2*t^68 + t^72 + 2*t^74 + t^76 + t^78 + 2*t^82 + 2*t^84 + 2*t^86 + 2*t^88 + 2*t^92 + 2*t^94 + t^96 + t^100 + 2*t^102 + t^104 + t^106 + 2*t^108 + 2*t^110 + t^114 + t^116 + t^120 + t^122 + t^126 + 2*t^134 + 2*t^136 + t^142 + t^144 + 2*t^146 + t^148 + t^150 + t^154 + 2*t^156 + 2*t^160 + t^162 + t^170 + t^172 + t^180 + t^182 + 2*t^184 + 2*t^186 + t^188 + 2*t^192 + O(t^195) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty(place = 0) + omega.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l(1)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l = AS.at_mospoles_forms(1)[1][?7h[?12l[?25h[?25l[?7lC.x.expansionat_infty(place = )[?7h[?12l[?25h[?25l[?7lomega = AS.atmost_poles_forms()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: omega = AS.at_most_poles_forms(1)[0] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = AS.at_most_poles_forms(1)[0][?7h[?12l[?25h[?25l[?7l.expansion_ainfty(place = 0) + omega.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lsage: omega.expansion_at_infty(place = 0) + omega.expansion_at_infty(place = 1) +[?7h[?12l[?25h[?2004l[?7h2*t^15 + t^21 + 2*t^41 + t^47 + t^51 + 2*t^57 + t^59 + 2*t^65 + 2*t^69 + 2*t^75 + 2*t^77 + t^93 + t^95 + t^99 + t^101 + 2*t^103 + t^105 + 2*t^117 + 2*t^123 + 2*t^125 + 2*t^127 + 2*t^137 + t^139 + t^141 + t^143 + t^145 + t^149 + t^155 + t^157 + 2*t^159 + t^165 + 2*t^167 + t^171 + t^173 + 2*t^177 + t^179 + t^181 + t^183 + t^185 + t^191 + 2*t^193 + t^195 + 2*t^197 + O(t^198) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?2004h]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$ loasage +[?2004l ┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Using Python 3.11.1. Type "help()" for help. │ +│ Enhanced for CoCalc. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llambdaa = (v1-v0)/(u0 - u1)[?7h[?12l[?25h[?25l[?7load('init.sage'[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^4*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^5*z0 + x^4*z0 + x^2*z1) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^7) * dx, 0 ), ( (x^11 + x^9) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^11*z0 + x^9*z0 + x^8 + x^5*z1) * dx, z0*z1/x ), ( (x^10 + x^8) * dx, z1/x^2 ), ( (x^4) * dx, z0/x^2 ), ( (x^10*z0 + x^8*z0 + x^4*z1) * dx, z0*z1/x^2 ), ( (x^9) * dx, z1/x^3 ), ( (0) * dx, z0/x^3 ), ( (x^9*z0 + x^7*z0 + x^3*z1) * dx, z0*z1/x^3 ), ( (x^8 + x^6) * dx, z1/x^4 ), ( (x^8*z0 + x^6*z0 + x^2*z1) * dx, z0*z1/x^4 ), ( (x^7*z0 + x^5*z0 + x^4*z0) * dx, z0*z1/x^5 ), ( (x^6*z0 + x^4*z0 + z1) * dx, z0*z1/x^6 ), ( (x^5*z0) * dx, z0*z1/x^7 ), ( (x^4*z0) * dx, z0*z1/x^8 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^7 +z1^2 - z1 = x^13 + x^11 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C, 1)[?7h[?12l[?25h[?25l[?7llpha[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = C.x^((M - m)/2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^((M - m)/2)[?7h[?12l[?25h[?25l[?7lsage: alpha = C.x^((M - m)/2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: M +[?7h[?12l[?25h[?2004l[?7h13 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty(place = 0) + omega.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lega.expansion_at_infty(place = 0) + omega.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = AS.at_mospoles_forms(1)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l.y0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l.z0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l]0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l[0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*x^4*C.dx[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lCx^4*C.dx[?7h[?12l[?25h[?25l[?7l.x^4*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega = C.z[0]*C.x^4*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor omega in AS.at_most_poles_forms(1):[?7h[?12l[?25h[?25l[?7l =x^3 -x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7l = C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0*z[1]/C.x^5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.z[1]/C.x^5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lift_to_de_rham[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]*C.x^4/(C.x^12 + C.x^10 + alpha*C.x^6) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.z[0]*C.x^4*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega + f.difn()[?7h[?12l[?25h[?25l[?7lmomega + f.difn()[?7h[?12l[?25h[?25l[?7l1omega + f.difn()[?7h[?12l[?25h[?25l[?7l omega + f.difn()[?7h[?12l[?25h[?25l[?7l=omega + f.difn()[?7h[?12l[?25h[?25l[?7l omega + f.difn()[?7h[?12l[?25h[?25l[?7lsage: om1 = omega + ff.diffn() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = omega + ff.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.valuation() +[?7h[?12l[?25h[?2004l[?7h14 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]*C.x^4/(C.x^12 + C.x^10 + alpha*C.x^6)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1 +[?7h[?12l[?25h[?2004l[?7h((x^13*z0 + x^11*z0 + x^10*z0 + x^10*z1 + x^8*z1 + x^7*z1 + z0*z1)/(x^12 + x^8 + x^6)) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7l = omega + ff.diffn()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz0*z1)/(x^12 + x^8 + x^6)) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l( z0*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz0*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7lCz0*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l.z0*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCz1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l.z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l])/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l.x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l.^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l.x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6) * dx[?7h[?12l[?25h[?25l[?7l.x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6)) * C.dx +[?7h[?12l[?25h[?2004l Cell In [10], line 1 + om1 -(C.z[Integer(0)]*C.z[Integer(1)])/(C.x**Integer(12) + C.x**Integer(8) + C.x**Integer(6))) * C.dx + ^ +SyntaxError: unmatched ')' + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6)) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() * C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx +[?7h[?12l[?25h[?2004l[?7h((x^4*z0 + x*z1)/(x^3 + x + 1)) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7lsage: om2 = om1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx\ +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = om1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx\[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1-(C.z[0]*C.z[1])/(C.x^12 + C.x^8+ C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2 = om1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx\[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om2.valuation() +[?7h[?12l[?25h[?2004l[?7h14 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lz[1].valuation()[?7h[?12l[?25h[?25l[?7l[1].valuation()[?7h[?12l[?25h[?25l[?7lsage: C.z[1].valuation() +[?7h[?12l[?25h[?2004l[?7h-26 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[1].valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l].valuation()[?7h[?12l[?25h[?25l[?7l0].valuation()[?7h[?12l[?25h[?25l[?7lsage: C.z[0].valuation() +[?7h[?12l[?25h[?2004l[?7h-14 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2+2[?7h[?12l[?25h[?25l[?7l*C.genus()[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: 2*M - 3*m +[?7h[?12l[?25h[?2004l[?7h5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [17], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :33 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :31 + +File :390, in de_rham_basis(self, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [18], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :33 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :31 + +File :390, in de_rham_basis(self, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [19], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :33 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :31 + +File :390, in de_rham_basis(self, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [20], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :33 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :31 + +File :393, in de_rham_basis(self, threshold) + +File :372, in lift_to_de_rham(self, fct, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms, only 16 of 17 +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [21], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :33 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :31 + +File :393, in de_rham_basis(self, threshold) + +File :372, in lift_to_de_rham(self, fct, threshold) + +File :147, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[0].valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^5*z0 + x^4*z1 + x^2*z1) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^4*z0 + x^3*z1) * dx, 0 ), ( (x^5*z0 + x^4*z1 + x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^7) * dx, 0 ), ( (x^8) * dx, 0 ), ( (x^11) * dx, z1/x ), ( (x^9) * dx, z0/x ), ( (x^11*z0 + x^10 + x^9*z1 + x^7*z0) * dx, z0*z1/x ), ( (x^10 + x^6) * dx, z1/x^2 ), ( (x^8) * dx, z0/x^2 ), ( (x^10*z0 + x^8*z1 + x^6*z0) * dx, z0*z1/x^2 ), ( (x^9) * dx, z1/x^3 ), ( (0) * dx, z0/x^3 ), ( (x^9*z0 + x^7*z1 + x^5*z0) * dx, z0*z1/x^3 ), ( (x^8 + x^4) * dx, z1/x^4 ), ( (x^6) * dx, z0/x^4 ), ( (x^8*z0 + x^6*z1 + x^4*z0) * dx, z0*z1/x^4 ), ( (x^7*z0 + x^5*z0 + x^5*z1 + x^4*z1) * dx, z0*z1/x^5 ), ( (x^6*z0 + x^4*z1 + x^2*z0) * dx, z0*z1/x^6 ), ( (x^5*z0 + x^4*z0) * dx, z0*z1/x^7 ), ( (x^4*z0 + x^2*z1 + z0) * dx, z0*z1/x^8 ), ( (x^5*z0 + x^4*z1) * dx, z0*z1/x^9 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li = 3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: i = 3 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp = p1*x + p0[?7h[?12l[?25h[?25l[?7lrint(licz)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[0].valuation()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^11 +z1^2 - z1 = x^13 + x^9 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha = C.x^((M - m)/2)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lha = C.x^((M - m)/2)[?7h[?12l[?25h[?25l[?7lsage: alpha = C.x^((M - m)/2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp = p1*x + p0[?7h[?12l[?25h[?25l[?7lrint(licz)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: prim = C.x^12 + C.x^8 + alpha*C.x^10 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega = C.z[0]*C.x^4*C.dx[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.x^4*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx[?7h[?12l[?25h[?25l[?7li*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega = C.z[0]*C.x^i*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]*C.x^4/(C.x^12 + C.x^10 + alpha*C.x^6)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]*C.x^4/(C.x^12 + C.x^10 + alpha*C.x^6)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l/(C.x^12 + C.x^10 + alpha*C.x^6)[?7h[?12l[?25h[?25l[?7li/(C.x^12 + C.x^10 + alpha*C.x^6)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]*C.x^i/prim +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.z[0]*C.x^i*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega + f.difn()[?7h[?12l[?25h[?25l[?7lmomega + f.difn()[?7h[?12l[?25h[?25l[?7l1omega + f.difn()[?7h[?12l[?25h[?25l[?7l omega + f.difn()[?7h[?12l[?25h[?25l[?7l=omega + f.difn()[?7h[?12l[?25h[?25l[?7l omega + f.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = omega + ff.diffn() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = omega + ff.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7luation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.valuation() +[?7h[?12l[?25h[?2004l[?7h10 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.valuation()[?7h[?12l[?25h[?25l[?7l = omega + ff.diffn()[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]*C.x^i/prim[?7h[?12l[?25h[?25l[?7lomega = C.z[0]*C.x^i*C.dx[?7h[?12l[?25h[?25l[?7lprim = C.x^12 + C.x^8 + alpha*C.x^10[?7h[?12l[?25h[?25l[?7lalpha = C.x^((M- m)/2)[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7li = 3[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l2*M - 3*m[?7h[?12l[?25h[?25l[?7lC.z[0].valuation()[?7h[?12l[?25h[?25l[?7l2*M - 3*m[?7h[?12l[?25h[?25l[?7lsage: 2*M - 3*m +[?7h[?12l[?25h[?2004l[?7h-7 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +[?2004l ┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 10.0, Release Date: 2023-05-20 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll = 5[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = RA.gens()[?7h[?12l[?25h[?25l[?7lS = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h5 +[?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[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +[?2004l ┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 10.0, Release Date: 2023-05-20 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^5*z0 + x^2*z1) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^6*z0 + x^3*z1) * dx, 0 ), ( (x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^4*z0) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^7) * dx, 0 ), ( (x^8) * dx, 0 ), ( (x^13) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^13*z0 + x^10 + x^7*z1) * dx, z0*z1/x ), ( (x^12) * dx, z1/x^2 ), ( (x^6) * dx, z0/x^2 ), ( (x^12*z0 + x^6*z1) * dx, z0*z1/x^2 ), ( (x^11) * dx, z1/x^3 ), ( (0) * dx, z0/x^3 ), ( (x^11*z0 + x^5*z1) * dx, z0*z1/x^3 ), ( (x^10) * dx, z1/x^4 ), ( (x^4) * dx, z0/x^4 ), ( (x^10*z0 + x^4*z1) * dx, z0*z1/x^4 ), ( (x^9) * dx, z1/x^5 ), ( (x^9*z0 + x^6*z0) * dx, z0*z1/x^5 ), ( (x^8*z0 + x^2*z1) * dx, z0*z1/x^6 ), ( (x^7*z0) * dx, z0*z1/x^7 ), ( (x^6*z0 + z1) * dx, z0*z1/x^8 ), ( (x^5*z0) * dx, z0*z1/x^9 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h18 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1 = a_cover(C1, [C1.x^2, C1.x^5], prec = 300)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l as_cover(C1, [C1.x^2, C1.x^5], prec = 300)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7lx], prec = 30)[?7h[?12l[?25h[?25l[?7l^], prec = 30)[?7h[?12l[?25h[?25l[?7l3], prec = 30)[?7h[?12l[?25h[?25l[?7l3], prec = 30)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x^3], prec = 30)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, [C.x^3], prec = 30)[?7h[?12l[?25h[?25l[?7lsage: AS1 = as_cover(C, [C.x^33], prec = 300) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C, [C.x^33], prec = 300)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS1.genus() +[?7h[?12l[?25h[?2004l[?7h16 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +[?2004l ┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 10.0, Release Date: 2023-05-20 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l18 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l18 +16 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l18 +16 +7 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.z[0].valuation()[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: C1.x.expansion + C1.x.expansion  + C1.x.expansion_at_infty + + + [?7h[?12l[?25h[?25l[?7l + C1.x.expansion  + + [?7h[?12l[?25h[?25l[?7l_at_infty + C1.x.expansion  + C1.x.expansion_at_infty[?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.x.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-3 + O(t^97) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lAS1.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different + AS2.exponent_of_different  + AS2.exponent_of_different_prim +  + + [?7h[?12l[?25h[?25l[?7l( + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS2.exponent_of_different() +[?7h[?12l[?25h[?2004l[?7h16 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lAS2.exponent_of_different()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS2.genus() +[?7h[?12l[?25h[?2004l[?7h7 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l18 +16 +9 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in product(*pr):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrang[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l18 +16 +9 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = 13[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: a = 3 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbeta = 1 + B[0]*t + B[1]*t^2 + B[2]*t^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: b = 5 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconj(pi)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: c = 11 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a+6*c > 6*b - 11[?7h[?12l[?25h[?25l[?7lsage: 3*a+6*c > 6*b - 11 +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in range(2, 15): +....:  for b in range(2, 15): +....:  for c in range(2, 15): +....:  if a%2 == 1 and b%2 == 1 and c%1 == 1 and a != b and a != c: +....:  if 3*a+6*c > 6*b - 11: +....:  print(a, b, c)[?7h[?12l[?25h[?25l[?7l....:  print(a, b, c) +....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(2, 15): +....:  for b in range(2, 15): +....:  for c in range(2, 15): +....:  if a%2 == 1 and b%2 == 1 and c%1 == 1 and a != b and a != c: +....:  if 3*a+6*c > 6*b - 11: +....:  print(a, b, c) +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in range(2, 15): +....:  for b in range(2, 15): +....:  for c in range(2, 15): +....:  if a%2 == 1 and b%2 == 1 and c%1 == 1 and a != b and a != c: +....:  if 3*a+6*c > 6*b - 11: +....:  print(a, b, c)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a+6*c > 6*b - 11 +  +  +  +  + [?7h[?12l[?25h[?25l[?7lc = 11[?7h[?12l[?25h[?25l[?7lb5[?7h[?12l[?25h[?25l[?7la3[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l18 +16 +9 +3 5 5 +3 5 7 +3 5 9 +3 5 11 +3 5 13 +3 7 5 +3 7 7 +3 7 9 +3 7 11 +3 7 13 +3 9 7 +3 9 9 +3 9 11 +3 9 13 +3 11 9 +3 11 11 +3 11 13 +3 13 11 +3 13 13 +5 3 3 +5 3 7 +5 3 9 +5 3 11 +5 3 13 +5 7 3 +5 7 7 +5 7 9 +5 7 11 +5 7 13 +5 9 7 +5 9 9 +5 9 11 +5 9 13 +5 11 7 +5 11 9 +5 11 11 +5 11 13 +5 13 9 +5 13 11 +5 13 13 +7 3 3 +7 3 5 +7 3 9 +7 3 11 +7 3 13 +7 5 3 +7 5 5 +7 5 9 +7 5 11 +7 5 13 +7 9 5 +7 9 9 +7 9 11 +7 9 13 +7 11 9 +7 11 11 +7 11 13 +7 13 9 +7 13 11 +7 13 13 +9 3 3 +9 3 5 +9 3 7 +9 3 11 +9 3 13 +9 5 3 +9 5 5 +9 5 7 +9 5 11 +9 5 13 +9 7 3 +9 7 5 +9 7 7 +9 7 11 +9 7 13 +9 11 5 +9 11 7 +9 11 11 +9 11 13 +9 13 7 +9 13 11 +9 13 13 +11 3 3 +11 3 5 +11 3 7 +11 3 9 +11 3 13 +11 5 3 +11 5 5 +11 5 7 +11 5 9 +11 5 13 +11 7 3 +11 7 5 +11 7 7 +11 7 9 +11 7 13 +11 9 3 +11 9 5 +11 9 7 +11 9 9 +11 9 13 +11 13 7 +11 13 9 +11 13 13 +13 3 3 +13 3 5 +13 3 7 +13 3 9 +13 3 11 +13 5 3 +13 5 5 +13 5 7 +13 5 9 +13 5 11 +13 7 3 +13 7 5 +13 7 7 +13 7 9 +13 7 11 +13 9 3 +13 9 5 +13 9 7 +13 9 9 +13 9 11 +13 11 3 +13 11 5 +13 11 7 +13 11 9 +13 11 11 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?2004h]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$ [?2004h]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$ [?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +[?2004l ┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 10.1, Release Date: 2023-08-20 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llambd = 1-z[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lno 8 -th root; divide by 2 +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [1], line 1 +----> 1 load('init.sage') + +File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :8 + +File :45, in __init__(self, C, list_of_fcts, branch_points, prec) + +ValueError: not enough values to unpack (expected 4, got 2) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [2], line 1 +----> 1 load('init.sage') + +File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :8 + +File :75, in __truediv__(self, other) + +File /ext/sage/10.1/src/sage/structure/element.pyx:488, in sage.structure.element.Element.__getattr__() + 486 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 487 """ +--> 488 return self.getattr_from_category(name) + 489 + 490 cdef getattr_from_category(self, name): + +File /ext/sage/10.1/src/sage/structure/element.pyx:501, in sage.structure.element.Element.getattr_from_category() + 499 else: + 500 cls = P._abstract_element_class +--> 501 return getattr_from_other_class(self, cls, name) + 502 + 503 def __dir__(self): + +File /ext/sage/10.1/src/sage/cpython/getattr.pyx:362, in sage.cpython.getattr.getattr_from_other_class() + 360 dummy_error_message.cls = type(self) + 361 dummy_error_message.name = name +--> 362 raise AttributeError(dummy_error_message) + 363 attribute = attr + 364 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [3], line 1 +----> 1 load('init.sage') + +File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32 + +File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :8 + +File :75, in __truediv__(self, other) + +File /ext/sage/10.1/src/sage/structure/element.pyx:488, in sage.structure.element.Element.__getattr__() + 486 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 487 """ +--> 488 return self.getattr_from_category(name) + 489 + 490 cdef getattr_from_category(self, name): + +File /ext/sage/10.1/src/sage/structure/element.pyx:501, in sage.structure.element.Element.getattr_from_category() + 499 else: + 500 cls = P._abstract_element_class +--> 501 return getattr_from_other_class(self, cls, name) + 502 + 503 def __dir__(self): + +File /ext/sage/10.1/src/sage/cpython/getattr.pyx:362, in sage.cpython.getattr.getattr_from_other_class() + 360 dummy_error_message.cls = type(self) + 361 dummy_error_message.name = name +--> 362 raise AttributeError(dummy_error_message) + 363 attribute = attr + 364 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.elements()[?7h[?12l[?25h[?25l[?7lS2.genus()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS1.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (z0^2) * dx, 0 ), + ( (x) * dx, 0 ), + ( (-x*z0) * dx, z0^2/x ), + ( (x*z0^2) * dx, z0^3/x ), + ( (-2*x*z0^3) * dx, z0^4/x ), + ( (-2*z0^3) * dx, z0^4/x^2 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: AS1 +[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation: + z^5 - z = x^3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS1.holomorphic_diffentials() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [7], line 1 +----> 1 AS1.holomorphic_diffentials() + +AttributeError: 'as_cover' object has no attribute 'holomorphic_diffentials' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1.holomorphic_diffentials()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.holomorphic_diffentials()[?7h[?12l[?25h[?25l[?7lsage: AS1.holomorphic_diffentials() + AS1.a_number AS1.branch_points AS1.de_rham_basis  + AS1.at_most_poles AS1.cartier_matrix AS1.dx  + AS1.at_most_poles_forms AS1.characteristic AS1.dx_series > + AS1.base_ring AS1.cohomology_of_structure_sheaf_basis AS1.exponent_of_different  + [?7h[?12l[?25h[?25l[?7la_number + AS1.a_number  + + + + [?7h[?12l[?25h[?25l[?7lbranch_points + AS1.a_number  AS1.branch_points [?7h[?12l[?25h[?25l[?7lde_rham_basi + AS1.branch_points  AS1.de_rham_basis [?7h[?12l[?25h[?25l[?7lexponent_of_different_prim + branch_pointsde_rham_basiexponent_of_different_prim + cartiermatrixdx fct_field +<characeristic dx_seris function + cohomoloy_of_structure_sheaf_basisexpnent_of_different genus [?7h[?12l[?25h[?25l[?7lgroup +de_rham_basiexponent_of_different_primgroup  +dx fct_fieldheight  +dx_seris functionholomorphic_differentials_basis +expnent_of_different genus ith_ramification_gp[?7h[?12l[?25h[?25l[?7ljumps +exponent_of_different_primgroup jumps +fct_fieldheight lift_o_de_rham +functionholomorphic_differentials_basismagical_element  +genus ith_ramification_gpnb_of_pts_at_nfty [?7h[?12l[?25h[?25l[?7lone +group jumpsone  +height lift_o_de_rhamprec  +holomorphic_differentials_basismagical_element pseudo_magical_element +ith_ramification_gpnb_of_pts_at_nfty quotien [?7h[?12l[?25h[?25l[?7lramification_jumps +jumpsone ramification_jumps +lift_o_de_rhamprec uniformizer +magical_element pseudo_magical_elementx  +nb_of_pts_at_nfty quotien x_series[?7h[?12l[?25h[?25l[?7ly +one ramification_jumpsy   +prec uniformizery_series   +pseudo_magical_elementx z  +quotien x_seriesz [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lramification_jumps + AS1.ramification_jumps  AS1.y [?7h[?12l[?25h[?25l[?7lone + AS1.one  AS1.ramification_jumps [?7h[?12l[?25h[?25l[?7ljumps +jumpsone ramification_jumps  +lift_to_de_rhamprec uniformizer  +magical_element pseudo_magical_elementx> +nb_of_ps_at_inftyquotientx [?7h[?12l[?25h[?25l[?7lgroup +groupjumpsone  +heigh lift_to_de_rhamprec  +holomorphic_differentials_basismagical_element pseudo_magical_element +ith_ramificaton_gpnb_of_ps_at_inftyquotient[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim +exponent_of_different_primgroupjumps +fct_fieldheigh lift_to_de_rham +functions holomorphic_differentials_basismagical_element  +genus ith_ramificaton_gpnb_of_ps_at_infty[?7h[?12l[?25h[?25l[?7lde_rham_basis +de_rham_basis exponent_of_different_primgroup +dx fct_fieldheigh  +dx_seriefunctions holomorphic_differentials_basis +exponent_of_differentgenus ith_ramificaton_gp[?7h[?12l[?25h[?25l[?7lbranch_point +branch_pointde_rham_basis exponent_of_different_prim +cartier_matrixdx fct_field +charactristicdx_seriefunctions  +cohmology_of_structure_sheaf_basisexponent_of_differentgenus [?7h[?12l[?25h[?25l[?7la_number + a_number branch_pointde_rham_basis  + at_mostpoles cartier_matrixdx  + at_mos_poles_formscharactristicdx_serie + base_rin cohmology_of_structure_sheaf_basisexponent_of_different[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + + + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.holomorphic_diffentials()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l + AS1.base_ring  + AS1.branch_points[?7h[?12l[?25h[?25l[?7l + +[?7h[?12l[?25h[?25l[?7lholomorphic_diffentials()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS1.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (z0) * dx, (z0^2) * dx, (x) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lfor d in range(1, 6):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l range(1, 6):[?7h[?12l[?25h[?25l[?7l +....: [?7h[?12l[?25h[?25l[?7lA = [[] for i in range(n)][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lC])[?7h[?12l[?25h[?25l[?7l.])[?7h[?12l[?25h[?25l[?7lx])[?7h[?12l[?25h[?25l[?7l^])[?7h[?12l[?25h[?25l[?7ld])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lA = [[] for i in range(n)][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for d in range(1, 6): +....:  AS = as_cover(C, [C.x^d]) +....:  AS.holomorphic_differentials_basis() +....:  +[?7h[?12l[?25h[?2004l[?7h[] +[?7h[(1) * dx, (z0) * dx] +Increase precision. +[?7h[(1) * dx, + (z0) * dx, + (z0^2) * dx, + (z0^3) * dx, + (z0^4) * dx, + (x) * dx, + (x*z0) * dx, + (x*z0^2) * dx, + (x*z0^3) * dx, + (x*z0^4) * dx, + (x^2) * dx, + (x^2*z0) * dx, + (x^2*z0^2) * dx, + (x^2*z0^3) * dx, + (x^2*z0^4) * dx, + (x^3) * dx, + (x^3*z0) * dx, + (x^3*z0^2) * dx, + (x^3*z0^3) * dx, + (x^3*z0^4) * dx, + (x^4) * dx, + (x^4*z0) * dx, + (x^4*z0^2) * dx, + (x^4*z0^3) * dx, + (x^4*z0^4) * dx, + (x^5) * dx, + (x^5*z0) * dx, + (x^5*z0^2) * dx, + (x^5*z0^3) * dx, + (x^5*z0^4) * dx, + (x^6) * dx, + (x^6*z0) * dx, + (x^6*z0^2) * dx, + (x^6*z0^3) * dx, + (x^6*z0^4) * dx, + (x^7) * dx, + (x^7*z0) * dx, + (x^7*z0^2) * dx, + (x^7*z0^3) * dx, + (x^7*z0^4) * dx] +Increase precision. +[?7h[(1) * dx, + (z0) * dx, + (z0^2) * dx, + (z0^3) * dx, + (z0^4) * dx, + (x) * dx, + (x*z0) * dx, + (x*z0^2) * dx, + (x*z0^3) * dx, + (x*z0^4) * dx, + (x^2) * dx, + (x^2*z0) * dx, + (x^2*z0^2) * dx, + (x^2*z0^3) * dx, + (x^2*z0^4) * dx, + (x^3) * dx, + (x^3*z0) * dx, + (x^3*z0^2) * dx, + (x^3*z0^3) * dx, + (x^3*z0^4) * dx, + (x^4) * dx, + (x^4*z0) * dx, + (x^4*z0^2) * dx, + (x^4*z0^3) * dx, + (x^4*z0^4) * dx, + (x^5) * dx, + (x^5*z0) * dx, + (x^5*z0^2) * dx, + (x^5*z0^3) * dx, + (x^5*z0^4) * dx, + (x^6) * dx, + (x^6*z0) * dx, + (x^6*z0^2) * dx, + (x^6*z0^3) * dx, + (x^6*z0^4) * dx, + (x^7) * dx, + (x^7*z0) * dx, + (x^7*z0^2) * dx, + (x^7*z0^3) * dx, + (x^7*z0^4) * dx] +Increase precision. +[?7h[(x^2 - 2*x*z0 + z0^2) * dx, + (2*x^3 + 2*x^2*z0 + z0^3) * dx, + (-2*x^4 + x^3*z0 + z0^4) * dx, + (x^3 - 2*x^2*z0 + x*z0^2) * dx, + (2*x^4 + 2*x^3*z0 + x*z0^3) * dx, + (-2*x^5 + x^4*z0 + x*z0^4) * dx, + (x^4 - 2*x^3*z0 + x^2*z0^2) * dx, + (2*x^5 + 2*x^4*z0 + x^2*z0^3) * dx, + (-2*x^6 + x^5*z0 + x^2*z0^4) * dx, + (x^5 - 2*x^4*z0 + x^3*z0^2) * dx, + (2*x^6 + 2*x^5*z0 + x^3*z0^3) * dx, + (-2*x^7 + x^6*z0 + x^3*z0^4) * dx, + (x^6 - 2*x^5*z0 + x^4*z0^2) * dx, + (2*x^7 + 2*x^6*z0 + x^4*z0^3) * dx, + (2*x^7*z0 + 2*x^6*z0^2 + x^4*z0^4) * dx, + (x^7 - 2*x^6*z0 + x^5*z0^2) * dx, + (x^7*z0 - 2*x^6*z0^2 + x^5*z0^3) * dx, + (x^7*z0^2 - 2*x^6*z0^3 + x^5*z0^4) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmatrix([[i - j for i in range(0, m)] for j in range(0, m)])[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef wyniki(n, infty_type):[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for d in range(1, 6): +....:  AS = as_cover(C, [C.x^d]) +....:  AS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAS1.holomorphic_differentials_basis() +  + [?7h[?12l[?25h[?25l[?7lntials()[?7h[?12l[?25h[?25l[?7lrentials_basis()[?7h[?12l[?25h[?25l[?7lfor d in range(1, 6): +....:  AS = as_cover(C, [C.x^d]) +....:  AS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l +[][?7h[?12l[?25h[?25l[?7l[] +[?7h[?12l[?25h[?25l[?7l +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: AS1 +[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation: + z^5 - z = x^3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = 5[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: basis = AS1.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis = AS1.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: basis[0] +[?7h[?12l[?25h[?2004l[?7h(1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis[0][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: basis[0].group_action([1]) +[?7h[?12l[?25h[?2004l[?7h(1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis[0].group_action([1])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: basis[1] +[?7h[?12l[?25h[?2004l[?7h(z0) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis[1][?7h[?12l[?25h[?25l[?7l[0].group_action([1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].group_action([1])[?7h[?12l[?25h[?25l[?7l1].group_action([1])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: basis[1].group_action([1]) +[?7h[?12l[?25h[?2004l[?7h(z0 + 1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis[1].group_action([1])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: basis[1].group_action([1]).coordinates() +[?7h[?12l[?25h[?2004l[?7h[1, 1, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 3[?7h[?12l[?25h[?25l[?7luo_rem(alpha*beta, t^4)[1][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() +[?7h[?12l[?25h[?2004l[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd .. +[?2004l [?2004h]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status +[?2004l On branch master +Your branch is up to date with 'origin/master'. + +Changes not staged for commit: + (use "git add ..." to update what will be committed) + (use "git restore ..." to discard changes in working directory) + modified: sage/.run.term-0.term + modified: sage/as_covers/as_cover_class.sage + modified: sage/as_covers/as_form_class.sage + modified: sage/as_covers/as_function_class.sage + modified: sage/as_covers/group_action_matrices.sage + modified: sage/drafty/draft.sage + modified: sage/init.sage + +Untracked files: + (use "git add ..." to include in what will be committed) + .crystalline_p2.ipynb.sage-jupyter2 + .deRhamComputation.ipynb.sage-jupyter2 + .elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2 + .git.x11-0.term + .superelliptic.ipynb.sage-jupyter2 + .superelliptic_alpha.ipynb.sage-jupyter2 + .superelliptic_arbitrary_field.ipynb.sage-jupyter2 + git.x11 + sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2 + sage/drafty/2gpcovers.sage + sage/drafty/as_cartier.sage + sage/drafty/better_trace.sage + sage/drafty/cartier_image_representation.sage + sage/drafty/convert_superelliptic_into_AS.sage + sage/drafty/draft4.sage + sage/drafty/draft5.sage + sage/drafty/draft6.sage + sage/drafty/draft7.sage + sage/drafty/draft8.sage + sage/drafty/draft_klein_covers.sage + sage/drafty/lift_to_de_rham.sage + sage/drafty/pole_numbers.sage + sage/superelliptic/frobenius_kernel.sage + superelliptic_arbitrary_field.ipynb + +no changes added to commit (use "git add" and/or "git commit -a") +[?2004h]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sage add git add C.x^33C.x^3C.x^33C.x^3 C.x^33C.x^3 sage/superelliptic/frobenius_kernel.sagesage/superelliptic/frobenius_kernel.sage +[?2004l [?2004h]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u \ No newline at end of file diff --git a/sage/as_covers/as_cover_class.sage b/sage/as_covers/as_cover_class.sage index 2f4d620..267f9ae 100644 --- a/sage/as_covers/as_cover_class.sage +++ b/sage/as_covers/as_cover_class.sage @@ -172,6 +172,7 @@ class as_cover: m = C.exponent r = C.polynomial.degree() RxyzQ, Rxyz, x, y, z = self.fct_field + F = C.base_ring Rt. = LaurentSeriesRing(F, default_prec=prec) #Tworzymy zbiór S form z^i x^j y^k dx/y o waluacji >= waluacja z^(p-1)*dx/y S = [] @@ -367,7 +368,7 @@ class as_cover: #Tworzymy zbiór S form z^i x^j y^k dx/y o waluacji >= waluacja z^(p-1)*dx/y S = [(fct.diffn(), fct.diffn().expansion_at_infty())] pr = [list(GF(p)) for _ in range(n)] - holo = self.holomorphic_differentials_basis() + holo = self.holomorphic_differentials_basis(threshold = threshold) for i in range(0, threshold*r): for j in range(0, m): for k in product(*pr): @@ -385,9 +386,9 @@ class as_cover: def de_rham_basis(self, threshold = 30): result = [] - for omega in self.holomorphic_differentials_basis(): + for omega in self.holomorphic_differentials_basis(threshold = threshold): result += [as_cech(self, omega, as_function(self, 0))] - for f in self.cohomology_of_structure_sheaf_basis(): + for f in self.cohomology_of_structure_sheaf_basis(threshold = threshold): omega = self.lift_to_de_rham(f, threshold = threshold) result += [as_cech(self, omega, f)] return result diff --git a/sage/as_covers/as_form_class.sage b/sage/as_covers/as_form_class.sage index b72a632..0544715 100644 --- a/sage/as_covers/as_form_class.sage +++ b/sage/as_covers/as_form_class.sage @@ -210,8 +210,8 @@ def are_forms_linearly_dependent(set_of_forms): denominators = prod(denominator(omega.form) for omega in set_of_forms) return is_linearly_dependent([Rxyz(denominators*omega.form) for omega in set_of_forms]) -#given a set S of (form, corresponding Laurent series at some pt), find their combinations holomorphic at that pt def holomorphic_combinations_fcts(S, pole_order): + '''given a set S of (form, corresponding Laurent series at some pt), find their combinations holomorphic at that pt''' C_AS = S[0][0].curve p = C_AS.characteristic F = C_AS.base_ring diff --git a/sage/as_covers/as_function_class.sage b/sage/as_covers/as_function_class.sage index 1d2e9f8..1042b9e 100644 --- a/sage/as_covers/as_function_class.sage +++ b/sage/as_covers/as_function_class.sage @@ -56,13 +56,13 @@ class as_function: g1 = self.function return as_function(C, g1^(exponent)) - def expansion_at_infty(self, i = 0): + def expansion_at_infty(self, place = 0): C = self.curve delta = C.nb_of_pts_at_infty F = C.base_ring - x_series = C.x_series[i] - y_series = C.y_series[i] - z_series = C.z_series[i] + x_series = C.x_series[place] + y_series = C.y_series[place] + z_series = C.z_series[place] n = C.height variable_names = 'x, y' for j in range(n): @@ -137,6 +137,22 @@ class as_function: result = as_reduction(AS, result) return superelliptic_function(C_super, Qxy(result)) + def coordinates(self, prec = 100, basis = 0): + "Return coordinates in H^1(X, OX)." + AS = self.curve + if basis == 0: + basis = [AS.holomorphic_differentials_basis(), AS.cohomology_of_structure_sheaf_basis()] + holo_diffs = basis[0] + coh_basis = basis[1] + f_products = [] + for f in coh_basis: + f_products += [[omega.serre_duality_pairing(f) for omega in holo_diffs]] + product_of_fct_and_omegas = [] + product_of_fct_and_omegas = [omega.serre_duality_pairing(self) for omega in holo_diffs] + + V = (F^(AS.genus())).span_of_basis([vector(a) for a in f_products]) + coh_coordinates = V.coordinates(product_of_fct_and_omegas) + return coh_coordinates def diffn(self): C = self.curve @@ -157,9 +173,9 @@ class as_function: result += f.derivative(z[i])*dz[i] return as_form(C, result) - def valuation(self, i = 0): + def valuation(self, place = 0): '''Return valuation at i-th place at infinity.''' C = self.curve F = C.base_ring Rt. = LaurentSeriesRing(F) - return Rt(self.expansion_at_infty(i)).valuation() + return Rt(self.expansion_at_infty(place = place)).valuation() diff --git a/sage/as_covers/group_action_matrices.sage b/sage/as_covers/group_action_matrices.sage index e6daa4a..edf0e74 100644 --- a/sage/as_covers/group_action_matrices.sage +++ b/sage/as_covers/group_action_matrices.sage @@ -55,11 +55,20 @@ def group_action_matrices_old(C_AS): A[i] = A[i].transpose() return A -def group_action_matrices_log(C_AS): +def group_action_matrices_log(AS): + n = AS.height + generators = [] + for i in range(n): + ei = n*[0] + ei[i] = 1 + generators += [ei] + return group_action_matrices(AS.at_most_poles_forms(1), generators, basis = AS.at_most_poles_forms(1)) + +def group_action_matrices_log_old(C_AS): F = C_AS.base_ring n = C_AS.height holo = C_AS.at_most_poles_forms(1) - holo_forms = [omega.form for omega in holo] + holo_forms = [omega for omega in holo] denom = LCM([denominator(omega) for omega in holo_forms]) variable_names = 'x, y' for j in range(n): diff --git a/sage/drafty/draft.sage b/sage/drafty/draft.sage index 7045bcd..4587746 100644 --- a/sage/drafty/draft.sage +++ b/sage/drafty/draft.sage @@ -1,39 +1,8 @@ -p = 3 -m = 2 -F = GF(p^2, 'a') -a = F.gens()[0] -Rxx. = PolynomialRing(F) -#f = (x^3 - x)^3 + x^3 - x -f = x^3 + a*x + 1 -f1 = f(x = x^p - x) -C = superelliptic(f, m) -C1 = superelliptic(f1, m, prec = 500) -#B = C.crystalline_cohomology_basis(prec = 100, info = 1) -#B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1) - -def crystalline_matrix(C, prec = 50): - B = C.crystalline_cohomology_basis(prec = prec) - g = C.genus() - p = C.characteristic - Zp2 = Integers(p^2) - M = matrix(Zp2, 2*g, 2*g) - for i, b in enumerate(B): - M[i, :] = vector(autom(b).coordinates(basis = B)) - return M - -#b0 = de_rham_witt_lift(C.de_rham_basis()[0], prec = 100) -#b1 = de_rham_witt_lift(C1.de_rham_basis()[2], prec = 300) -#print(b0.regular_form()) -#print(b1.regular_form()) -for b in C1.de_rham_basis(): - print(mult_by_p(b.omega0).regular_form()) - -#for b in B: -# print(b.regular_form()) - -#for b in B1: -# print(b.regular_form()) - -#M = crystalline_matrix(C, prec = 150) -#print(M) -#print(M^3) \ No newline at end of file +p = 5 +m = 1 +F = GF(p) +Rx. = PolynomialRing(F) +f = x +C = superelliptic(f, 1) +AS1 = as_cover(C, [C.x^3], prec = 200) +print(AS1.genus()) \ No newline at end of file diff --git a/sage/init.sage b/sage/init.sage index 2ea9902..088fd47 100644 --- a/sage/init.sage +++ b/sage/init.sage @@ -28,8 +28,9 @@ load('auxilliaries/linear_combination_polynomials.sage') load('auxilliaries/laurent_analytic_part.sage') ############## ############## -load('drafty/convert_superelliptic_into_AS.sage') +#load('drafty/convert_superelliptic_into_AS.sage') load('drafty/draft.sage') #load('drafty/draft_klein_covers.sage') +#load('drafty/draft_klein_covers.sage') #load('drafty/2gpcovers.sage') load('drafty/pole_numbers.sage') \ No newline at end of file diff --git a/sage/superelliptic/frobenius_kernel.sage b/sage/superelliptic/frobenius_kernel.sage new file mode 100644 index 0000000..ffcd84c --- /dev/null +++ b/sage/superelliptic/frobenius_kernel.sage @@ -0,0 +1,25 @@ +def frobenius_kernel(C, prec=50): + M = C.frobenius_matrix(prec=prec).transpose() + K = M.kernel().basis() + g = C.genus() + result = [] + basis = C.cohomology_of_structure_sheaf_basis() + for v in K: + coh = 0*C.x + for i in range(g): + coh += v[i] * basis[i] + result += [coh] + return result + +def cartier_kernel(C, prec=50): + M = C.cartier_matrix(prec=prec).transpose() + K = M.kernel().basis() + g = C.genus() + result = [] + basis = C.holomorphic_differentials_basis() + for v in K: + coh = 0*C.dx + for i in range(g): + coh += v[i] * basis[i] + result += [coh] + return result \ No newline at end of file